a new alpha power type-1 family of distributions and modelling the overdispersed count outcome

In this paper‎, ‎we introduce a novel family of statistical models called a new alpha power type-1 family of distributions‎. ‎three sub-cases of the family are discussed‎. ‎based on the novel family‎, ‎a special model‎, ‎explicitly‎, ‎a new alpha power type-1-weibull distribution is studied in depth‎. ‎the new model has very interesting patterns of failure rates like increasing‎, ‎decreasing‎, ‎bathtub‎, ‎and parabola-down‎. ‎hence‎, ‎it is so flexible‎. ‎based on the comparison analysis‎, ‎among five well-known models‎, ‎it has an impact on health data analysis‎. ‎furthermore‎, ‎the count data models capable of handling overdispersion and zero-inflation are discussed and applied the real health data‎. ‎the zero-inflated negative binomial model in the frequentist approach has shown its popularity in handling both overdispersion and zero-inflation simultaneously‎, ‎while the discrete weibull model with the logit(q) link in the bayesian approach outperformed its counterparts.