Model Definition for Weibull Distribution
/*--------------------------------------------------------------
SAS Sample Library
Name: svrtwbul.sas
Description: Example Program from SAS/ETS User's Guide,
The SEVERITY Procedure
Title: Model Definition for Weibull Distribution
Product: SAS/ETS Software
Keys: fitting continuous distributions
PROC: SEVERITY
Notes: If you run this sample program without any modification, then
the Sasuser.Svrtdist library contains functions and subroutines
that are identical to those in the Sashelp.Svrtdist library.
Further, if you run this sample without any modification to the
names of functions and subroutines, then PROC FCMP writes
warnings of the following nature to the SAS log:
WARNING: Function <name> was defined in a previous package.
Function <name> as defined in the current program will
be used as default when the package is not specified.
You can ignore such warnings; they appear because the functions
defined in this sample are already defined in the input library
Sashelp.Svrtdist.
--------------------------------------------------------------*/
proc fcmp library=sashelp.svrtdist outlib=sasuser.svrtdist.models;
function WEIBULL_DESCRIPTION() $32;
length model $32;
model = "Weibull Distribution";
return(model);
endsub;
function WEIBULL_PARMCOUNT();
return(2);
endsub;
function WEIBULL_LOGPDF(x, Theta, Tau);
/* Theta : Scale */
/* Tau : Shape */
if (x >= 2.220446E-16) then do; /* constant('MACEPS') */
z = (x/Theta)**Tau;
return (log(Tau * z / x) - z);
end;
else
return (-180.218266); /* constant('LOGSMALL') */
endsub;
function WEIBULL_PDF(x, Theta, Tau);
/* Theta : Scale */
/* Tau : Shape */
if (x >= 2.220446E-16) then do; /* constant('MACEPS') */
z = (x/Theta)**Tau;
return ((Tau / x) * z * exp(-z));
end;
else
return (0);
endsub;
function WEIBULL_LOGCDF(x, Theta, Tau);
/* Theta : Scale */
/* Tau : Shape */
if (x >= 2.220446E-16) then do; /* constant('MACEPS') */
z = (x/Theta)**Tau;
c = exp(-z);
if (c < 1) then
return (log1px(-c));
else
return (-180.218266); /* constant('LOGSMALL') */
end;
else
return (-180.218266); /* constant('LOGSMALL') */
endsub;
function WEIBULL_CDF(x, Theta, Tau);
/* Theta : Scale */
/* Tau : Shape */
if (x >= 2.220446E-16) then do; /* constant('MACEPS') */
z = (x/Theta)**Tau;
return (1 - exp(-z));
end;
else
return (0);
endsub;
function WEIBULL_LOGSDF(x, Theta, Tau);
/* Theta : Scale */
/* Tau : Shape */
if (x >= 2.220446E-16) then do; /* constant('MACEPS') */
z = (x/Theta)**Tau;
return (-z);
end;
else
return (0);
endsub;
function WEIBULL_SDF(x, Theta, Tau);
/* Theta : Scale */
/* Tau : Shape */
if (x >= 2.220446E-16) then do; /* constant('MACEPS') */
z = (x/Theta)**Tau;
return (exp(-z));
end;
else
return (1);
endsub;
subroutine WEIBULL_PARMINIT(dim, x[*], nx[*], F[*], Ftype, Theta, Tau);
outargs Theta, Tau;
/* Compute estimates using percentile matching method */
q1 = svrtutil_percentile(0.25, dim, x, F, Ftype); /* First quartile */
q3 = svrtutil_percentile(0.75, dim, x, F, Ftype); /* Third quartile */
if (missing(q1) or missing(q3)) then do;
Theta = .;
Tau = .;
end;
else do;
ll4 = log(log(4));
lq3 = log(q3);
lratio = ll4/log(log(4/3));
ltheta = (lratio*log(q1) - lq3)/(lratio-1);
if (ltheta < 174.673089) then do; /* constant('LOGBIG') */
Theta = exp(ltheta);
lq3 = lq3 - ltheta;
if (lq3 > 2.220446E-16) then /* constant('MACEPS') */
Tau = ll4/lq3;
else
Tau = .;
end;
else do;
Theta = .;
Tau = .;
end;
end;
endsub;
function WEIBULL_QUANTILE(p, Theta, Tau);
/* Theta : Scale */
/* Tau : Shape */
if (p >= 1-2.220446E-16) then /* constant('MACEPS') */
return (.);
return (Theta*(-log1px(-p))**(1/Tau));
endsub;
function WEIBULL_MEAN(x, Theta, Tau);
return (Theta*gamma(1 + 1/Tau));
endsub;
quit;