Inference for generalized inverse Lindley distribution based on generalized order statistics
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Inference for generalized inverse Lindley distribution based on generalized order statistics Devendra Kumar1
· Mazen Nassar2,3 · Sanku Dey4
Received: 31 October 2017 / Accepted: 26 April 2020 © African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2020
Abstract This article addresses the problem of deriving the explicit expressions for single and product moments of order statistics, generalized order statistics and dual generalized order statistics from the generalized Lindley distribution. The means and variances of order statistics, lower record values and progressively type-II censored order statistics for various values of the parameters are tabulated. Furthermore, the maximum likelihood estimators for the parameters of the model using generalized order statistics are obtained. The Bayes estimators under squared error and LINEX (Linear exponential) loss functions using Markov Chain Monte Carlo (MCMC) technique are obtained. Finally, three real data examples to lower record values, type-II censored and progressively type-II censored order statistics have been analyzed for illustrative purposes. Keywords Generalized inverse Lindley distribution · Order statistics · Generalized order statistics · Dual generalized order statistics · Lower record values · Progressively type-II censoring Mathematics Subject Classification 62F15 · 62F10 · 62F99
1 Introduction Lindley [26] introduced the one parameter distribution, which was later called Lindley distribution, in the context of Bayesian statistics, as a counter example of fudicial statistics. This distribution is a mixture of exp(θ ) and gamma(2, θ ) distributions. Ghitany et al. [12,13] established through their studies that Lindley distribution exibits better results compared to exponential distribution in terms of data analysis. However, Lindley distribution is not suit-
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Devendra Kumar [email protected]
1
Department of Statistics, Central University of Haryana, Jant, India
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Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia
3
Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig, Egypt
4
Department of Statistics, St. Anthony’s College, Shillong, Meghalaya 793001, India
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able for modeling different kinds of lifetime data as it does not have enough flexibility and exibits only increasing failure rate. Thus, to overcome this defficiency, in recent years, several authors have developed generalization of Lindley distribution. Prominent among these generalizations which we are aware of are: discrete Poisson–Lindley distribution by Sankaran [33], zero-truncated Poisson–Lindley distribution by Ghitany et al. [12,13], a three-parameter generalization of the Lindley distribution by Zakerzadeh and Dolati [38], weighted Lindley distribution by Ghitany et al. (2011), generalized Lindley distribution by Nadarajah et al. [31], exponentiated Lindley distribution by Bakouch et al. [7], exponential Poisson Lindley distribution
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