Transmuted exponential-compound Weibull distribution for modelling of positively skewed data

Abstract

Nowadays, there are many lifetime datasets that many existing probability distributions cannot provides a better fit to them as they continue to exhibit complexity and changes in shape. Furthermore, many of these lifetime datasets generated are often characterized by problems of elongation and asymmetry, which make it difficult for the classical distributions to provide an adequate fit to them. However, in this study, an efficient lifetime distribution called the Transmuted Exponential-Compound Weibull is developed to model lifetime datasets especially those that the existing competing lifetime distributions cannot fit efficiently well. The new model is characterized by a flexible structure ideal for analyzing positive data and featuring a hazard rate function that has bathtub shaped which makes it to offer more flexibility to solve the problem of elongation and asymmetry than the competing distributions. Some fundamental mathematical and statistical properties associated with this new distribution, such as ordinary moments, moment generating function, mean, variance, quantile function, survival function, hazard function, Renyi entropy and order statistics were derived and presented in an explicit structure. The parameters of the proposed model were estimated using maximum likelihood estimation approach. A simulation study was carried out to assess the performance of the maximum likelihood estimator (MLE) in terms of bias, variance and mean squared error under different sample sizes. The results showed that the MLE is good to estimate the unknown parameters of the proposed model. The application of this distribution was demonstrated by fitting it to two lifetime datasets and the results showed superior goodness-of-fit when compared with existing distributions using established statistical metrics.