XploRe Help : estBurr

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	stats
See also:	pdfBurr cdfBurr

Quantlet:		estBurr
Description:		computes estimators of parameters (alpha, lambda, tau) of the Burr distribution.

Reference(s):

K. Burnecki, A. Misiorek, R.Weron (2004) "Loss distibution", in “Statistical Tools for Finance and Insurance”, eds. P. Cizek, W. Härdle, R. Weron, Springer.

Usage:	`{db,de,vb,ve,w2b,w2e,a2b,a2e,alpha,lambda,tau,alphamin,lambdamin,taumin,likconv} = estBurr(analyzedsample,method,numberofiterations)`
Input:
	`analyzedsample`	n x 1 vector, sample for which Burr distribution parameters will be estimated.
	`method`	integer, estimation method selection flag (0 - all methods, 1 - ML, 2 - A2).
	`numberofiterations`	integer, number of iterations for minimization procedures.
Output:
	`db`	scalar, Value of Kolmogorov statistic for ML parameters.
	`de`	scalar, Value of Kolmogorov statistic for A2 parameters.
	`vb`	scalar, Value of Kuiper statistic for ML parameters.
	`ve`	scalar, Value of Kuiper statistic for A2 parameters.
	`w2b`	scalar, Value of Cramer-von Mises statistic for ML parameters.
	`w2e`	scalar, Value of Cramer-von Mises statistic for A2 parameters.
	`a2b`	scalar, Value of Anderson-Darling statistic for ML parameters.
	`a2e`	scalar, Value of Anderson-Darling statistic for A2 parameters.
	`alpha`	scalar, Parameter alpha from ML estimation.
	`lambda`	scalar, Parameter lambda from ML estimation.
	`tau`	scalar, Parameter tau from ML estimation.
	`alphamin`	scalar, Parameter alpha from A2 estimation.
	`lambdamin`	scalar, Parameter lambda from A2 estimation.
	`taumin`	scalar, Parameter tau from A2 estimation.
	`likconv`	scalar, 1 - if ML estimation converged, 0 - otherwise.

Example:

library("xplore") library("stats") library("distribs") library("nummath") randomize(101) sample=rndBurr(1000,1,3,2,1) estBurr(sample,0,3000)

Result:

Contents of _tmp.db
[1,]  0.22056
Contents of _tmp.de
[1,]  0.012182
Contents of _tmp.vb
[1,]  0.22401
Contents of _tmp.ve
[1,]  0.022584
Contents of _tmp.w2b
[1,]   22.231
Contents of _tmp.w2e
[1,]  0.02013
Contents of _tmp.a2b
[1,]    111.2
Contents of _tmp.a2e
[1,]  0.15733
Contents of _tmp.alpha
[1,]   2.6105
Contents of _tmp.lambda
[1,]   1.6537
Contents of _tmp.tau
[1,]   1.0446
Contents of _tmp.alphamin
[1,]   2.8031
Contents of _tmp.lambdamin
[1,]   1.8161
Contents of _tmp.taumin
[1,]   1.0262
Contents of _tmp.likconv
[1,]        1

Author: A. Misiorek, 20041110 license MD*Tech