Bayesian Estimation of a Scale Parameter of the Gumbel-Lomax Distribution Using Informative and Non Informative Priors
Douglas Jah Pam *
Department Mathematical Sciences, Abubakar Tafawa Balewa University, P.M.B. 0248, Bauchi, Nigeria.
Kazeem Eyitayo Lasisi
Department Mathematical Sciences, Abubakar Tafawa Balewa University, P.M.B. 0248, Bauchi, Nigeria.
Umar Farouk Abbas
Department Mathematical Sciences, Abubakar Tafawa Balewa University, P.M.B. 0248, Bauchi, Nigeria.
Mustapha Tijani
Department of Statistics, University of Ilorin, Nigeria.
Sheyi Mafolasire
Department of Statistics, Federal College of Forestry, Jos, Nigeria.
Blessing Uke Agbor
a Department Mathematical Sciences, Abubakar Tafawa Balewa University, P.M.B. 0248, Bauchi, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Estimating the scale parameter of the Gumbel-Lomax Distribution using the Bayesian method of estimation and evaluating the estimators by assuming two non-informative prior distributions and one informative prior distribution is very important for the general application of the Gumbel-Lomax distribution. These estimators are obtained using the squared error loss function (SELF), Quadratic loss function (QLF) and precautionary loss function (PLF). The posterior distributions of the scale parameter of the Gumbel-Lomax distribution are derived and the Estimators are also obtained using the above mentioned priors and loss functions. Furthermore, a simulation using a package in R software is carried out to assess the performance of the estimators by making use of the Mean Squared Errors of the Estimators under the Bayesian approach and Maximum likelihood method. Our results show that Bayesian Method using PLF under all priors produces the best estimators of the scale parameter compared to estimators using the Maximum Likelihood method, SELF and QLF under all the priors irrespective of the values of the parameters and the different sample sizes. It is also discovered that the other parameters have no effect on the estimators of the scale parameter.
Keywords: Gumbel-Lomax distribution, Bayesian method, priors, loss functions, MLE, simulation, MSE