New class of Lindley distributions: properties and applications

Duha Hamed () and Ahmad Alzaghal ()
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Duha Hamed: Winthrop University
Ahmad Alzaghal: State University of New York at Farmingdale

Journal of Statistical Distributions and Applications, 2021, vol. 8, issue 1, 1-22

Abstract: Abstract A new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

Keywords: Two parameters Lindley distribution; Moments; Maximum likelihood estimation; The T-R{Y} framework (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1186/s40488-021-00127-y

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