XploRe Help : estln

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:	pdfln cdfln

Quantlet:		estln
Description:		computes estimators of parameters (mu, sigma) of lognormal 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,mu,sigma,mulik,sigmalik,mumin,sigmamin,caution}=estln(analyzedsample,method,numberofiterations)`
Input:
	`analyzedsample`	n x 1 vector, sample for which lognormal 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.
	`mu`	scalar, Parameter mu from MoM estimation.
	`sigma`	scalar, Parameter sigma from MoM estimation.
	`mulik`	scalar, Parameter mu from ML estimation.
	`sigmalik`	scalar, Parameter sigma from ML estimation.
	`mumin`	scalar, Parameter mu from A2 estimation.
	`sigmamin`	scalar, Parameter sigma 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=rndln(1000,1,-1,2) estln(sample,0,3000)

Result:

Contents of _tmp.db
[1,]  0.078449
Contents of _tmp.delik
[1,]  0.014309
Contents of _tmp.demin
[1,]  0.011967
Contents of _tmp.vb
[1,]  0.085496
Contents of _tmp.velik
[1,]  0.023936
Contents of _tmp.vemin
[1,]  0.02263
Contents of _tmp.w2b
[1,]   2.2217
Contents of _tmp.w2elik
[1,]  0.025582
Contents of _tmp.w2emin
[1,]  0.018499
Contents of _tmp.a2b
[1,]   14.294
Contents of _tmp.a2elik
[1,]  0.21735
Contents of _tmp.a2emin
[1,]  0.19558
Contents of _tmp.mu
[1,] -0.80711
Contents of _tmp.sigma
[1,]   1.8445
Contents of _tmp.mulik
[1,]  -1.1054
Contents of _tmp.sigmalik
[1,]   2.0493
Contents of _tmp.mumin
[1,]  -1.0917
Contents of _tmp.sigmamin
[1,]   2.0468
Contents of _tmp.caution
[1,]        0

Author: A. Misiorek, 20041110 license MD*Tech