XploRe Help : estmixexp

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:	pdfmixexp cdfmixexp

Quantlet:		estmixexp
Description:		computes estimators of parameters (a, beta1, beta2) of mixture of 2 exponentials 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,delik,demin,vb,velik,vemin,w2b,w2elik,w2emin,a2b,a2elik,a2emin,p,b1,b2,plik,b1lik,b2lik,pmin,b1min,b2min,caution}=estmixexp(analyzedsample,method,numberofiterations)`
Input:
	`analyzedsample`	n x 1 vector, sample for which mixture of exponentials 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 MoM parameters.
	`delik`	scalar, Value of Kolmogorov statistic for ML parameters.
	`demin`	scalar, Value of Kolmogorov statistic for A2 parameters.
	`vb`	scalar, Value of Kuiper statistic for MoM parameters.
	`velik`	scalar, Value of Kuiper statistic for ML parameters.
	`vemin`	scalar, Value of Kuiper statistic for A2 parameters.
	`w2b`	scalar, Value of Cramer-von Mises statistic for MoM parameters.
	`w2elik`	scalar, Value of Cramer-von Mises statistic for ML parameters.
	`w2emin`	scalar, Value of Cramer-von Mises statistic for A2 parameters.
	`a2b`	scalar, Value of Anderson-Darling statistic for MoM parameters.
	`a2elik`	scalar, Value of Anderson-Darling statistic for ML parameters.
	`a2emin`	scalar, Value of Anderson-Darling statistic for A2 parameters.
	`p`	scalar, Parameter a from MoM estimation.
	`b1`	scalar, Parameter beta1 from MoM estimation.
	`b2`	scalar, Parameter beta2 from MoM estimation.
	`plik`	scalar, Parameter a from ML estimation.
	`b1lik`	scalar, Parameter beta1 from ML estimation.
	`b2lik`	scalar, Parameter beta2 from ML estimation.
	`pmin`	scalar, Parameter a from A2 estimation.
	`b1min`	scalar, Parameter beta1 from A2 estimation.
	`b2min`	scalar, Parameter beta2 from A2 estimation.
	`caution`	scalar, 1 - if MoM estimators can not be computed, 0 - otherwise.

Example:

library("xplore") library("stats") library("distribs") library("nummath") randomize(101) sample=rndmixexp(1000,1,0.2,5,1) estmixexp(sample,0,3000)

Result:

Contents of _tmp.db
[1,]  0.017689
Contents of _tmp.delik
[1,]  0.018185
Contents of _tmp.demin
[1,]  0.014712
Contents of _tmp.vb
[1,]  0.03164
Contents of _tmp.velik
[1,]  0.027508
Contents of _tmp.vemin
[1,]  0.027964
Contents of _tmp.w2b
[1,]  0.035635
Contents of _tmp.w2elik
[1,]  0.057544
Contents of _tmp.w2emin
[1,]  0.028682
Contents of _tmp.a2b
[1,]  0.27531
Contents of _tmp.a2elik
[1,]  0.38656
Contents of _tmp.a2emin
[1,]  0.24601
Contents of _tmp.p
[1,]  0.81183
Contents of _tmp.b1
[1,]   1.0001
Contents of _tmp.b2
[1,]   5.2528
Contents of _tmp.plik
[1,]  0.83348
Contents of _tmp.b1lik
[1,]   1.0068
Contents of _tmp.b2lik
[1,]   5.3228
Contents of _tmp.pmin
[1,]  0.83542
Contents of _tmp.b1min
[1,]    1.025
Contents of _tmp.b2min
[1,]   5.7517
Contents of _tmp.caution
[1,]        0

Author: A. Misiorek, 20041110 license MD*Tech