This paper aims at making Bayesian analysis on the shape parameter of the exponential inverse exponential distribution using informative and non-informative priors. Bayesian estimation was carried out through a Monte Carlo study under 10,000 replications. To assess the effects of the assumed prior distributions and loss function on the Bayesian estimators, the mean square error has been used as a criterion. Overall, simulation results indicate that Bayesian estimation under QLF outperforms the maximum likelihood estimation and Bayesian estimation under alternative loss functions irrespective of the nature of the prior and the sample size. Also, for large sample sizes, all methods perform equally well.

This article uses the odd Lomax-G family of distributions to study a new extension of the Kumaraswamy distribution called “odd Lomax-Kumaraswamy distribution”. In this article, the density and distribution functions of the odd Lomax-Kumaraswamy distribution are defined and studied with many other properties of the distribution such as the ordinary moments, moment generating function, characteristic function, quantile function, reliability functions, order statistics and other useful measures. The model parameters are estimated by the method of maximum likelihood. The goodness-of-fit of the proposed distribution is demonstrated using two real data sets.

The Rayleigh was obtained from the amplitude of sound resulting from many important sources by Rayleigh. It is continuous probability distribution with a wide range of applications such as in life testing experiments, reliability analysis, applied statistics and clinical studies. However, it is not flexible enough for modeling heavily skewed datasets as compared to compound distributions. In this paper, we introduce a new extension of the Rayleigh distribution by using a Gompertz-G family of distributions. This paper defines and studies a three-parameter distribution called “Gompertz-Rayleigh distribution”. Some properties of the proposed distribution are derived and discussed comprehensively in this paper and the three parameters are estimated using the method of maximum likelihood estimation. The goodness-of-fit of the proposed distribution is also evaluated by fitting it in comparison with some other existing distributions using a real life data.