A New Type 1 Alpha Power Family of Distributions and Modeling Data with Correlation, Overdispersion, and Zero-Inflation in the Health Data Sets

In the recent era, introduction of a new family distributions has gotten great attention due to curbs classical univariate distributions. This study introduces novel called type 1 alpha power Based on family, special model Weibull is studied in depth. The very interesting patterns and it flexible. Thus, can real data with failure rate increasing, decreasing, parabola-down, bathtub. Its applicability by applying health sector data, time-to-recovery breast cancer patients, its performance compared seven well-known models. comparison, best fit health-related no exceptional features. Furthermore, popular models for features such as correlation, overdispersion, zero-inflation aggregate are explored applications epileptic seizer data. Sometimes, these beyond probability distribution Hence, this implemented eight possible separately they based standard techniques. Accordingly, zero-inflated Poisson-normal-gamma which includes random effects linear predictor handle three simultaneously shown supremacy over others