Abstract
In this paper, a new three-parameter model which can be used in lifetime data analysis is introduced. Its failure rate function can be decreasing, increasing, constant and bathtub-shaped depending on its parameters. We derive explicit expressions for some of its statistical and mathematical quantities including the ordinary moments, generating function, incomplete moments, order statistics, moment of residual life and reversed residual life. Some useful characterizations are presented. Maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimators are discussed in case of uncensored data. The censored maximum likelihood estimation is presented in the general case of the multi-censored data. We demonstrate empirically the importance and flexibility of the new model in modeling real data set. https://doi.org/10.28919/jmcs/3417
Highlights
Statistical distributions are very useful in describing and predicting real world phenomena
Simulation results to assess the performance of the maximum likelihood estimators are discussed in case of uncensored data
We present our characterizations (i) and (ii) in two subsections. 3.1 Characterizations based on a truncated moment Our first characterization employs a version of a theorem due to Glanzel (1987), see Theorem 1 of Appendix A .The result, holds when the interval H is not closed since the condition of Theorem 1 is on the interior of H
Summary
Statistical distributions are very useful in describing and predicting real world phenomena. The cumulative distribution function (cdf) is given by. Nadarajah and Haghighi (2011) pointed out that the density function (2) has the attractive feature of always having the zero mode. We shall refer to the new distribution using (1) and (2) as the Odd Lindley-Nadarajah-Haghighi (OLNH) model using the Odd Lindley-G (OL-G) family of distributions which introduced by. The pdf and cdf of the OL-G family of distributions are given by f(x; a, ξ). Where a is a positive shape parameter To this end, we use (1), (2) and (3) to obtain the three-parameter OLNH pdf (for x > 0). Equation (7) is obtained by the general result given by Silva et al (2017) in their relation (19). Equation (8) is obtained by the general result given by Silva et al (2017)
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