 Dataplot Vol 2 Vol 1

BU4CDF

Name:
BU4CDF (LET)
Type:
Library Function
Purpose:
Compute the Burr type 4 cumulative distribution function with shape parameters r and c.
Description:
The Burr type 4 distribution is typically defined in terms of its cuumulative distribution function: -INF < x < INF; r, k, s > 0">

with r, k, l, and s denoting the two shape parameters, the location parameter, and the scale parameter, respectively.

The case where l = 0 and s = 1 is referred to as the standard Burr type 6 distribution.

Syntax:
LET <y> = BU4CDF(<x>,<r>,<k>,<loc>,<scale>)
<SUBSET/EXCEPT/FOR qualification>
where <x> is a number, parameter, or variable;
<y> is a variable or a parameter (depending on what <x> is) where the computed Burr type 4 cdf value is stored;
<r> is a positive number, parameter, or variable that specifies the first shape parameter;
<k> 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 = BU4CDF(0.3,0.2,1.7)
LET Y = BU4CDF(X,0.5,2.2,0,5)
PLOT BU4CDF(X,2,1.8) FOR X = -1.57 0.01 1.57
Default:
None
Synonyms:
BURR TYPE IV is a synonym for BURR TYPE 4.
Related Commands:
 BU4PDF = Compute the Burr type 4 probability density function. BU4PPF = Compute the Burr type 4 percent point 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)
LET STOP = C - 0.01
TITLE R = ^r, K = ^k
PLOT BU4CDF(X,R,C) FOR X = 0.01  0.01  STOP
END OF LOOP
END OF LOOP
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Burr Type 4 Cumulative Distribution Functions
``` Date created: 12/17/2007
Last updated: 12/17/2007