Abstract
In this paper, we consider power odd generalized exponential-Gompertz (POGE-G) distribution which is capable of life tables to calculate death rates (failure). Based on simulated data from the PPOGE-G distribution, we consider the problem of estimation of parameters under classical approaches and Bayesian approaches. In this regard, we obtain maximum likelihood (ML) estimates, maximum product of spacing (MPS) and Bayes estimates under squared error loss function. We also compute 95% asymptotic confidence interval and highest posterior density interval estimates. The Monte Carlo simulation will be conduct to study and compare the performance of the various proposed estimators (simulation study indicates that the performance of MPS estimates is better MLE estimates and the performance of Bayes estimates is also better). Finally, application of a real data from the projections of the future population for the total of the Egyptian Arabic Republic for the period 2017-2052, depending on the book which introduced from the central agency for public mobilization and statistics in Feb (2019) from this application it could be said that this distributions can be applied to mortality rate data set. The present paper can also be extended to design of progressive censoring sampling plan and other censoring schemes can also be considered.
Highlights
There are several new families of probability distributions which are proposed by several authors
We suggest utilizing the technique of Chen and Shao [7] to calculate highest posterior density (HPD) interval estimates for the unknown parameters of the GIE distribution
We have studied the problem of estimation of the power odd generalized exponential-Gompertz (POGE-G) distribution from classical and Bayesian viewpoints
Summary
There are several new families of probability distributions which are proposed by several authors Such families have great flexibility and generalize many well-known distributions. Several classes have been proposed, in the statistical literature, by adding one or more parameters to generate new distributions. Among this literature exponential Lomax El-Bassiouny et al [10], exponentiated WeibullLomax Hassan and Abd-Allah [13], the odd lomax generator Cordeiro et al [8] The generalized odd inverted exponentialG family Chesneau et al [5], The odd log-logistic Lindley-G Alizadeh et al [2] and The Odd Dagum Family of Distributions Afify et al [1]. For parameter estimation of the unknown parameters of the POGE-G distribution , , , , there are three methods: Maximum likelihood estimation, maximum product spacing and Bayesian estimation
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