The Lomax-Lindley distribution: properties and applications to lifetime data

Abstract

This paper introduces a new three-parameter distribution which is obtained by combining the Lomax and Lindley distributions in a serial system and is called the Lomax-Lindley distribution. The new distribution is quite flexible to model lifetime data. This distribution provides a simple form for hazard rate function which can be increasing, decreasing, bathtub-shaped and unimodal for different choices of the parameter values. Some statistical properties of the Lomax-Lindley distribution such as quantiles, moments, order statistics, Renyi entropy and mean deviations are discussed. The maximum likelihood estimators of its unknown parameters are obtained and the approximate confidence intervals of the parameters are provided. A Monte Carlo simulation study is conducted to investigate the performance of the maximum likelihood estimators and their corresponding confidence intervals. Finally, two real data sets having bathtub-shaped and unimodal hazard rate functions are analyzed and it is shown that the proposed distribution can provide a better fit than other distributions for both lifetime data.

Keywords

• Lomax distribution
• Lindley distribution
• maximum likehood estimation
• lifetime data analysis

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