ABSTRACT
In this study, a novel family of distributions called the T-Generalized Inverse Exponential{Y} family is obtained through the modification of the Generalized Inverse Exponential Distribution (GIED) using the T-R{Y} approach. Some statistical properties of the novel family and those of three of its subfamilies, namely the T-Generalized Inverse Exponential{Uniform}, T-Generalized Inverse Exponential{Log-logistic} and T-Generalized Inverse Exponential{Logistic} families are obtained. Furthermore, three specific member of the family, namely the Kumaraswamy-Generalized Inverse Exponential{Uniform} Distribution (KGIEUD), Weibull-Generalized Inverse Exponential{Log-logistic} Distribution (WGIELLD) and Gumbel-Generalized Inverse Exponential{Logistic} Distribution (GGIELD) are studied.
The parameters of the WGIELLD are estimated using the maximum likelihood method of estimation; and a simulation study is conducted to evaluate the performance of the method in estimating the parameters of the distribution. Nine datasets exhibiting various shapes are collected for the study from the National Bureau of Statistics (NBS), Nigeria. To select the distributions that best explain the datasets, the Log-likelihood (LL), Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), Kolmogorov-Simnorv (K-S) and p-values of the KGIEUD, WGIELLD and GGIELD, GIED, Exponentiated Generalized Inverse Exponential Distribution (EGIED) and Inverse Exponential Distribution (IED) are obtained. Additionally, the likelihood ratio test is conducted to compare the performance of the KGIEUD, WGIELLD and GGIELD over GIED, EGIED and IED in fitting the datasets.
The results of the simulation study reveal that the maximum likelihood estimation method is suitable in estimating the parameters of the WGIELLD as the average bias, root mean square errors (RMSE) and average widths of the estimated parameters decrease with increase in the sample size of the generated random samples. The KGIEUD, WGIELLD and GGIELD are selected over GIED, EGIED and IED as the most adequate and best distributions that describe the datasets since in each case they have the highest Log-likelihood and p-values and the smallest AIC, BIC and K-S statistic values compared to the GIED, EGIED and IED. Finally, the results of likelihood ratio test reveal that the additional parameters of the KGIEUD, WGIELLD and GGIELD are significant. In other word, KGIEUD, WGIELLD and GGIELD performed much better than GIED, EGIED and IED in fitting the datasets.
