On Modelling of Infant Mortality Rate in Nigeria with Exponentiated Cubic Transmuted Exponential Distribution

Abstract

The idea of introducing extra parameters into the existing model in enhancing more flexibility is a giant stride in research. Transmutation map technique is one of the recent methods of introducing additional properties such as skewness, kurtosis and bimodality into the baseline distribution. In this article, a new exponentiated exponential distribution is developed using transmutation map. This model is referred to as exponentiated cubic transmuted exponential distribution (ECTED). The mathematical properties of the model which include survival function, hazard function, central and non- central moments, moment generating function and order statistics are established. The inherent parameters in the model are estimated using method of maximum likelihood estimation (MLE). The system of equations obtained is non-linear in parameters therefore non-linear optimization algorithms are implemented in R package. The distribution is used to model data on infant mortality rate in Nigeria. The performance of the subject model is compared with its baseline exponential distribution (ED), transmuted exponential distribution (TED), exponentiated transmuted exponential distribution (ETED) and cubic transmuted exponential distribution (CTED) using Akaike Information criterion (AIC), Corrected Akaike Information criterion (AICC) and Bayesian Information criterion (BIC). It is hope that this will serve as an alternative distribution in modelling complex real life data arising from various fields of human endeavors.