On A Shape Parameter of Gompertz Inverse Exponential Distribution Using Classical and Non Classical Methods of Estimation
Terna Godfrey Ieren *
Department of Statistics and Operations Research, MAUTech, P.M.B. 2076, Yola, Nigeria.
Adana’a Felix Chama
Department of Mathematical Sciences, Taraba State University, Jalingo, Nigeria.
Olateju Alao Bamigbala
Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.
Jerry Joel
Department of Statistics and Operations Research, MAUTech, P.M.B. 2076, Yola, Nigeria.
Felix M. Kromtit
Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi, Nigeria.
Innocent Boyle Eraikhuemen
Department of Physical Sciences, Benson Idahosa University, Benin City, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The Gompertz inverse exponential distribution is a three-parameter lifetime model with greater flexibility and performance for analyzing real life data. It has one scale parameter and two shape parameters responsible for the flexibility of the distribution. Despite the importance and necessity of parameter estimation in model fitting and application, it has not been established that a particular estimation method is better for any of these three parameters of the Gompertz inverse exponential distribution. This article focuses on the development of Bayesian estimators for a shape of the Gompertz inverse exponential distribution using two non-informative prior distributions (Jeffery and Uniform) and one informative prior distribution (Gamma prior) under Square error loss function (SELF), Quadratic loss function (QLF) and Precautionary loss function (PLF). These results are compared with the maximum likelihood counterpart using Monte Carlo simulations. Our results indicate that Bayesian estimators under Quadratic loss function (QLF) with any of the three prior distributions provide the smallest mean square error for all sample sizes and different values of parameters.
Keywords: Bayesian method, uniform prior, Jeffrey’s prior, gamma prior, loss functions, MLE, MSE, sample sizes.