Abstract
Exponentiated power Lindley distribution is proposed as a generalization of some widely well-known distributions such as Lindley, power Lindley, and generalized Lindley distributions. In this paper, the exact explicit expressions for moments of order statistics from the exponentiated power Lindley distribution are derived. By using these relations, the best linear unbiased estimates of the location and scale parameters, based on type-II right-censored sample, are obtained. Next, the mean, variance, and coefficients of skewness and kurtosis of some certain linear functions of order statistics are calculated and then used to derive the approximate confidence interval for the location and scale parameters using the Edgeworth approximation. Finally, some numerical illustrations and two real data applications are presented.
Highlights
Ashour and Eltehiwy [1] introduced the exponentiated power Lindley (EPL) distribution as a generalization of twoparameter power Lindley distribution and they studied some mathematical properties of the EPL distribution. ey showed that this distribution provides more flexibility to analyze a complex real data set
We have considered the EPL distribution when data are available in the form of order statistics
We have calculated the best linear unbiased estimates (BLUEs) of the location and scale parameters and the coefficient of skewness and kurtosis for some linear pivotal quantities
Summary
Ashour and Eltehiwy [1] introduced the exponentiated power Lindley (EPL) distribution as a generalization of twoparameter power Lindley distribution and they studied some mathematical properties of the EPL distribution. ey showed that this distribution provides more flexibility to analyze a complex real data set. Numerous papers dealing with moments and estimation of parameters of different lifetime distributions based on order statistics can be found in literature. Sultan and AL- ubyani [19] developed the higher-order moments and inferential procedure for estimating parameters of Lindley distribution. First is to obtain the exact explicit expressions for moments of order statistics from the EPL distribution, and second is to derive the best linear unbiased estimates (BLUEs) of the location and scale parameters of the EPL distribution based on order statistics. E rest of this paper is organized as follows: in Section 2, the moments of EPL distribution are derived based on order statistics.
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