Model Definition for Generalized Pareto Distribution
/*--------------------------------------------------------------
SAS Sample Library
Name: svrtgpd.sas
Description: Example Program from SAS/ETS User's Guide,
The SEVERITY Procedure
Title: Model Definition for Generalized Pareto 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 was defined in a previous package.
Function 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 GPD_DESCRIPTION() $32;
length model $32;
model = "Generalized Pareto Distribution";
return(model);
endsub;
function GPD_PARMCOUNT();
return(2);
endsub;
function GPD_LOGPDF(x, Theta, Xi);
/* Theta : Scale */
/* Xi : Shape */
if (x < 0) then do;
return (.);
end;
else do;
if (Xi > constant('MACEPS')) then
logpdf = (-1-(1/Xi)) * log1px(Xi*(x/Theta)) - log(Theta);
else
logpdf = -x/Theta - log(Theta); /* for Xi ~ 0, exponential */
return (logpdf);
end;
endsub;
function GPD_PDF(x, Theta, Xi);
/* Theta : Scale */
/* Xi : Shape */
if (x < 0) then do;
return (0);
end;
else do;
logpdf = GPD_LOGPDF(x, Theta, Xi);
if (not(missing(logpdf)) and logpdf < 174) then
return ( exp(logpdf) );
else
return ( . );
end;
endsub;
function GPD_LOGCDF(x, Theta, Xi);
/* Theta : Scale */
/* Xi : Shape */
if (x < 0) then do;
return (.);
end;
else do;
if (Xi > constant('MACEPS')) then
return (log1px(-(1 + Xi*(x/Theta))**(-1/Xi)));
else
return (log1px(- exp(-x/Theta))); /* for Xi ~ 0, exponential */
end;
endsub;
function GPD_CDF(x, Theta, Xi);
/* Theta : Scale */
/* Xi : Shape */
if (x < 0) then do;
return (0);
end;
else do;
if (Xi > constant('MACEPS')) then
return (1 - (1 + Xi*(x/Theta))**(-1/Xi));
else
return (1 - exp(-x/Theta)); /* for Xi ~ 0, exponential */
end;
endsub;
function GPD_LOGSDF(x, Theta, Xi);
/* Theta : Scale */
/* Xi : Shape */
if (x < 0) then do;
return (0);
end;
else do;
if (Xi > constant('MACEPS')) then
return ((-1/Xi)*log1px(Xi*(x/Theta)));
else
return (-x/Theta); /* for Xi ~ 0, exponential */
end;
endsub;
function GPD_SDF(x, Theta, Xi);
/* Theta : Scale */
/* Xi : Shape */
if (x < 0) then do;
return (1);
end;
else do;
if (Xi > constant('MACEPS')) then
return ((1 + Xi*(x/Theta))**(-1/Xi));
else
return (exp(-x/Theta)); /* for Xi ~ 0, exponential */
end;
endsub;
subroutine GPD_PARMINIT(dim, x[*], nx[*], F[*], Ftype, Theta, Xi);
outargs Theta, Xi;
array m[2] / nosymbols;
/* Use Method of Moments */
call svrtutil_rawmoments(dim, x, nx, 2, m);
if (missing(m[1])) then do;
Theta = .;
Xi = .;
end;
else do;
t1 = m[2] - m[1]**2;
t2 = 2*t1 - m[2];
eps = constant('MACEPS');
if (t1 < eps or t2 < eps) then do;
Theta = m[1]/2;
Xi = 1/2;
end;
else do;
Theta = (m[1]*m[2])/(2*t1);
Xi = t2/(2*t1);
end;
end;
endsub;
function GPD_QUANTILE(p, Theta, Xi);
/* Theta : Scale */
/* Xi : Shape */
return (((1-p)**(-Xi)-1)*Theta/Xi);
endsub;
quit;