The New Kumaraswamy Kumaraswamy Family of Generalized Distributions with Application

Mohamed Ali Ahmed, Mahmoud Riad Mahmoud, Elsayed Ahmed ElSherbini

Abstract


Finding the best fitted distribution for data set becomes practically an important problem in world of data sets so that it is useful to use new families of distributions to fit more cases or get better fits than before.  In this paper, a new generating family of generalized distributions so called the Kumaraswamy - Kumaraswamy (KW-KW) family is presented. Four important common families of distributions are illustrated as special cases from the KW KW family. Moments, probability weighted moments, moment generating function, quantile function, median, mean deviation, order statistics and moments of order statistics are obtained. Parameters estimation and variance covariance matrix are computed using maximum likelihood method. A real data set is used to illustrate the potentiality of the KW KW weibull distribution (which derived from the kw kw family) compared with other distributions.


Keywords


Kumaraswamy Kumaraswamy Distribution, Moments, Order Statistics, quantile function, Maximum Likelihood Estimation

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DOI: http://dx.doi.org/10.18187/pjsor.v11i2.969

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Title

The New Kumaraswamy Kumaraswamy Family of Generalized Distributions with Application

Keywords

Kumaraswamy Kumaraswamy Distribution, Moments, Order Statistics, quantile function, Maximum Likelihood Estimation

Description

Finding the best fitted distribution for data set becomes practically an important problem in world of data sets so that it is useful to use new families of distributions to fit more cases or get better fits than before.  In this paper, a new generating family of generalized distributions so called the Kumaraswamy - Kumaraswamy (KW-KW) family is presented. Four important common families of distributions are illustrated as special cases from the KW KW family. Moments, probability weighted moments, moment generating function, quantile function, median, mean deviation, order statistics and moments of order statistics are obtained. Parameters estimation and variance covariance matrix are computed using maximum likelihood method. A real data set is used to illustrate the potentiality of the KW KW weibull distribution (which derived from the kw kw family) compared with other distributions.


Date

2015-08-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 11 No. 2, 2015



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810