Dataplot Vol 2 Vol 1

# B10PPF

Name:
B10PPF (LET)
Type:
Library Function
Purpose:
Compute the Burr type 10 percent point function with shape parameter r.
Description:
The standard Burr type 10 distribution has the following percent point function:

with r denoting the shape parameter.

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

If r = 1, the Burr type 10 distribution is equivalent to the Rayleigh distribution. For this reason, the Burr type 10 distribution is also referred to as the generalized Rayleigh distribution. It has found use in reliability applications.

Syntax:
LET <y> = B10PPF(<p>,<r>,<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 10 ppf value is stored;
<r> is a positive number, parameter, or variable that specifies the 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 = B10PPF(0.95,0.8)
LET Y = B10PPF(P,1.6,0,5)
PLOT B10PPF(P,2,0,3) FOR P = 0.01 0.01 0.99
Default:
None
Synonyms:
BURR TYPE X is a synonym for BURR TYPE 10.
Related Commands:
 B10CDF = Compute the Burr type 10 cumulative distribution function. B10PDF = Compute the Burr type 10 probability density function. BU2PDF = Compute the Burr type 2 probability density function. BU3PDF = Compute the Burr type 3 probability density function. BU4PDF = Compute the Burr type 4 probability density function. BU5PDF = Compute the Burr type 5 probability density function. BU5PDF = 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. 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.

Raqab and Kundu (2006), "Burr Type X Distributions: Revisited", Journal of Probability and Statistical Sciences, Vol. 4, No. 2, pp. 179-193.

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 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 2
.
LET R  = 0.5
TITLE R = ^r
PLOT B10PPF(P,R) FOR P = 0.01  0.01  0.99
.
LET R  = 1
TITLE R = ^r
PLOT B10PPF(P,R) FOR P = 0.01  0.01  0.99
.
LET R  = 2
TITLE R = ^r
PLOT B10PPF(P,R) FOR P = 0.01  0.01  0.99
.
LET R  = 5
TITLE R = ^r
PLOT B10PPF(P,R) FOR P = 0.01  0.01  0.99
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Burr Type 10 Percent Point Functions
```

Date created: 11/27/2007
Last updated: 11/27/2007