Dataplot Vol 2 Vol 1

# BU4PPF

Name:
BU4PPF (LET)
Type:
Library Function
Purpose:
Compute the Burr type 4 percent point function with shape parameters r and c.
Description:
The standard Burr type 4 distribution has the following percent point function:

with r and c denoting the shape parameters.

This distribution can be generalized with location and scale parameters in the usual way using the relation

Syntax:
LET <y> = BU4PPF(<p>,<r>,<c>,<loc>,<scale>)
<SUBSET/EXCEPT/FOR qualification>
where <p> is a number, parameter, or variable in the interval (0,1);
<y> is a variable or a parameter (depending on what <p> is) where the computed Burr type 4 ppf value is stored;
<r> is a positive number, parameter, or variable that specifies the first shape parameter;
<c> is a positive number, parameter, or variable that specifies the second shape parameter;
<loc> is a number, parameter, or variable that specifies the location parameter;
<scale> is a positive number, parameter, or variable that specifies the scale parameter;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

If <loc> and <scale> are omitted, they default to 0 and 1, respectively.

Examples:
LET A = BU4PPF(0.95,0.2,1.7)
LET Y = BU4PPF(P,0.5,2.2,0,5)
PLOT BU4PPF(P,2,1.8,0,5) FOR P = 0.01 0.01 0.99
Default:
None
Synonyms:
BURR TYPE IV is a synonym for BURR TYPE 4.
Related Commands:
 BU4PDF = Compute the Burr type 4 probability density function. BU4CDF = Compute the Burr type 4 cumulative distribution function. BU2PDF = Compute the Burr type 2 probability density function. BU3PDF = Compute the Burr type 3 probability density function. BU5PDF = Compute the Burr type 5 probability density function. BU6PDF = Compute the Burr type 6 probability density function. BU7PDF = Compute the Burr type 7 probability density function. BU8PDF = Compute the Burr type 8 probability density function. BU9PDF = Compute the Burr type 9 probability density function. B10PDF = Compute the Burr type 10 probability density function. B11PDF = Compute the Burr type 11 probability density function. B12PDF = Compute the Burr type 12 probability density function. RAYPDF = Compute the Rayleigh probability density function. WEIPDF = Compute the Weibull probability density function. EWEPDF = Compute the exponentiated Weibull probability density function.
Reference:
Burr (1942), "Cumulative Frequency Functions", Annals of Mathematical Statistics, 13, pp. 215-232.

Johnson, Kotz, and Balakrishnan (1994), "Contiunuous Univariate Distributions--Volume 1", Second Edition, Wiley, pp. 53-54.

Devroye (1986), "Non-Uniform Random Variate Generation", Springer-Verlang, pp. 476-477.

Applications:
Distributional Modeling
Implementation Date:
2007/10
Program:
```
LABEL CASE ASIS
TITLE CASE ASIS
TITLE OFFSET 2
.
MULTIPLOT 4 4
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 4
.
LET RVAL = DATA 0.5  1  2  5
LET CVAL = DATA 0.5  1  2  5
.
LOOP FOR IROW = 1 1 4
LOOP FOR ICOL = 1 1 4
LET R  = RVAL(IROW)
LET C = CVAL(ICOL)
TITLE R = ^r, C = ^c
PLOT BU4PPF(P,R,C) FOR P = 0  0.01  0.99
END OF LOOP
END OF LOOP
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Burr Type 4 Percent Point Functions
```

Date created: 12/17/2007
Last updated: 12/17/2007