Estimating three parameters of Weibull — Poisson distribution with biological application

This paper deals with introducing a new compound distribution, called Weibull - Poisson, with three parameters (λ, α, β), which have excellent modeling and applications for Bio-Informatics (in Computer Science). The probability compound model build according to the biological data, and then the parameters (λ, α, β) are estimated by different algorithms like maximum likelihood method, percentile method, and also proposed method, where all the required programs necessary for estimation and comparison are written by using Math Lab (2010), and also the application is done on observation about time to failure for cancer disease where the fitting programs focus on compound Weibull Poisson distribution. So, our paper explains this distribution and introduces all the required methods for estimation and application.