The Gamma-Akash probability Model for Survival Analysis of Cancer Patients

The search for a suitable probability models for the survival analysis of cancer patients are really challenging because survival times of cancer patients are stochastic in nature and are highly positively skewed. The classical well-known one parameter and two-parameter probability models rarely provide better fit to survival times of cancer patients. In this paper a compound probability model called gamma-Akash distribution, which is a compounding of gamma and Akash distribution, has been proposed for the modeling of survival times of cancer patients. Many important properties of the suggested distribution including its shape, moments (negative moments), hazard function, reversed hazard function, quantile function have been discussed. Method of maximum likelihood has been used to estimate its parameters. A simulation study has been conducted to know the consistency of maximum likelihood estimators. Two real datasets, one relating to acute bone cancer and the other relating to head and neck cancer, has been considered to examine the applicability, suitability and flexibility of the proposed distribution. The goodness of fit of the proposed distribution shows quite satisfactory fit over other considered distributions.