Exponentiated power Lindley distribution

Samir K Ashour; Mahmoud A Eltehiwy

doi:10.1016/j.jare.2014.08.005

Exponentiated power Lindley distribution

J Adv Res. 2015 Nov;6(6):895-905. doi: 10.1016/j.jare.2014.08.005. Epub 2014 Aug 24.

Authors

Samir K Ashour¹, Mahmoud A Eltehiwy²

Affiliations

¹ Institute of Statistical Studies & Research, Department of Mathematical Statistics, Cairo University, Egypt.
² Faculty of Commerce, Department of Statistics, South Valley University, Egypt.

Abstract

A new generalization of the Lindley distribution is recently proposed by Ghitany et al. [1], called as the power Lindley distribution. Another generalization of the Lindley distribution was introduced by Nadarajah et al. [2], named as the generalized Lindley distribution. This paper proposes a more generalization of the Lindley distribution which generalizes the two. We refer to this new generalization as the exponentiated power Lindley distribution. The new distribution is important since it contains as special sub-models some widely well-known distributions in addition to the above two models, such as the Lindley distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Least square estimation is used to evaluate the parameters. Three algorithms are proposed for generating random data from the proposed distribution. An application of the model to a real data set is analyzed using the new distribution, which shows that the exponentiated power Lindley distribution can be used quite effectively in analyzing real lifetime data.

Keywords: AIC, Akaike information criterion; BGLD, Beta generalized Lindley distribution; BIC, Bayesian information criterion; Cdf, Cumulative distribution function; E(Xr), The rth moment; EE, Exponentiated exponential distribution; EPLD, Exponentiated power Lindley distribution; GLD, Generalized Lindley distribution; K–S, Kolmogorov–Smirnov test; LD, Lindley distribution; LSE, Least square estimator; Lambert function; Least square estimation; MLE, Maximum likelihood estimator; MSE, mean square error; MW, Modified Weibull distribution; MX(t), The moment generating function; Maximum likelihood estimation; Order statistics; PLD, Power Lindley distribution; Power Lindley distribution; Q(p), Quantile function; WD, Weibull distribution; [Formula: see text], Log-likelihood function; h(t), Hazard rate function; pdf, Probability density function.