Dataplot Vol 2 Vol 1

# BWECDF

Name:
BWECDF (LET)
Type:
Library Function
Purpose:
Compute the Bi-Weibull cumulative distribution function with shape parameters SCALE1, GAMMA1, LOC2, SCALE2, and GAMMA2.
Description:
The Bi-Weibull distribution is a mixture of two Weibull distributions: a "burn-in" Weibull and a "wear out" Weibull. This makes it a very flexible distribution for reliability applications.

The cumulative distribution function for the bi-Weibull distribution is:

with s1, , s2, > 0 and 0.

This is a mixture of a 2-parameter Weibull (the burn-in) and a 3-parameter Weibull (the wear out). This is related to, but slightly different than, the standard Weibull mixture which is simply a weighted sum of two or more Weibull distributions.

Note that Evans, Hastings, and Peacock define the first scale parameter as the reciprocal of what we have defined above.

Syntax:
LET <y> = BWECDF(<x>,<scale1>,<gamma>,<loc2>,<scale2>,<gamma2>)
<SUBSET/EXCEPT/FOR qualification>
where <x> is a variable, number, or parameter;
<y> is a variable or a parameter (depending on what <x> is) where the computed Bi-Weibull cumulative distribution value is stored;
<scale1> is a positive number, parameter, or variable that specifies the scale parameter for the first Weibull component;
<gamma1> is a positive number, parameter, or variable that specifies the shape parameter for the first Weibull component;
<loc2> is a positive number, parameter, or variable that specifies the location parameter for the second Weibull component;
<scale2> is a positive number, parameter, or variable that specifies the scale parameter for the second Weibull component;
<gamma2> is a positive number, parameter, or variable that specifies the shape parameter for the second Weibull component;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = BWECDF(3,10,0.6,4,5,2.5)
LET A = BWECDF(X,S1,G1,L2,S2,G2)
PLOT BWECDF(X,10,0.7,4,4,3) FOR X = 0.01 0.01 15
Default:
None
Synonyms:
None
Related Commands:
 BWECHAZ = Compute the Bi-Weibull cumulative hazard function. BWEHAZ = Compute the Bi-Weibull hazard function. BWEPDF = Compute the Bi-Weibull probability density function. BWEPPF = Compute the Bi-Weibull percent point function. WEIPDF = Compute the Weibull probability density function. EXPPDF = Compute the exponential probability density function. LGNPDF = Compute the lognormal probability density function.
Reference:
"Statistical Distributions", Third Edition, Evans, Hastings, and Peacock, Wiley and Sons, 2001.
Applications:
Reliability Analysis
Implementation Date:
2002/5
Program:
```LET SCALE1 = 10
LET GAMMA1 = 0.7
LET LOC2 = 4
LET SCALE2 = 4
LET GAMMA2 = 3
Y1LABEL PROBABILITY
X1LABEL X
TITLE BI-WEIBULL CUMULATIVE DISTRIBUTION FUNCTION CR() ...
S1 = ^SCALE1, G1 = ^GAMMA1, LOC2 = ^LOC2, S2 = ^SCALE2, G2 = ^GAMMA2
PLOT BWECDF(X,SCALE1,GAMMA1,LOC2,SCALE2,GAMMA2) FOR X = .01 .01 10
```

Date created: 5/31/2002
Last updated: 4/4/2003