Abstract
The Lindley distribution may serve as a useful reliability model. Applications of this distribution are presented in statistical literature. In this article, a powerful goodness of fit test for the Lindley distribution is proposed. In order to compute the proposed test statistic, we use the maximum likelihood estimate (MLE) suggested by Ghitany et al. (2008), which is simple explicit estimator. By Monte Carlo simulation, critical points of the proposed test statistic for different sample sizes are obtained. Power values of the proposed test are compared with the competing tests against various alternatives via simulations. Finally, two real data are presented and analyzed.
Highlights
The modeling and analyzing lifetime data are crucial in many applied sciences including medicine, engineering, insurance and finance, amongst others
It is well known that the Lindley distribution is one of the fundamental models applied for reliability models
Many researchers have been interested in goodness of fit tests for different distributions and different tests are developed in the literature
Summary
The modeling and analyzing lifetime data are crucial in many applied sciences including medicine, engineering, insurance and finance, amongst others. Since the distribution was proposed, it has been overlooked in the literature partly due to the popularity of the exponential distribution in the context of reliability analysis It has recently received considerable attention as a lifetime model to analyze survival data in the competing risks analysis and stress-strength reliability studies; see, for example, Ghitany et al (2008), Mazucheli and Achcar (2011), Gupta and Singh (2013), Al-Mutairi el al. We propose a goodness of fit test statistic for the Lindley distribution based on an estimate of Kullback-Leibler divergence. The Lindley distribution and test Statistic we express some properties of the Lindley distribution and construct a goodness of fit test statistic for this distribution
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