NEW LIFE-TIME CONTINUOUS PROBABILITY DISTRIBUTION WITH FLEXIBLE FAILURE RATE FUNCTION - Manu, Faruk; Usman, U.; Audu, A. (FUDMA Journal of Sciences, 2023)
Recently, the area of distribution theory has been receiving increased interest in generating or defining new classes of continuous probability distributions by way of extending the existing distributions. The new generated distribution is expected to be more flexible and have wider acceptability in modeling and predicting real world data sets.  In this research, we proposed and study an extension of Ikum distribution using Zubai G- Family (2018) of distribution called Z-Ikum distribution. Expression of some basic structural properties of the new distribution such as cdf, pdf, quantile functions, moments, moment generating function, characteristics function and order statistics was derived. Survival function, hazard rate function, commutative hazard rate function and reversed hazard rate function was also discussed. Plots of the hazard rate function showincrease, decrease and bathtub shapes.Estimation of the proposed distribution parameters was carried out using MLE method. Performance of the parameter estimation was also evaluated via simulation studies. Result of the simulation studies indicates that our estimator is consistent. Three life data sets were used to evaluate the performance of our proposed distribution over some existing distributions. Result of the empherical study revealed that our proposed distribution performwell in modeling real life data than the competing distributions.
Keywords: Ikum; Bathtub; Hazard rate; Failure rate; Simulation