Abstract:
The development of new families of generalized distributions in recent decades have attracted the interest of both theoretical and applied statisticians due to their flexible and tractable statistical properties. In this study, the Exponentiated Cubic Transmuted-G family of distributions were developed. The statistical properties of the new family were derived, and sub-families were defined which includes the Exponentiated Cubic Transmuted Weibull distribution, Exponentiated cubic Transmuted Exponential distribution, Exponentiated Cubic Transmuted Gompertz distribution, Exponentiated Cubic Transmuted Lomax distribution, and Exponentiated Cubic Transmuted Pareto distribution. The structural properties such as an expression for the moment, moment generating function, quantile function, order statistics and Renyl entropy were studied. Inferences were made on two of the newly developed distributions which includes the Exponentiated Cubic Transmuted Weibull and the Exponentiated Cubic Transmuted Exponential distribution to further examine the flexibility of the distributions. Monte Carlo simulations were performed to investigate the properties of the maximum likelihood estimators for the parameters of the developed distributions. The results revealed that the maximum likelihood estimators for the parameters were consistent. The Mean Square Error (MSE) of the estimates of the parameters decayed to zero as the number of sample size increases. Applications of the developed distributions were demonstrated using two real data sets and their performance were compared with their existing sub-models using results obtained from the measures of goodness of fit: namely, Anderson darling, Kolmogorov-Smirnov, Crammer-von Misses, Akaike information criterion, Bayesian information criterion and Consistent Akaike information criterion. The results obtained showed that the values of the information criteria were least for the newly developed models which indicates that the models considered were more flexible in modeling real life data exhibiting different shape of hazard functions than its existing sub-models.
