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. 2019 Jul 8;47(2):354-375.
doi: 10.1080/02664763.2019.1638893. eCollection 2020.

A new two-parameter exponentiated discrete Lindley distribution: properties, estimation and applications

M El-Morshedy  1 , M S Eliwa  1 , H Nagy  1
Affiliations

A new two-parameter exponentiated discrete Lindley distribution: properties, estimation and applications

M El-Morshedy et al. J Appl Stat. .

Abstract

This paper introduces a new two-parameter exponentiated discrete Lindley distribution. A wide range of its structural properties are investigated. This includes the shape of the probability mass function, hazard rate function, moments, skewness, kurtosis, stress-strength reliability, mean residual lifetime, mean past lifetime, order statistics and L-moment statistics. The hazard rate function can be increasing, decreasing, decreasing-increasing-decreasing, increasing-decreasing-increasing, unimodal, bathtub, and J-shaped depending on its parameters values. Two methods are used herein to estimate the model parameters, namely, the maximum likelihood, and the proportion. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood and proportion estimators. The flexibility of the proposed model is explained by using four distinctive data sets. It can serve as an alternative model to other lifetime distributions in the existing statistical literature for modeling positive real data in many areas.

Keywords: Discrete lindley distribution; L-moment statistics; estimation methods; hazard rate function; mean residual lifetime.

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Conflict of interest statement

No potential conflict of interest was reported by the authors.

Figures

Figure 1.
Figure 1.
The PMF of the EDLi distribution.
Figure 2.
Figure 2.
The HRF of the EDLi distribution.
Figure 3.
Figure 3.
The RHRF of the EDLi distribution.
Figure 4.
Figure 4.
The fitted PMFs for data set I.
Figure 5.
Figure 5.
The fitted PMFs for data set II.
Figure 6.
Figure 6.
The estimated CDFs for data set III.
Figure 7.
Figure 7.
The P–P plots for data set III.
Figure 8.
Figure 8.
The fitted PMFs for data set IV.
Figure 9.
Figure 9.
The HRF and RHRF for data sets using the EDLi model.
See this image and copyright information in PMC

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