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.
Tekle, G., Roozegar, R., & Bidram, H. (2023). A new alpha power type-1 family of distributions and modelling the overdispersed count outcome. Journal of Statistical Modelling: Theory and Applications, 3(1), 83-101. doi: 10.22034/jsmta.2023.19128.1069
MLA
Getachew Tekle; Rasool Roozegar; Hamid Bidram. "A new alpha power type-1 family of distributions and modelling the overdispersed count outcome". Journal of Statistical Modelling: Theory and Applications, 3, 1, 2023, 83-101. doi: 10.22034/jsmta.2023.19128.1069
HARVARD
Tekle, G., Roozegar, R., Bidram, H. (2023). 'A new alpha power type-1 family of distributions and modelling the overdispersed count outcome', Journal of Statistical Modelling: Theory and Applications, 3(1), pp. 83-101. doi: 10.22034/jsmta.2023.19128.1069
VANCOUVER
Tekle, G., Roozegar, R., Bidram, H. A new alpha power type-1 family of distributions and modelling the overdispersed count outcome. Journal of Statistical Modelling: Theory and Applications, 2023; 3(1): 83-101. doi: 10.22034/jsmta.2023.19128.1069
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