Appendix A: GAMS Index

IMSL STAT/LIBRARY

C............ ELEMENTARY AND SPECIAL FUNCTIONS (search also class L5)

C3.......... Polynomials

C3a........ Orthogonal

OPOLY

    Generate orthogonal polynomials with respect to x values and specified weights.

C7.......... Gamma

C7e........ Incomplete gamma

CHIDF

  Evaluate the chi-squared distribution function.

CHIIN

  Evaluate the inverse of the chi-squared distribution function.

GAMDF

Evaluate the gamma distribution function.

GAMIN

  Evaluate the inverse of the gamma distribution function.

C7f......... Incomplete gamma

BETDF

  Evaluate the beta probability distribution function.

BETIN

  Evaluate the inverse of the beta distribution function.

C8.......... Error functions

C8a........ Error functions, their inverses, integrals, including the normal distribution function

ANORDF

  Evaluate the standard normal (Gaussian) distribution function.

ANORIN

Evaluate the inverse of the standard normal (Gaussian) distribution function.

K............ APPROXIMATION (search also class L8)

K1.......... Least squares (L2) approximation

K1a........ Linear least squares (search also classes D5, D6, D9)

K1a1...... Unconstrained

RCOV

   Fit a multiple linear regression model given the variance-covariance matrix.

RGIVN

  Fit a multivariate linear regression model via fast Givens transformations.

RGLM

   Fit a multivariate general linear model.

RLSE

   Fit a multiple linear regression model using least squares.

K1a1a.... Univariate data (curve fitting)

K1ala2... Polynomials

RCURV

  Fit a polynomial curve using least squares.

RFORP

  Fit an orthogonal polynomial regression model.

RPOLY

   Analyze a polynomial regression model.

K1a2...... Constrained

K1a2a.... Linear constraints

RLEQU

  Fit a multivariate linear regression model with linear equality restrictions HΒ = G imposed on the regression parameters given results from IMSL routine RGIVN after IDO = 1 and IDO = 2 and prior to IDO = 3.

K1b........ Nonlinear least squares

K1b1...... Unconstrained

K1b1a.... Smooth functions

K1b1a1.. User provides no derivatives

RNLIN

    Fit a nonlinear regression model.

K1b1a2.. User provides first derivatives

RNLIN

    Fit a nonlinear regression model.

K2.......... Minimax (L) approximation

RLMV

   Fit a multiple linear regression model using the minimax criterion.

K3.......... Least absolute value (L1) approximation

RLLP

   Fit a multiple linear regression model using the Lp norm criterion.

K4.......... Other analytic approximations (e.g., Taylor polynomial, Pade)

RLLP

   Fit a multiple linear regression model using the Lp norm criterion.

L............. STATISTICS, PROBABILITY

L1........... Data summarization

L1a......... One-dimensional data

L1a1....... Raw data

EQTIL

    Compute empirical quantiles.

LETTR

   Produce a letter value summary.

ORDST

  Determine order statistics.

L1a1a..... Location

UVSTA

  Compute basic univariate statistics.

L1a1b.... Disperson

UVSTA

  Compute basic univariate statistics.

L1a1c..... Shape

UVSTA

  Compute basic univariate statistics.

L1a1e..... Ties

NTIES

  Compute tie statistics for a sample of observations.

 

L1a3....... Grouped data

GRPES

  Compute basic statistics from grouped data.

L1c......... Multi-dimensional data

L1c1....... Raw data

CSTAT

  Compute cell frequencies, cell means, and cell sums of squares for multivariate data.

L1c1b.... Covariance, correlation

CORVC

  Compute the variance-covariance or correlation matrix.

PCORR

  Compute partial correlations or covariances from the covariance or correlation matrix.

RBCOV

  Compute a robust estimate of a covariance matrix and mean vector.

L2........... Data manipulation

L2a......... Transform (search also classes L10a, N6, and N8)

BCTR

   Perform a forward or an inverse Box-Cox (power) transformation.

GCSCP

  Generate centered variables, squares, and crossproducts.

OPOLY

    Generate orthogonal polynomials with respect to x values and specified weights.

RANKS

  Compute the ranks, normal scores, or exponential scores for a vector of observations.

L2b........ Tally

CSTAT

  Compute cell frequencies, cell means, and cell sums of squares for multivariate data.

FREQ

   Tally multivariate observations into a multi-way frequency table.

OWFRQ

  Tally observations into a one-way frequency table.

TWFRQ

  Tally observations into a two-way frequency table.

L2e......... Construct new variables (e.g., indicator variables)

GRGLM

  Generate regressors for a general linear model.

L3........... Elementary statistical graphics (search also class Q)

L3a......... One-dimensional data

L3a1....... Histograms

HHSTP

   Print a horizontal histogram.

VHSTP

   Print a vertical histogram.

L3a2....... Frequency, cumulative frequency, percentile plots

CDFP

   Print a sample cumulative distribution function (CDF), a theoretical CDF, and confidence band information.

L3a3....... EDA graphics (e.g., box plots)

BOXP

     Print boxplots for one or more samples.

STMLP

  Print a stem-and-leaf plot.

L3a4....... Bar charts

HHSTP

   Print a horizontal histogram.

VHSTP

   Print a vertical histogram.

L3b........ Two-dimensional data (search also class L3e)

L3b1...... Histograms (superimposed and bivariate)

VHS2P

  Print a vertical histogram with every bar subdivided into two parts.

L3b2...... Frequency, cumulative frequency

CDF2P

  Print a plot of two sample cumulative distribution functions.

L3e......... Multi-dimensional data

L3e3....... Scatter diagrams

L3e3a..... Superimposed Y vs. X

PLOTP

   Print a plot of up to ten sets of points.

SCTP

   Print a scatterplot of several groups of data.

L3e4....... EDA

BOXP

     Print boxplots for one or more samples.

L4........... Elementary data analaysis

L4a......... One-dimensional data

L4a1....... Raw data

L4a1a..... Parametric analysis

CDFP

   Print a sample cumulative distribution function (CDF), a theoretical CDF, and confidence band information.

L4a1a2... Probability plots

L4a1a2e. Exponential, extreme value

PROBP

    Print a probability plot.

L4a1a2h Halfnormal

PROBP

    Print a probability plot.

L4a1a21. Lambfa, logistic, lognormal

PROBP

    Print a probability plot.

L4a1a2n Negative binomial, normal

PROBP

    Print a probability plot.

L4a1a2w Weibull

PROBP

    Print a probability plot.

L4a1a4... Parameter estimates and tests

MLE         Calculates maximum likelihood estimates for the parameters of one of several univariate probability distributions.

L4a1a4b Binomial

BINES

  Estimate the parameter p of the binomial distribution.

 

L4a1a4p Poisson

POIES

  Estimate the parameter of the Poisson distribution.

L4a1b.... Nonparametric analysis

L4a1b1.. Estimates and test regarding location (e.g., median), dispersion and shape

SIGNT

  Perform a sign test of the hypothesis that a given value is a specified quantile of a distribution.

SNRNK

  Perform a Wilcoxon signed rank test.

L4a1b2.. Density function estimation

DESKN

  Perform nonparametric probability density function estimation by the kernel method.

DESPL

  Perform nonparametric probability density function estimation by the penalized likelihood method.

DESPT

  Estimate a probability density function at specified points using linear or cubic interpolation.

DNFFT

  Compute Gaussian kernel estimates of a univariate density via the fast Fourier transform over a fixed interval.

L4a1c..... Goodness-of-fit tests

ADNRM  Performs an Anderson-Darling test for normality.

CHIGF

  Perform a chi-squared goodness-of-fit test.

CVMNRM Performs a Cramer-von Mises test for normality.

KSONE

  Perform a Kolmogorov-Smirnov one-sample test for continuous distributions.

LILLF

  Perform Lilliefors test for an exponential or normal distribution.

SPWLK

  Perform a Shapiro-Wilk W-test for normality.

L4ald..... Analysis of a sequnce of numbers (search also class L10a)

DCUBE

  Perform a triplets test.

DSQAR

  Perform a D-square test.

NCTRD

  Perform the Noether test for cyclical trend.

PAIRS

    Perform a pairs test.

RUNS

     Perform a runs up test.

SDPLC

  Perform the Cox and Stuart sign test for trends in dispersion and location.

L4a3....... Grouped (and/or censored) data

GRPES

  Compute basic statistics from grouped data.

NRCES

  Compute maximum likelihood estimates of the mean and variance from grouped and/or censored normal data.

L4a4....... Data sampled from a finite population

SMPPR  Compute statistics for inferences regarding the population proportion and total, given proportion data from a simple random sample.

SMPPS

  Compute statistics for inferences regarding the population proportion and total, given proportion data from a stratified random sample.

SMPSC

  Compute statistics for inferences regarding the population mean and total using single-stage cluster sampling with continuous data.

SMPSR

  Compute statistics for inferences regarding the population mean and total, given data from a simple random sample.

SMPSS

  Compute statistics for inferences regarding the population mean and total, given data from a stratified random sample.

SMPST

  Compute statistics for inferences regarding the population mean and total, given continuous data from a two-stage sample with equisized primary units.

L4b........ Two dimensional data (search also class L4c)

L4b1...... Pairwise independent data

L4b1a.... Parametric analysis

L4b1a4.. Parameter estimates and hypothesis tests

TWOMV

  Compute statistics for mean and variance inferences using samples from two normal populations.

L4b1b.... Nonparametric analysis (e.g., tests based on ranks)

CNCRD

  Calculate and test the significance of the Kendall coefficient of concordance.

INCLD

    Perform an includance test.

KENDL

  Compute and test Kendall’s rank correlation coefficient.

RNKSM

Perform the Wilcoxon rank sum test.

L4b1c.... Goodness-of-fit tests

KSTWO

  Perform a Kolmogorov-Smirnov two-sample test.

L4b4...... Pairwise dependent grouped data

CTRHO

  Estimate the bivariate normal correlation coefficient using a contingency table.

TETCC

  Categorize bivariate data and compute the tetrachoric correlation coefficient.

L4b5...... Data sampled from a finite population

SMPRR

  Compute statistics for inferences regarding the population mean and total using ratio or regression estimation, or inferences regarding the population ratio, given a simple random sample.

SMPRS

  Compute statistics for inferences regarding the population mean and total using ratio or regression estimation, given continuous data from a stratified random sample.

L4c......... Multi-dimensional data (search also classes L4b and L7a1)

L4c1....... Independent data

L4c1b.... Nonparametric analysis

BHAKV

Perform a Bhapkar V test.

KRSKL

  Perform a Kruskal-Wallis test for identical population medians.

KTRND

  Perform a k-sample trends test against ordered alternatives.

MVMMT

  Compute Mardia’s multivariate measures of skewness and kurtosis and test for multivariate normality.

QTEST

  Perform a Cochran Q test for related observations.

L4e......... Multiple multi-dimensional data sets

MVIND

  Compute a test for the independence of k sets of multivariate normal variables.

L5........... Function evaluation (search also class C)

L5a......... Univariate

L5a1....... Cumulative distribution functions, probability density functions

L5a1b.... Beta, binomial

BETDF    Evaluate the beta probability distribution function.

BETNDF  Evaluate the noncentral beta cumulative distribution function.

BETNPR  Evaluate the noncentral beta probability density function.

BINDF    Evaluate the binomial distribution function.

BINPR    Evaluate the binomial probability function.

L5a1c..... Cauchy, chi-squared

CHIDF

  Evaluate the chi-squared distribution function.

CSNDF

  Evaluate the noncentral chi-squared distribution function.

CSNPR

  Evaluates the noncentral chi-squared probability density function.

L5a1f..... F distribution

FDF         Evaluate the F distribution function.

FNDF       Evaluate the noncentral F cumulative distribution function (CDF).

FNPR       Evaluate the noncentral F probability density function.

L5a1g.... Gamma, general, geometric

GAMDF

Evaluate the gamma distribution function.

GCDF

   Evaluate a general continuous cumulative distribution function given ordinates of the density.

L5a1h.... Halfnormal, hyergeometric

HYPDF

  Evaluate the hypergeometric distribution function.

HYPPR

  Evaluate the hypergeometric probability function.

L5a1k..... Kendall F statistic, Kolmogorsv-Smirnov

AKS1DF

Evaluate the distribution function of the one-sided Kolmogorov-Smirnov goodness-of-fit D+ or D test statistic based on continuous data for one sample.

AKS2DF

Evaluate the distribution function of the Kolmogorov-Smirnov goodness-of-fit D test statistic based on continuous data for two samples.

KENDP

  Compute the frequency distribution of the total score in Kendall’s rank correlation coefficient.

L5a1n.... Negative binomial, normal

ANORDF

  Evaluate the standard normal (Gaussian) distribution function.

 

 

L5a1p.... Pareto, Poisson

POIDF

  Evaluate the Poisson distribution function.

POIPR

  Evaluate the Poisson probability function.

L5a1t..... t distribution

TDF

    Evaluate the Student’s t distribution function.

TNDF

   Evaluate the noncentral Student’s t distribution function.

TNPR

   Evaluate the noncentral Student's t probability density function.

L5a2....... Inverse cumulative distribution functions, sparsity functions

L5a2b.... Beta, binomial

BETIN

  Evaluate the inverse of the beta distribution function.

BETNIN This function evaluates the inverse of the noncentral beta cumulative distribution function (CDF).

BETNPR This function evaluates the noncentral beta probability density function.

L5a2c..... Cauchy, chi-squared

CHIIN

  Evaluate the inverse of the chi-squared distribution function.

CSNIN

  Evaluate the inverse of the noncentral chi-squared function.

L5a2f..... F distribution

FIN

    Evaluate the inverse of the F distribution function.

FNIN       Evaluate the inverse of the F cumulative distribution function (CDF).

L5a2g.... Gamma, general, geometric

GAMIN

  Evaluate the inverse of the gamma distribution function.

GCIN

   Evaluate the inverse of a general continuous cumulative distribution function given ordinates of the density.

GFNIN

  Evaluate the inverse of a general continuous cumulative distribution function given in a subprogram.

L5a2t..... t distribution

TIN

    Evaluate the inverse of the Student’s t distribution function.

TNIN

   Evaluate the inverse of the noncentral Student’s t distribution function.

L5b........ Multivariate

L5b1...... Cumulative distribution functions, probability density functions

L5b1n.... Normal

BNRDF

  Evaluate the bivariate normal distribution function.

L6........... Random number generation

L6a......... Univariate

L6a2....... Beta, binomial, Boolean

RNBET

  Generate pseudorandom numbers from a beta distribution.

RNBIN

  Generate pseudorandom numbers from a binomial distribution.

L6a3....... Cauchy, chi-squared

RNCHI

  Generate pseudorandom numbers from a chi-squared distribution.

 

RNCHY

  Generate pseudorandom numbers from a Cauchy distribution.

L6a5....... Exponential, extreme value

RNEXP

  Generate pseudorandom numbers from a standard exponential distribution.

RNEXT

  Generate pseudorandom numbers from a mixture of two exponential distributions.

L6a7....... Gamma, general (continuous, discrete), geometric

RNGAM

  Generate pseudorandom numbers from a standard gamma distribution.

RNGCS

  Set up table to generate pseudorandom numbers from a general continuous distribution.

RNGCT

  Generate pseudorandom numbers from a general continuous distribution.

RNGDA

  Generate pseudorandom numbers from a general discrete distribution using an alias method.

RNGDS

  Set up table to generate pseudorandom numbers from a general discrete distribution.

RNGDT

  Generate pseudorandom numbers from a general discrete distribution using a table lookup method.

RNGEO

  Generate pseudorandom numbers from a geometric distribution.

L6a8....... Halfnormal, hypergeometric

RNHYP

  Generate pseudorandom numbers from a hypergeometric distribution.

L6a12..... Lambda, logistic, lognormal

RNLGR

  Generate pseudorandom numbers from a logarithmic distribution.

RNLNL

  Generate pseudorandom numbers from a lognormal distribution.

L6a14..... Negative binomial, normal, normal order statistics

RNNBN

  Generate pseudorandom numbers from a negative binomial distribution.

RNNOA

  Generate pseudorandom numbers from a standard normal distribution using an acceptance/rejection method.

RNNOF

  Generate a pseudorandom number from a standard normal distribution.

RNNOR

  Generate pseudorandom numbers from a standard normal distribution using an inverse CDF method.

RNNOS

  Generate pseudorandom order statistics from a standard normal distribution.

L6a16..... Pareto, Pascal, permutations, Poisson

RNNPP

  Generate pseudorandom numbers from a nonhomogeneous Poisson process.

 

RNPER

   Generate a pseudorandom permutation.

RNPOI

  Generate pseudorandom numbers from a Poisson distribution.

L6a19..... Samples, stable distribution

RNSRI

  Generate a simple pseudorandom sample of indices.

RNSRS

  Generate a simple pseudorandom sample from a finite population.

RNSTA

  Generate pseudorandom numbers from a stable distribution.

L6a20..... t distribution, time series, triangular

RNARM

  Generate a time series from a specified ARMA model.

RNNPP

  Generate pseudorandom numbers from a nonhomogeneous Poisson process.

RNSTT

  Generate pseudorandom numbers from a Student’s t distribution.

RNTRI

  Generate pseudorandom numbers from a triangular distribution on the interval (0,1).

L6a21..... Uniform (continuous, discrete), uniform order statistics

RNUN

   Generate pseudorandom numbers from a uniform (0,1) distribution.

RNUND

  Generate pseudorandom numbers from a discrete uniform distribution.

RNUNF

  Generate a pseudorandom number from a uniform (0, 1) distribution.

RNUNO

  Generate pseudorandom order statistics from a uniform (0, 1) distribution.

L6a22..... Von Mises

RNVMS

  Generate pseudorandom numbers from a von Mises distribution.

L6a23..... Weibull

RNWIB

  Generate pseudorandom numbers from a Weibull distribution.

L6b........ Multivariate

RNDAT

  Generate pseudorandom numbers from a multivariate distribution determined from a given sample.

RNMVGC

Given a Cholesky factorization of a correlation matrix, generates pseudorandom numbers from a Gaussian Copula distribution.

RNMVTC

Given a Cholesky factorization of a correlation matrix, generates pseudorandom numbers from a Student‘s t Copula distribution.

L6b3...... Contingency table, correlation matrix

RNCOR

  Generate a pseudorandom orthogonal matrix or a correlation matrix.

RNTAB

    Generate a pseudorandom two-way table.

L6b13.... Multinomial

RNMTN

  Generate pseudorandom numbers from a multinomial distribution.

 

L6b14.... Normal

RNMVN

  Generate pseudorandom numbers from a multivariate normal distribution.

L6b15.... Orthogonal matrix

RNCOR

  Generate a pseudorandom orthogonal matrix or a correlation matrix.

L6b21.... Linear L-1 (least absolute value) approximation random numbers

FAURE_INIT                         Shuffles Faure sequence initialization.

FAURE_FREE                    Frees the structure containing information about the Faure sequence.

FAURE_NEXT                    Computes a shuffled Faure sequence.

L6b21.... Uniform

RNSPH

  Generate pseudorandom points on a unit circle or K-dimensional sphere.

L6c......... Service routines (e.g., seed)

RNGEF  Retrieve the current value of the array used in the IMSL GFSR random number generator.

RNGES  Retrieve the current value of the table in the IMSL random number generators that use shuffling.

RNGET  Retrieve the current value of the seed used in the IMSL random number generators.

RNISD  Determine a seed that yields a stream beginning 100,000 numbers beyond the beginning of the stream yielded by a given seed used in IMSL multiplicative congruential generators (with no shufflings).

RNOPG  Retrieve the indicator of the type of uniform random number generator.

RNOPT  Select the uniform (0, 1) multiplicative congruential pseudorandom number generator.

RNSEF  Initialize the array used in the IMSL GFSR random number generator.

RNSES  Initialize the table in the IMSL random number generators that use shuffling.

RNSET  Initialize a random seed for use in the IMSL randomnumber generators.

L7........... Analysis of variance (including analysis of covariance)

L7a......... One-way

L7a1....... Parametric

AONEC

  Analyze a one-way classification model with covariates.

AONEW

                                                      Analyze a one-way classification model.

CTRST

  Compute contrast estimates and sums of squares.

SCIPM

  Compute simultaneous confidence intervals on all pairwise differences of means.

SNKMC

  Perform Student-Newman-Keuls multiple comparison test.

L7b........ Two-way (search also class L7d)

ATWOB

  Analyze a randomized block design or a two-way balanced design.

 

FRDMN

  Perform Friedman’s test for a randomized complete block design.

MEDPL

  Compute a median polish of a two-way table.

L7c......... Three-way (e.g., Latin squares) (search also class L7d)

ALATN

Analyze a Latin square design.

L7d........ Multi-way

L7d1...... Balanced complete data (e.g., factorial designs)

ABALD

  Analyze a balanced complete experimental design for a fixed, random, or mixed model.

ANEST

  Analyze a completely nested random model with possibly unequal numbers in the subgroups.

ANWAY

  Analyze a balanced n-way classification model with fixed effects.

CIDMS

  Compute a confidence interval on a variance component estimated as proportional to the difference in two mean squares in a balanced complete experimental design.

ROREX

  Reorder the responses from a balanced complete experimental design.

L7d2...... Balanced incomplete data (e.g., fractional factorial designs)

ABIBD

  Analyze a balanced incomplete block design or a balanced lattice design.

L7d3...... General linear models (unbalanced data)

ANEST

  Analyze a completely nested random model with possibly unequal numbers in the subgroups.

RGLM

   Fit a multivariate general linear model.

L7e......... Multivariate

RGLM

   Fit a multivariate general linear model.

L7f......... Generate experimental designs

RCOMP

  Generate an orthogonal central composite design.

L8........... Regression (search also classes D5, D6, D9, G, K)

L8a......... Simple linear (e.g., y = β0 + β1x + ɛ)

L8a1....... Ordinary least squares

RONE

   Analyze a simple linear regression model.

L8a1a..... Parameter estimation

L8a1a1... Unweighted data

RLINE

  Fit a line to a set of data points using least squares.

L8a1d.... Inference (e.g., calibration) (search also class L8a1a)

RINCF

  Perform response control given a fitted simple linear regression model.

RINPF

  Perform inverse prediction given a fitted simple linear regression model.

L8a2....... Lp for p different from 2 (e.g., least absolute value, minimax)

RLAV

   Fit a multiple linear regression model using the least absolute values criterion.

RLLP

   Fit a multiple linear regression model using the Lp norm criterion.

RLMV

   Fit a multiple linear regression model using the minimax criterion.

L8b........ Polynomial (e.g., y = β0 + β1x + β2x2 + ɛ) (search also class L8c)

L8b1...... Ordinary least squares

L8b1a.... Degree determination

RFORP

  Fit an orthogonal polynomial regression model.

RPOLY

    Analyze a polynomial regression model.

L8b1b.... Parameter estimation

L8b1b2.. Using orthogonal polynomials

RCURV

  Fit a polynomial curve using least squares.

RFORP

  Fit an orthogonal polynomial regression model.

RPOLY

    Analyze a polynomial regression model.

L8b1c.... Analysis (search also class L8b1b)

RCASP

  Compute case statistics for a polynomial regression model given the fit based on orthogonal polynomials.

RPOLY

    Analyze a polynomial regression model.

RSTAP

  Compute summary statistics for a polynomial regression model given the fit based on orthogonal polynomials.

L8b1d.... Inference (search also class L8b1b)

RCASP

  Compute case statistics for a polynomial regression model given the fit based on orthogonal polynomials.

RPOLY

    Analyze a polynomial regression model.

RSTAP

  Compute summary statistics for a polynomial regression model given the fit based on orthogonal polynomials.

L8c......... Multiple linear (e.g., y = β0 + β1x1 ++ βkxk + ɛ)

PLSR

   Performs partial least squares regression for one or more response variables and a set of one or more predictor variables.

L8c1....... Ordinary least squares

L8c1a..... Variable selection

L8c1a2... Using correlation or covariance data

GSWEP

  Perform a generalized sweep of a row of a nonnegative definite matrix.

RBEST

  Select the best multiple linear regression models.

RSTEP

  Build multiple linear regression models using forward selection, backward selection, or stepwise selection.

L8c1b.... Parameter estimation (search also class L8c1a)

L8c1b1.. Using raw data

RGIVN

  Fit a multivariate linear regression model via fast Givens transformations.

RGLM

   Fit a multivariate general linear model.

RLSE

   Fit a multiple linear regression model using least squares.

L8c1b2.. Using correlation data

RCOV

   Fit a multiple linear regression model given the variance-covariance matrix.

L8c1c..... Analysis (search also classes L8c1a and L8c1b)

RCASE

  Compute case statistics and diagnostics given data points, coefficient estimates, and the R matrix for a fitted general linear model.

RCOVB  Compute the estimated variance-covariance matrix of the estimated regression coefficients given the R matrix.

RLOFE  Compute a lack-of-fit test based on exact replicates for a fitted regression model.

RLOFN  Compute a lack-of-fit test based on near replicates for a fitted regression model.

ROTIN  Compute diagnostics for detection of outliers and influential data points given residuals and the R matrix for a fitted general linear model.

RSTAT

  Compute statistics related to a regression fit given the coefficient estimates  and the R matrix.

L8c1d.... Inference (search also classes L8c1a and L8c1b)

CESTI  Construct an equivalent completely testable multivariate general linear hypothesis HBU = G from a partially testable hypothesis HpBU = Gp.

RCASE

  Compute case statistics and diagnostics given data points, coefficient estimates , and the R matrix for a fitted general linear model.

RHPSS

    Compute the matrix of sums of squares and crossproducts for the multivariate general linear hypothesis HBU = G given the coefficient estimates  and the R matrix.

RHPTE

  Perform tests for a multivariate general linear hypothesis HBU = G given the hypothesis sums of squares and crossproducts matrix SH and the error sums of squares and crossproducts matrix SE.

RSTAT

  Compute statistics related to a regression fit given the coefficient estimates  and the R matrix.

L8c3....... Lp for p different from 2

RLAV

   Fit a multiple linear regression model using the least absolute values criterion.

RLLP

   Fit a multiple linear regression model using the Lp norm criterion.

RLMV

   Fit a multiple linear regression model using the minimax criterion.

L8d........ Polynomial in several variables

RCOMP

  Generate an orthogonal central composite design.

TCSCP

  Transform coefficients from a quadratic regression model generated from squares and crossproducts of centered variables to a model using uncentered variables.

L8e......... Nonlinear (i.e., y = f(X; θ) + ɛ)

L8e1....... Ordinary least squares

L8e1b.... Parameter estimation

RNLIN

    Fit a nonlinear regression model.

L8f......... Simultaneous (i.e., Y = XB + ɛ)

RCOV

   Fit a multiple linear regression model given the variance-covariance matrix.

RGIVN

  Fit a multivariate linear regression model via fast Givens transformations.

RGLM

   Fit a multivariate general linear model.

RHPSS

    Compute the matrix of sums of squares and crossproducts for the multivariate general linear hypothesis HBU = G given the coefficient estimates  and the R matrix.

RHPTE

  Perform tests for a multivariate general linear hypothesis HBU = G given the hypothesis sums of squares and crossproducts matrix SH and the error sums of squares and crossproducts matrix SE.

RLEQU

  Fit a multivariate linear regression model with linear equality restrictions HΒ = G imposed on the regression parameters given results from IMSL routine RGIVN after IDO = 1 and IDO = 2 and prior to IDO = 3.

L8i.......... Service routines (e.g., matrix manipulation for variable selection)

GCLAS

  Get the unique values of each classification variable.

GCSCP

  Generate centered variables, squares, and crossproducts.

GRGLM

  Generate regressors for a general linear model.

RORDM

  Reorder rows and columns of a symmetric matrix.

RSUBM

  Retrieve a symmetric submatrix from a symmetric matrix.

L9........... Categorical data analysis

CTGLM

  Analyze categorical data using logistic, Probit, Poisson, and other generalized linear models.

CTRAN

  Perform generalized Mantel-Haenszel tests in a stratified contingency table.

 

 

L9a......... 2-by-2 tables

CTTWO

  Perform a chi-squared analysis of a 2 by 2 contingency table.

L9b........ Two-way tables (search also class L9d)

CTCHI

  Perform a chi-squared analysis of a two-way contingency table.

CTEPR

  Compute Fisher’s exact test probability and a hybrid approximation to the Fisher exact test probability for a contingency table using the network algorithm.

CTPRB

  Compute exact probabilities in a two-way contingency table.

CTRHO

  Estimate the bivariate normal correlation coefficient using a contingency table.

CTWLS

  Perform a generalized linear least squares analysis of transformed probabilities in a two-dimensional contingency table.

MEDPL

  Compute a median polish of a two-way table.

TWFRQ

  Tally observations into a two-way frequency table.

L9c......... Log-linear model

CTASC

  Compute partial association statistics for log-linear models in a multidimensional contingency table.

CTLLN

  Compute model estimates and associated statistics for a hierarchical log-linear model.

CTPAR

  Compute model estimates and covariances in a fitted log-linear model.

CTSTP

  Build hierarchical log-linear models using forward selection, backward selection, or stepwise selection.

PRPFT

  Perform iterative proportional fitting of a contingency table using a loglinear model.

L9d........ EDA (e.g., median polish)

MEDPL

  Compute a median polish of a two-way table.

L10......... Time series analysis (search also class J)

L10a....... Univariate

REG_ARIMA

............. Fits a univariate, non seasonal ARIMA time series model with the inclusion of one or more regression variables.

L10a1..... Transformations

L10a1b.. Stationarity (search also class L8a1)

BCTR

   Perform a forward or an inverse Box-Cox (power) transformation.

L10a1c... Filters

L10a1c1. Difference (nonseasonal and seasonal)

DIFF

       Difference a time series.

L10a2..... Time domain analysis

AUTO_ARIMA                    Automatically identifies time series outliers, determines parameters of a multiplicative seasonal ARIMA ( p,0, q)×(0, d,0)s model and produces forecasts that incorporate the effects of outliers whose effects persist beyond the end of the series.

AUTO_FPE_MUL_AR               Automatic selection and fitting of a multivariate autoregressive time series model using Akaike’s  Multivariate Final Prediction Error (MFPE) criteria.

AUTO_FPE_UNI_AR               Automatic selection and fitting of a univariate autoregressive time series model using Akaike’s Final Prediction Error (FPE) criteria.

AUTO_MUL_AR                   Automatic selection and fitting of a multivariate autoregressive time series model.

AUTO_PARM                     Estimates structural breaks in non-stationary univariate time series.

AUTO_UNI_AR                   Automatic selection and fitting of a univariate autoregressive time series model.

BAY_SEA                       Model allows for a decomposition of a time series into trend, seasonal, and an error component.

GARCH  Computes estimates of the parameters of a GARCH (p,q) model.

MAX_ARMA                                                    Exact maximum likelihood estimation of the parameters in a univariate ARMA (auto-regressive, moving average) time series model.

TS_OUTLIER_FORECAST           Detects and determines outliers and simultaneously estimates the model parameters in a time series.

TS_OUTLIER_IDENTIFICATION     Detects and determines outliers and simultaneously estimates the model parameters in a time series whose underlying outlier free series follows a general seasonal or nonseasonal ARMA model.

L10a2a... Summary statistics

L10a2a1. Autocovariances and autocorrelations

ACF

    Compute the sample autocorrelation function of a stationary time series.

LOFCF

  Perform lack-of-fit test for a univariate time series or transfer function given the appropriate correlation function.

L10a2a2. Partial autocorrelations

PACF

   Compute the sample partial autocorrelation function of a stationary time series.

L10a2c... Autoregressive models

SPWF

   Compute the Wiener forecast operator for a stationary stochastic process.

L10a2d.. ARMA and ARIMA models (including Box-Jenkins methods)

AUTO_PARM

                     Estimates structural breaks in non-stationary univariate time series.

REG_ARIMA

                     Fits a univariate, non seasonal ARIMA time series model with the inclusion of one or more regression variables.

L10a2d2 Parameter estimation

ARMME

  Compute method of moments estimates of the autoregressive parameters of an ARMA model.

MAMME

  Compute method of moments estimates of the moving average parameters of an ARMA model.

NSLSE

  Compute least squares estimates of parameters for a nonseasonal ARMA model.

NSPE

   Compute preliminary estimates of the autoregressive and moving average parameters of an ARMA model.

MAX_ARMA                                                    Exact maximum likelihood estimation of the parameters in a univariate ARMA (auto-regressive, moving average) time series model.

L10a2d3 Forecasting

NSBJF

  Compute Box-Jenkins forecasts and their associated probability limits for a nonseasonal ARMA model.

L10a2e... State-space analysis (e.g., Kalman filtering)

KALMN

  Perform Kalman filtering and evaluate the likelihood function for the state-space model.

L10a3..... Frequency domain analysis (search also class J1)

L10a3a... Spectral Analysis

ARMA_SPEC                     Calculates the rational power spectrum for an ARMA model.

L10a3a2. Periodogram analysis

PFFT

   Compute the periodogram of a stationary time series using a fast Fourier transform.

L10a3a3. Spectrum estimation using the periodogram

SSWD

   Estimate the nonnormalized spectral density of a stationary time series using a spectral window given the time series data.

SSWP

   Estimate the nonnormalized spectral density of a stationary time series using a spectral window given the periodogram.

SWED

   Estimation of the nonnormalized spectral density of a stationary time series based on specified periodogram weights given the time series data.

 

SWEP

   Estimation of the nonnormalized spectral density of a stationary time series based on specified periodogram weights given the periodogram.

L10a3a6. Spectral windows

DIRIC

    Compute the Dirichlet kernel.

FEJER

    Compute the Fejér kernel.

L10b...... Two time series (search also classes L10c and L10d)

L10b2.... Time domain analysis

L10b2a.. Summary statistics (e.g., cross-correlations)

CCF

    Compute the sample cross-correlation function of two stationary time series.

L10b2b.. Transfer function models

IRNSE

  Compute estimates of the impulse response weights and noise series of a univariate transfer function model.

TFPE

   Compute preliminary estimates of parameters for a univariate transfer function model.

L10b3.... Frequency domain analysis (search also class J1)

L10b3a.. Cross-spectral analysis

L10b3a3 Cross-spectrum estimation using the cross-periodogram

CSSWD

  Estimate the nonnormalized cross-spectral density of two stationary time series using a spectral window given the time series data.

CSSWP

  Estimate the nonnormalized cross-spectral density of two stationary time series using a spectral window given the spectral densities and cross periodogram.

CSWED

  Estimate the nonnormalized cross-spectral density of two stationary time series using a weighted cross periodogram given the time series data.

CSWEP

  Estimate the nonnormalized cross-spectral density of two stationary time series using a weighted cross periodogram given the spectral densities and cross periodogram.

L10c....... Multivariate time series (search also classes J1, L3e3 and L10b)

KALMN

  Perform Kalman filtering and evaluate the likelihood function for the state-space model.

OPT_DES                       Allows for multiple channels for both the controlled and manipulated variables

L10d...... Two multi-channel time series

MCCF

   Compute the multichannel cross-correlation function of two mutually stationary multichannel time series.

MLSE

   Compute least squares estimates of a linear regression model for a multichannel time series with a specified base channel.

MWFE

   Compute least squares estimates of the multichannel Wiener filter coefficients for two mutually stationary multichannel time series.

L11......... Correlation analysis (search also classes L4 and L13c)

BSCAT

  Compute the biserial correlation coefficient for a dichotomous variable and a classification variable.

BSPBS

  Compute the biserial and point-biserial correlation coefficients for a dichotomous variable and a numerically measurable classification variable.

CANCOR Given an input array of deviate values, generates a canonical correlation array.

CORVC

  Compute the variance-covariance or correlation matrix.

COVPL

  Compute a pooled variance-covariance matrix from the observations.

CTRHO

  Estimate the bivariate normal correlation coefficient using a contingency table.

KENDP

  Compute the frequency distribution of the total score in Kendall’s rank correlation coefficient.

PCORR

  Compute partial correlations or covariances from the covariance or correlation matrix.

RBCOV

  Compute a robust estimate of a covariance matrix and mean vector.

TETCC

  Categorize bivariate data and compute the tetrachoric correlation coefficient.

L12......... Discriminant analysis

DMSCR

  Use Fisher’s linear discriminant analysis method to reduce the number of variables.

DSCRM

  Perform a linear or a quadratic discriminant function analysis among several known groups.

NNBRD

  Perform a k nearest neighbor discrimination.

L13......... Covariance structures models

L13a....... Factor analysis

FACTR

  Extract initial factor-loading estimates in factor analysis.

FCOEF

  Compute a matrix of factor score coefficients for input to the following IMSL routine (FSCOR).

FDOBL

  Compute a direct oblimin rotation of a factor-loading matrix.

FGCRF

  Compute direct oblique rotation according to a generalized fourth-degree polynomial criterion.

FHARR

  Compute an oblique rotation of an unrotated factor-loading matrix using the Harris-Kaiser method.

FIMAG

  Compute the image transformation matrix.

FOPCS

  Compute an orthogonal Procrustes rotation of a factor-loading matrix using a target matrix.

FPRMX

  Compute an oblique Promax or Procrustes rotation of a factor-loading matrix using a target matrix, including pivot and power vector options.

FRESI

  Compute commonalities and the standardized factor residual correlation matrix.

FROTA

  Compute an orthogonal rotation of a factor-loading matrix using a generalized orthomax criterion, including quartimax, varimax, and equamax rotations.

FRVAR

  Compute the factor structures and the variance explained by each factor.

FSCOR

  Compute a set of factor scores given the factor score coefficient matrix.

L13b...... Principal components analysis

KPRIN

  Maximum likelihood or least-squares estimates for principle components from one or more matrices.

PRINC

  Compute principal components from a variance-covariance matrix or a correlation matrix.

L13c....... Canonical correlation

CANCR

  Perform canonical correlation analysis from a data matrix.

CANVC

  Perform canonical correlation analysis from a variance-covariance matrix or a correlation matrix.

L14......... Cluster analysis

L14a....... One-way

L14a1..... Unconstrained

L14a1a... Nested

L14a1a1. Joining (e.g., single link)

CLINK

  Perform a hierarchical cluster analysis given a distance matrix.

L14a1b.. Non-nested (e.g., K means)

KMEAN  Perform a K-means (centroid) cluster analysis.

L14c....... Display

TREEP

    Print a binary tree.

L14d...... Service routines (e.g., compute distance matrix)

CDIST

  Compute a matrix of dissimilarities (or similarities) between the columns (or rows) of a matrix.

CNUMB

  Compute cluster membership for a hierarchical cluster tree.

L15......... Life testing, survival analysis

ACTBL

  Produce population and cohort life tables.

HAZEZ

  Perform nonparametric hazard rate estimation using kernel functions. Easy-to-use version of the previous IMSL subroutine (HAZRD).

HAZRD

  Perform nonparametric hazard rate estimation using kernel functions and quasi-likelihoods.

HAZST

  Perform hazard rate estimation over a grid of points using a kernel function.

KAPMR

  Compute Kaplan-Meier estimates of survival probabilities in stratified samples.

KTBLE

  Print Kaplan-Meier estimates of survival probabilities in stratified samples.

NRCES

  Compute maximum likelihood estimates of the mean and variance from grouped and/or censored normal data.

PHGLM

  Analyze time event data via the proportional hazards model.

STBLE

  Estimate survival probabilities and hazard rates for various parametric models.

SVGLM

  Analyze censored survival data using a generalized linear model.

TRNBL

  Compute Turnbull’s generalized Kaplan-Meier estimates of survival probabilities in samples with interval censoring.

L16......... Multidimensional scaling

MSDBL

  Obtain normalized product-moment (double centered) matrices from dissimilarity matrices.

MSDST

  Compute distances in a multidimensional scaling model.

MSIDV

  Perform individual-differences multidimensional scaling for metric data using alternating least squares.

MSINI

  Compute initial estimates in multidimensional scaling models.

MSSTN

  Transform dissimilarity/similarity matrices and replace missing values by estimates to obtain standardized dissimilarity matrices.

MSTRS

  Compute various stress criteria in multidimensional scaling.

L17......... Statistical data sets

GDATA

Retrieve a commonly analyzed data set.

N............ DATA HANDLING (search also class L2)

N1.......... Input, output

PGOPT

  Set or retrieve page width and length for printing.

WRIRL

  Print an integer rectangular matrix with a given format and labels.

WRIRN

  Print an integer rectangular matrix with integer row and column labels.

WROPT

  Set or retrieve an option for printing a matrix.

WRRRL

  Print a real rectangular matrix with a given format and labels.

WRRRN

  Print a real rectangular matrix with integer row and column labels.

N3.......... Character manipulation

ACHAR

Return a character given its ASCII value.

CVTSI

  Convert a character string containing an integer number into the corresponding integer form.

IACHAR

Return the integer ASCII value of a character argument.

ICASE

  Return the ASCII value of a character converted to uppercase.

IICSR

  Compare two character strings using the ASCII collating sequence without regard to case.

IIDEX

  Determine the position in a string at which a given character sequence begins without regard to case.

N5.......... Searching

N5a........ Extreme value

EQTIL

    Compute empirical quantiles.

ORDST

  Determine order statistics.

N5b........ Insertion position

ISRCH

  Search a sorted integer vector for a given integer and return its index.

SRCH

   Search a sorted vector for a given scalar and return its index.

SSRCH

  Search a character vector, sorted in ascending ASCII order, for a given string and return its index.

N5c........ On a key

IIDEX

  Determine the position in a string at which a given character sequence begins without regard to case.

ISRCH

  Search a sorted integer vector for a given integer and return its index.

SRCH

   Search a sorted vector for a given scalar and return its index.

SSRCH

  Search a character vector, sorted in ascending ASCII order, for a given string and return its index.

N6.......... Sorting

N6a........ Internal

N6a1...... Passive (i.e., construct pointer array, rank)

N6a1a.... Integer

SVIGP

  Sort an integer array by algebraic value and return the permutations.

N6a1b.... Real

RANKS

  Compute the ranks, normal scores, or exponential scores for a vector of observations.

SCOLR

  Sort columns of a real rectangular matrix using keys in rows.

SROWR

  Sort rows of a real rectangular matrix using keys in columns.

SVRGP

  Sort a real array by algebraic value and return the permutations.

N6a2...... Active

N6a2a.... Integer

SVIGN

    Sort an integer array by algebraic value.

SVIGP

  Sort an integer array by algebraically increasing value and return the permutation that rearranges the array.

N6a2b.... Real

SCOLR

  Sort columns of a real rectangular matrix using keys in rows.

SROWR

  Sort rows of a real rectangular matrix using keys in columns.

SVRGN

   Sort a real array by algebraic value.

SVRGP

  Sort a real array by algebraic value and return the permutations.

N8.......... Permuting

MVNAN

  Move any rows of a matrix with the IMSL missing value code NaN (not a number) in the specified columns to the last rows of the matrix.

PERMA

Permute the rows or columns of a matrix.

PERMU

  Rearrange the elements of an array as specified by a permutation.

RORDM

  Reorder rows and columns of a symmetric matrix.

Q............ GRAPHICS (search also classes L3)

BOXP

     Print boxplots for one or more samples.

CDF2P

  Print a plot of two sample cumulative distribution functions.

CDFP

   Print a sample cumulative distribution function (CDF), a theoretical CDF, and confidence band information.

HHSTP

   Print a horizontal histogram.

PLOTP

   Print a plot of up to ten sets of points.

PROBP

   Print a probability plot.

SCTP

   Print a scatterplot of several groups of data.

STMLP

  Print a stem-and-leaf plot.

TREEP

    Print a binary tree.

VHS2P

  Print a vertical histogram with every bar subdivided into two parts.

VHSTP

   Print a vertical histogram.

R............ SERVICE ROUTINES

IDYWK

  Compute the day of the week for a given date.

NDAYS

  Compute the number of days from January 1, 1900, to the given date.

NDYIN

  Give the date corresponding to the number of days since January 1, 1900.

TDATE

  Get today’s date.

TIMDY

  Get time of day.

VERSL

  Obtain STAT/LIBRARY-related version, system and license numbers.

R1.......... Machine-dependent constants

AMACH

                                                      Retrieve machine constants.

IFNAN  Check if a floating-point number is NaN (not a number).

IMACH  Retrieve integer machine constants.

UMACH  Set or retrieve input or output device unit numbers.

R3.......... Error handling

R3b........ Set unit number for error messages

UMACH  Set or retrieve input or output device unit numbers.

R3c........ Other utilities

ERSET  Set error handler default print and stop actions.

IERCD  Retrieve the code for an informational error.

N1RTY  Retrieve an error type for the most recently called IMSL routine.

S............. SOFTWARE DEVELOPMENT TOOLS

CPSEC  Return CPU time used in seconds.



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