A study of moments and likelihood estimators of the odd Weibull distribution

Q Mathematics

Statistical Methodology Pub Date : 2015-09-01 DOI:10.1016/j.stamet.2015.03.003

Kahadawala Cooray

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引用次数: 7

Abstract

The odd Weibull distribution is a three-parameter generalization of the Weibull and the inverse Weibull distributions having rich density and hazard shapes for modeling lifetime data. This paper explored the odd Weibull parameter regions having finite moments and examined the relation to some well-known distributions based on skewness and kurtosis functions. The existence of maximum likelihood estimators have shown with complete data for any sample size. The proof for the uniqueness of these estimators is given only when the absolute value of the second shape parameter is between zero and one. Furthermore, elements of the Fisher information matrix are obtained based on complete data using a single integral representation which have shown to exist for any parameter values. The performance of the odd Weibull distribution over various density and hazard shapes is compared with generalized gamma distribution using two different test statistics. Finally, analysis of two data sets has been performed for illustrative purposes.

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奇威布尔分布矩量和似然估计的研究

奇威布尔分布是威布尔分布和逆威布尔分布的三参数推广，具有丰富的密度和危险形状，用于建模寿命数据。本文研究了具有有限矩的奇威布尔参数区域，并基于偏度和峰度函数考察了它们与一些已知分布的关系。对于任何样本量的完整数据，都证明了极大似然估计量的存在性。只有当第二个形状参数的绝对值在0到1之间时，才证明了这些估计量的唯一性。此外，Fisher信息矩阵的元素是基于完整的数据，使用一个单一的积分表示得到的，它已经显示存在于任何参数值。用两种不同的检验统计量比较了奇威布尔分布在不同密度和危险形状上的性能。最后，为了说明问题，对两个数据集进行了分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistical Methodology STATISTICS & PROBABILITY-

CiteScore

0.59

自引率

0.00%

发文量

期刊介绍： Statistical Methodology aims to publish articles of high quality reflecting the varied facets of contemporary statistical theory as well as of significant applications. In addition to helping to stimulate research, the journal intends to bring about interactions among statisticians and scientists in other disciplines broadly interested in statistical methodology. The journal focuses on traditional areas such as statistical inference, multivariate analysis, design of experiments, sampling theory, regression analysis, re-sampling methods, time series, nonparametric statistics, etc., and also gives special emphasis to established as well as emerging applied areas.