Chapter 16: Line Printer Graphics

CDFP

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

Required Arguments

CDF — User-supplied FUNCTION to compute the cumulative distribution function. The form is CDF(P), where
P — Sample point.   (Input)
CDF — Theoretical probability at the point P or integral of the
                                probability density function at the point P.   (Output)

X —Vector of length NOBS containing the sample.   (Input)

Optional Arguments

NOBS — Number of observations.   (Input)
Default: NOBS = size (X,1).

N12 —Confidence band option.   (Input)
If N12 = 0, then no confidence bands are printed. If N12 = 1, then positive or upper one-sided confidence band information is printed. If N12 = −1, then negative or lower one-sided confidence band information is printed. If N12 = 2, then two-sided confidence band information is printed.
Default: N12 = 2.

N95 —Confidence band option.   (Input)
If N95 = 95, the 95-percent band is desired. Otherwise, the 99-percent band is desired.
Default: N95 = 95.

IPRINT — Print option.   (Input)
If IPRINT = 1, then CDFP prints the sample CDF, the theoretical CDF, and the confidence band on the CDF. If IPRINT = 0, then the above information will not be printed.
Default: IPRINT = 1.

FORTRAN 90 Interface

Generic:                              CALL CDFP (CDF, X [,…])

Specific:                             The specific interface names are S_CDFP and D_CDFP.

FORTRAN 77 Interface

Single:                                CALL CDFP (CDF, NOBS, X, N12, N95, IPRINT)

Double:                              The double precision name is DCDFP.

Description

When IPRINT = 1, CDFP prints the sample cumulative distribution function (CDF), the theoretical CDF, and confidence bands on the CDF. The theoretical CDF will be plotted with or without the confidence band information. The sample CDF is calculated. The theoretical CDF is calculated by calling the user supplied FUNCTION subprogram CDF. Asymptotic critical values are used (from the Smirnov tables) for confidence interval calculations.

Comments

1.         Workspace may be explicitly provided, if desired, by use of C2FP/DC2FP. The reference is:

CALL C2FP (CDF, NOBS, X, N12, N95, IPRINT, WKX, WK)

The additional arguments are as follows:

WKX — Vector of length NOBS containing the sorted data X in ascending order.   (Output)

WK — Vector of length 4 * NOBS containing confidence band values.   (Output)
WK may be dimensioned 3 * NOBS instead of 4 * NOBS for a lower or upper confidence band.

2.         Note that sample CDFs are step functions.

3.         Confidence bands are plotted around the sample CDF.

4.         Output is written to the unit specified by the routine UMACH (see the Reference Material section in this manual ;).

5.         Printing starts on a new page with default page width 78 columns and default page length 60 rows. The user may change these values by calling the routine PGOPT.p<.STCH19.DOC!PGOPT;; in advance.

Example

This example prints and plots the sample CDF, the theoretical CDF, and the two-sided 95 percent band information using 70 observations. Routines RNSET and RNUN are called to generate these uniform (0, 1) random numbers.

 

      USE PGOPT_INT

      USE RNSET_INT

      USE RNUN_INT

      USE CDFP_INT

 

      IMPLICIT   NONE

      INTEGER    IPAGE, ISEED, NOBS

      PARAMETER  (NOBS=70)

      REAL       CDF, X(NOBS)

      EXTERNAL   CDF

!

      ISEED = 123457

!                                 Two-sided confidence band option.

!                                 95-percent band option.

!                                 Set page width and length.

      IPAGE =  78

      CALL PGOPT (-1, IPAGE)

      IPAGE=40

      CALL PGOPT (-2, IPAGE)

!                                 Initialize the seed.

      CALL RNSET (ISEED)

!                                 Generate pseudo-random numbers from

!                                 a uniform (0,1) distribution.

      CALL RNUN (X)

!                                 Plot

      CALL CDFP (CDF, X, IPRINT=0)

      END

!

      REAL FUNCTION CDF (X)

      REAL       X

!

      CDF = X

      RETURN

      END

Output

 

                      Cumulative Sample and Theoretical CDFs


             +::::::::::::::::+::::::::::::::::+::::::::::::::4444:4MM

        0.95 +                                               44    M2+

             .                                              44  MM   .

             .                                          44 4  2M1    .

             .                                       44 4   22 1    33

        0.80 +                                      44     2 11    33+

             .                                    4 4   22   1  33 3 .

             .                                  4    22  1 11  33    .

P            .                                44    2 1 1      3     .

r       0.65 +                             4 4    2  1        33     +

o            .                           4     22 1 1        3       .

b            .                          4    22 1 1        33        .

a            .                     44  4   2  11        33           .

b       0.50 +                   4 4    22   11      33              +

i            .               4  4      221 1        33               .

l            .            4 4           11      3 3                  .

i            .         444         2M  11      33                    .

t       0.35 +       4 4         2 1         33                      +

y            .      44       1  M1       3 3 3                       .

             .    44      1 MM          33                           .

             .  4       112            33                            .

        0.20 + 4       122         33                                +

             .4      M 2        33 3                                 .

             .    11M2      33                                       .

             .  1 M2     33                                          .

        0.05 + MM      33                                            +

             +MM3:3333:3::::::+::::::::::::::::+::::::::::::::::+:::::

            0.0              0.3              0.6              0.9


                                   Sample Values

                      Sample CDF = 1      Theoretical CDF = 2

                             Confidence bands = 3 and 4



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