A Power Gompertz Distribution: Model, Properties and Application to Bladder Cancer Data
Terna Godfrey Ieren *
Department of Statistics and Operations Research, MAUTech, P.M.B. 2076, Yola, Nigeria.
Felix M. Kromtit
Department of Mathematical Science, Abubakar Tafawa Balewa University, Bauchi, Nigeria.
Blessing Uke Agbor
Department of Mathematical Science, Abubakar Tafawa Balewa University, Bauchi, Nigeria.
Innocent Boyle Eraikhuemen
Department of Mathematics and Computer Science, Benson Idahosa University, Benin City, Nigeria.
Peter Oluwaseun Koleoso
Department of Statistics, University of Ibadan, Ibadan, Oyo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper uses a power transformation approach to introduce a three-parameter probability distribution which gives another extension of the Gompertz distribution known as “Power Gompertz distribution”. The statistical features of the power Gompertz distribution are systematically derived and studied appropriately. The three parameters of the new model are being estimated using the method of maximum likelihood estimation. The proposed distribution has also been compared to the Gompertz distribution using a real life dataset and the result shows that the Power Gompertz distribution has better performance than the Gompertz distribution and hence will be more useful and effective if applied in some real life situations especially survival analysis and cure fraction modeling just like the conventional Gompertz distribution.
Keywords: Power transformation, Gompertz distribution, statistical properties, parameters, method of maximum likelihood estimation, real life data, performance.