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Estimacao por blocos dos parametrs da distribuicao de Frechet Comparacao de metodos expeditos

By Maria Manuela Costa Neves Figueiredo

Abstract

Frechet distribution is one of the three asymptotic distributions of extreme values, in general referred to maximal behavior. the estimation of the parameters is difficult because the method of moments cannot be applied (only the moments of order smaller than the value of shape parameter exist) and the maximum likelihood method can only be solved by interactive procedures that require initial estimators. An estimation method based on suitably chosen contiguous blocks of order statistics is presented in a detailed way. We find estimators of the location and scale parameters which are linear combinations of means of three (four) blocks. The estimator i of the shape parameter is a function of the quotient of the differences between the three block means. The estimation for right and left censored samples is considered and a measure for comparing censored and complete case is defined. Via Monte Carlo Simulations, block estimators are compared with simple estimators (of which a systematic study is presented), using them as starting values for obtaining the maximum likelihood solutions. We can state that block estimation gives the best results mainly when all parameters are unknown, or only the shape parameter is known. Finally, we consider an application of order statistics to estimate the quantiles of the distributionAvailable from Fundacao para a Ciencia e a Tecnologia, Servico de Informacao e Documentacao, Av. D. Carlos I, 126, 1200 Lisboa / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga

Topics: 12B - Statistics, operations research
Year: 1990
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Provided by: OpenGrey Repository
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