tailieunhanh - Exponentiated power Lindley distribution

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. | Journal of Advanced Research 2015 6 895-905 Cairo University Journal of Advanced Research ORIGINAL ARTICLE Exponentiated power Lindley distribution CrossMark Samir K. Ashour a Mahmoud A. Eltehiwy b a Institute of Statistical Studies Research Department of Mathematical Statistics Cairo University Egypt b Faculty of Commerce Department of Statistics South Valley University Egypt ARTICLE INFO ABSTRACT Article history Received 15 July 2014 Received in revised form 11 August 2014 Accepted 17 August 2014 Available online 24 August 2014 Keywords Lambert function Least square estimation Maximum likelihood estimation Order statistics Power Lindley distribution 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. 2014 Production and hosting by Elsevier . on behalf of Cairo University. Abbreviations EPLD Exponentiated power Lindley .