A new four-parameter lifetime distribution |
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Authors: | Mojtaba Alizadeh Seyyed Fazel Bagheri Mohammad Alizadeh Saralees Nadarajah |
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Institution: | 1. Branch of Mazandaran, Statistical Center of Iran, Sari, Iran;2. Department of Mathematics, College of Basic Science, Yadegar-e-Imam Khomeini (RAH) Branch, Islamic Azad University, Tehran, Iran;3. Department of Mathematical Sciences, University of Mazandaran, Mazandaran, Iran;4. School of Mathematics, University of Manchester, Manchester, UK |
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Abstract: | Generalizing lifetime distributions is always precious for applied statisticians. In this paper, we introduce a new four-parameter generalization of the exponentiated power Lindley (EPL) distribution, called the exponentiated power Lindley geometric (EPLG) distribution, obtained by compounding EPL and geometric distributions. The new distribution arises in a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The distribution exhibits decreasing, increasing, unimodal and bathtub-shaped hazard rate functions, depending on its parameters. It contains several lifetime distributions as particular cases: EPL, new generalized Lindley, generalized Lindley, power Lindley and Lindley geometric distributions. We derive several properties of the new distribution such as closed-form expressions for the density, cumulative distribution function, survival function, hazard rate function, the rth raw moment, and also the moments of order statistics. Moreover, we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix. Simulation studies are also provided. Finally, two real data applications are given for showing the flexibility and potentiality of the new distribution. |
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Keywords: | Exponentiated power Lindley distribution maximum likelihood estimation modelselection criteria probability weighted moments residual life function |
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