Open AccessThe method of three-parameter Weibull distribution estimation
Author(s) -
Vaida Bartkutú,
Leonidas Sakalauskas
Publication year - 2008
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.276
H-Index - 6
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2008.12.06
Subject(s) - weibull distribution , mathematics , maximum likelihood , statistics , order statistic , estimation , estimation theory , shape parameter , scale parameter , function (biology) , scale (ratio) , sample (material) , variable (mathematics) , likelihood function , sample size determination , mathematical optimization , computer science , mathematical analysis , engineering , physics , chemistry , systems engineering , chromatography , quantum mechanics , evolutionary biology , biology
In this paper we develop Maximum Likelihood (ML) and Improved Analytical (IA) numerical algorithms to estimate parameters of the Weibull distribution, namely, location, scale and shape parameters, using order statistics of a noncensored sample. Since ML methodleads to multiextremal numerical problem we establish conditions to localize extremes of the ML function, which enables us to avoid problems related with ML estimation failure and to create a simple estimation procedure by solving one-dimensional equation. IA estimation also has been developed by solving the equation in one variable. The estimates proposed are studied by computer modeling and compared with the theoretical ones with respect to sample size and number of order statistics used for estimation. Recommendations for implementation of the estimates are also discussed.