The exponentiated Kumaraswamy distribution and its log-transform

被引：72

作者：

Lemonte, Artur J. ^{[1
]}

Barreto-Souza, Wagner ^{[1
]}

Cordeiro, Gauss M. ^{[2
]}

机构：

[1] Univ Sao Paulo, Dept Estat, Sao Paulo, Brazil

[2] Univ Fed Pernambuco, Dept Estat, Recife, PE, Brazil

来源：

BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS | 2013年 / 27卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Beta distribution; Kumaraswamy distribution; maximum likelihood estimation; mean deviation; order statistic; PROBABILITY DENSITY-FUNCTION; WEIBULL FAMILY; YIELD; SYSTEMS;

D O I：

10.1214/11-BJPS149

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The paper by Kumaraswamy (Journal of Hydrology 46 (1980) 79-88) introduced a probability distribution for double bounded random processes which has considerable attention in hydrology and related areas. Based on this distribution, we propose a generalization of the Kumaraswamy distribution refereed to as the exponentiated Kumaraswamy distribution. We derive the moments, moment generating function, mean deviations, Bonferroni and Lorentz curves, density of the order statistics and their moments. We also present a related distribution, so-called the log-exponentiated Kumaraswamy distribution, which extends the generalized exponential (Aust. N. Z. J. Stat. 41 (1999) 173-188) and double generalized exponential (J. Stat. Comput. Simul. 80 (2010) 159-172) distributions. We discuss maximum likelihood estimation of the model parameters. In applications to real data sets, we show that the log-exponentiated Kumaraswamy model can be used quite effectively in analyzing lifetime data.

引用

页码：31 / 53

页数：23

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