Abstract
A generalized Laplace distribution using the Kumaraswamy distribution is introduced. Different structural properties of this new distribution are derived, including the moments, and the moment generating function. We discuss maximum likelihood estimation of the model parameters and obtain the observed and expected information matrix. A real data set is used to compare the new model with widely known distributions.
Highlights
For many years, cdf G through exponentiation produces another cdf labeled is always richer and more flexible for data modeling.Mudhokar and Srivastava (1993) successfully applied the exponentiatedWeibull (EW) to analyze bathtub failure data. Gupta and Kundu (2001) concentrated on the study of the exponentiated exponential and found out that it describes situations better than the Weibull or gamma but at least in certain circumstances Exponentiated Exponential might work better than Weibull or gamma
The Beta distribution, which is one of the most basic distributions supported on finite range (0, 1), has been used widely in both practical and theoretical generalizations aspects of statistics (see Nadarajah and Kotz (2004&2005), Kong et al (2007), Akinsete et al (2008) Pescim et al (2010), Souza et al (2010), Nassar and Elmasry (2012) and Nassar and Nada (2011 & 2012 & 2013)
An alternative distribution like the beta distribution, which is easier to work with, is the Kumaraswamy distribution proposed by Kumaraswamy (1980)
Summary
Cdf G through exponentiation produces another cdf labeled is always richer and more flexible for data modeling.Mudhokar and Srivastava (1993) successfully applied the exponentiatedWeibull (EW) to analyze bathtub failure data. Gupta and Kundu (2001) concentrated on the study of the exponentiated exponential and found out that it describes situations better than the Weibull or gamma but at least in certain circumstances Exponentiated Exponential might work better than Weibull or gamma. An alternative distribution like the beta distribution, which is easier to work with, is the Kumaraswamy distribution proposed by Kumaraswamy (1980). This distribution has a simple form, where the probability density function (pdf) and the cumulative distribution function (cdf) are given by respectively:. The Kumaraswamy distribution is like the beta distribution in many ways, for example, Kumaraswamy's densities are unimodal, uniantimodal, increasing, decreasing or constant depending in the same way as the beta distribution on the values of its parameters. De Santana et al (2012) introduced the Kumaraswamy-log-logistic distribution which contains several important distributions as sub-models such as the Log- Logistic, exponentiated Log-Logistic and Burr distributions.
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