The Topp Leone Kumaraswamy-G Family of Distributions with Applications to Cancer Disease Data

Abstract

Background: In the last few years, statisticians have introduced new generated families of univariate distributions. These new generators are obtained by adding one or more extra shape parameters to the underlying distribution to get more flexibility in fitting data in different areas such as medical sciences, economics, finance and environmental sciences. The addition of parameter(s) has been proven useful in exploring tail properties and also for improving the goodness-of-fit of the family of distributions under study. Methods: A new three parameter family of distributions was introduced by using the idea of T-X methodology. Some statistical properties of the new family were derived and studied. Results: A new Topp Leone Kumaraswamy-G family of distributions was introduced. Two special sub-models, that is, the Topp Leone Kumaraswamy exponential distribution and Topp Leone Kumaraswamy log-logistic distribution were investigated. Two real data sets were used to assess the flexibility of the sub-models. Conclusion: The results suggest that the two sub-models performed better than their competitors.

Keywords

• Hazard function;
• Topp Leone Kumaraswamy-G family;
• Modi distribution;
• T-X family;
• Topp Leone Kumaraswamy exponential;
• Topp Leone Kumaraswamy log-logistic.