Proc severity/univariate

[Azeddine]

Hello,

When i use Proc severity and proc univariate to estimate parameters,

i have a difference between my 2 estimate parameters.

How i can resolve this problem?

I would like to have exactly the same parameter.

Exemple :

DATA Grave2;

INPUT Var1;

CARDS;

148234

17967

24066

20357

2409

93913

24879

75094

42631

50359

22077

63590

25720

57214

228177

105531

77630

62990

99790

477139

;

RUN;

/*a)Estimate parameter with proc Univariate*/

rsubmit;

proc univariate data=Grave2;

var VAR1;

histogram / gamma(theta=0);

qqplot / gamma(theta=0 alpha=est Sigma=est);

ppplot / gamma(theta=0 alpha=est Sigma=est);

histogram / lognormal(theta=0);

qqplot / lognormal(theta=0 zeta=est Sigma=est);

ppplot / gamma(theta=0 alpha=est Sigma=est);

histogram / weibull(theta=0);

qqplot / weibull(theta=0 C=est Sigma=est);

ppplot / weibull(theta=0 C=est Sigma=est);

histogram / pareto(theta=0);

qqplot / pareto(theta=0 alpha=est Sigma=est);

ppplot / pareto(theta=0 alpha=est Sigma=est);

run;

endrsubmit;

/*b) Estimate parameter with Proc severity*/

rsubmit;

proc severity data=Grave2 crit=aic covout plots=none; /* call proc on view */loss VAR1;

title "Statistique des sinistres et selection de la loi par critère AIC";

dist gamma logn weibull gpd /*Pareto donne des résultats trop differents entre severity et univariate*/;

/*dist _predefined_; Preselection de lois utilisées en réassurance*/

run;

endrsubmit;

Regards,

[Rick_SAS]

There are many ways to fit distributional parameters to data: method of moments, optimization of the likelihhod equation, optimization of an approximate likelihood, matching percentiles, and so forth.  The estimates can also depend on the initial guess and the numerical optimization technique.

The documentation for the procedures descrbe how the parameters are estimated. The doc tor PROC SEVERITY shows how parameters are initialized and what estimation techniques are used. For example, for a gamma distribution, an APPROXIMATE MLE is formed by approximating the digamma function.  This results in a fast estimation. In contrast, the UNIVARIATE procedure solves the true MLE by using the full digamma fnuction.  It is slower, but more accurate.

In short, you are not going to be able to get exactly the same answers for the distributions for which SEVERITY and UNIVARIATE use different estimation methods. For distributions like the gamma, the documentation indicates that the estimates might be off by a few percentage points.