Abstract
In this article, we generalize the power Lindley distribution using aquadratic rank transmutation map to develop a transmuted power Lindley distribution. The new distribution exhibits, in addition to decreasing, increasing and bathtub hazard rate, depending on its parameters also unimodal hazard rate. A comprehensive mathematical properties of this distribution is provided. Some expressions for the moments, order statistics, quantiles function are derived. The model parameters are estimated by the maximumlikelihood method. A Monte Carlo experiment on the finite sample behavior of the MLEs is performed. A real climatological data set was used in order to show the applicability of the new model and different statistics of fit were used as selection criteria.
Highlights
The Lindley distribution was proposed by Lindley (1958) and have been widely used in survival analysis and reliability fields
In order to compare the models seven different statistics of fit were used as selection criteria in Section 6.2: −2× log-likelihood (Neg2LogLike), Akaike’s information criterion (AIC), corrected Akaike’s information criterion (AICC), Kolmogorov-Smirnov statistic (KS), Anderson-Darling statistic (AD) and Cramér-von-Mises statistic (CvM)
Seven different statistics of fit were used as selection criteria: −2× log-likelihood (Neg2LogLike), AIC, AICC, KS, AD and CvM
Summary
The Lindley distribution was proposed by Lindley (1958) and have been widely used in survival analysis and reliability fields. Different applications and modifications have been proposed for this model such as: Ghitany et al (2008) that argue that the Lindley distribution could be a better lifetime model than the exponential distribution through a numerical example; Nadarajah et al (2011) and Zakerzadeh and Dolati (2009) in the proposition of a generalization; Merovci and Elbatal (2014) introduced a new lifetime distribution;Warahena-Liyanage and Pararai (2014) proposed an exponentiated power Lindley distribution with applications. We introduce a new lifetime distribution by transmuted and compounding power Lindley distribution named Transmuted Power Lindley (TPL) distribution It is the functional composition of a cumulative distribution function on a distribution with the inverse cumulative distribution (quantile) function of a non-Gaussian distribution, see Shaw and Buckley (2007).
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