T-INVERSE EXPONENTIAL {Y} FAMILY OF DISTRIBUTIONS

Abstract

Recently, statisticians have been exploring the generalization and extension of classes of distributions to make them more flexible for data analysis. There are a lot of data sets that are either extremely skewed, bimodal, bathtub or have heavy tails. However, inverse exponential distribution cannot model data sets that exhibit these features properly. In this study, a new family of inverse exponential distribution called T-inverse exponential {Y} family based on quantile function approach has been developed to fill some of the gaps identified in the inverse exponential distribution. Statistical properties such as quantile function, mode, entropy and moments of the family have been derived. Three sub-families namely, T-IE{Weibull} T IE{Logistic} and T-IE{Lomax} families were defined. Three (3) special cases of these family of distributions namely, Log-logistic-IE{Weibull}, Weibull-IE {Logistic} and Gumbel-IE{Lomax} distributions were developed. Monte Carlo simulations were done to investigate the properties of the maximum likelihood estimation, ordinary least square estimators, weighted least square estimators, Cramér-von Mises minimum distance estimators and Percentile based estimators for estimating the parameters of the special distributions. It was revealed that, maximum likelihood estimators for the parameters of the special distributions were consistent. Empirical applications of the special distributions to real life data sets were done and they showed greater flexibility for different kinds of lifetime data sets than other competing distributions. It is recommended that, parametric regression models for the special distributions can be developed to examine the relationship between the dependent and the independent variables of the distributions.