Derivation of Some Properties of New Topp Leone Exponential – Weibul Distribution and Its Application on Cancer Data Sets

Abstract

The obtainable breast and bladder cancer data sets are asymmetric and skewed in nature with heavy tail and variable hazard function; therefore, a new Topp Leone Exponential – Weibul (TLE-W) distribution with four distinct parameters was developed to fit these asymmetric data sets. Thus, this new distribution was developed by incorporating existing Weibul distribution into Topp Leone Exponential G family of distributions. More so, the respective density and distribution functions of this new Topp Leone Exponential – Weibul distribution were derived alongside with some respective mathematical properties such as moments, quantile function, renyi entropy and order statistics. Also, maximum likelihood estimation and maximum product of spacing methods were used to estimate the distinct four parameters of TLE – W. However, in the simulation study conducted; the results show that the four estimated parameters of Topp Leone Exponential – Weibul distribution are consistent as the bias and root mean square error approach zero. Conclusively, the breast and bladder cancer survival time data sets were used to validate the results obtained from MLE methods on this new distribution. The results show that Topp Leone Exponential – Weibul distribution best fit the two cancer data sets compare to the competitive distributions used in this study. Perhaps, this new distribution would be useful to model positive real life time data sets that are asymmetrical in nature with heavy tails and as well handle data’s volatility during instability.