Abstract
In this work, we study the beta exponentiated Lindley distribution which includes as special cases several models such as the Lindley, exponentiated Lindley and beta Lindley distributions. Some structural properties of the proposed distribution are studied including expressions for the moments. The estimation of parameters using the methods of moments and maximum likelihood is also discussed. The flexibility of this distribution is illustrated in an application to a real data set.
Highlights
In recent years, generalized distributions have been widely studied in statistics as they possess flexibility in applications
We study the beta exponentiated Lindley distribution which includes as special cases several models such as the Lindley, exponentiated Lindley and beta Lindley distributions
The following distributions are special of the beta exponentiated Lindley (BEL) distribution: (1) When α = 1, the BEL distribution is the beta Lindley (BL) distribution, with the density given by: f (x)
Summary
In recent years, generalized distributions have been widely studied in statistics as they possess flexibility in applications This is justified because the traditional distributions often do not provide good fit in relation to the real data set studied. [20] obtained the two-parameter Lindley distribution and discussed its various properties and applications. The three-parameter Lindley distribution was introduced by [6], who used the distribution for modeling survival data. We propose a new distribution that extend the exponentiated Lindley distribution. Some of the main structural properties of this distribution are derived The flexibility of this distribution is illustrated in an application to a real data set.
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