Inference On Gompertz Distribution Based On Upper k Record Values

Inference based on upper k records

In this paper, we introduce a new generalization of univariate and bivariate modified discrete Weibull distribution. Various properties of the univariate generalized modified discrete Weibull distribution, such as survival function, probability mass function, hazard rate function, probability generating function, and moment generating function, are derived. The joint distribution function, joint probability mass function, marginal distributions, moment generating function, and conditional distribution of the proposed bivariate distribution are derived. Parameters of the distributions are estimated using maximum likelihood estimation. The use of these distributions is illustrated using real-life datasets.

In this paper, we consider the inference based on upper k -record values for a two parameter Gompertz distribution. The maximum likelihood estimators of the parameters are obtained. The Bayes estimates of the parameters are also developed by using Markov chain Monte Carlo method under symmetric and asymmetric loss functions. The problem of predicting the future record values based on past record values is also considered. Finally, a simulation study is performed to find the performance of different estimators developed in this paper.