
BWEPDFName:
The probability density function for the biWeibull distribution is computed as:
with s_{1}, , s_{2}, > 0 and 0. F denotes the cumulative distribution function and h the hazard function of the BiWeibull distribution. The formulas for the cumulative distribution and hazard functions can be obtained from HELP BWECDF and HELP BWEHAZ, respectively. This is a mixture of a 2parameter Weibull (the burnin) and a 3parameter 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.
<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 BiWeibull pdf 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.
LET A = BWEPDF(X,S1,G1,L2,S2,G2) PLOT BWEPDF(X,10,0.7,4,4,3) FOR X = 0.01 0.01 15
LET SCALE1 = 10 LET GAMMA1 = 0.7 LET LOC2 = 4 LET SCALE2 = 4 LET GAMMA2 = 3 Y1LABEL CUMULATIVE HAZARD X1LABEL X TITLE BIWEIBULL PROBABILITY DENSITY FUNCTION CR() ... S1 = ^SCALE1, G1 = ^GAMMA1, LOC2 = ^LOC2, S2 = ^SCALE2, G2 = ^GAMMA2 PLOT BWEPDF(X,SCALE1,GAMMA1,LOC2,SCALE2,GAMMA2) FOR X = .01 .01 10
Date created: 5/31/2002 