There is a growing interest in establishing the relationship between the count data y and numerous covariates x through a generalized linear model (GLM), such as explaining the road crash counts from the geometry and environmental factors. This paper proposes a hierarchical Bayesian method to deal with the negative binomial GLM. The Negative Binomial distribution is preferred for modeling nonne...

*Correspondence: [email protected] 3Departamento de Estatística, Universidade Federal de Pernambuco, PE 50740-540, Recife, Brazil Full list of author information is available at the end of the article Abstract We propose and study a new compounded model to extend the half-Cauchy and power-Cauchy distributions, which offers more flexibility in modeling lifetime data. The proposed model is ...

This paper proposes the application of the two well known models of negative binomial regression, namely the NB-1 and the NB-2, and the functional form of negative binomial regression, namely the NB-P, for the analysis of vehicle theft crime. The advantage of using the NB-P is that it parametrically nests both the NB-1 and the NB-2, and allows statistical tests of the NB-1 and the NB-2 models a...

Proof: The first and second derivatives of f(z) = − ln(1 − pz) are f ′(z) = p 1−pz and f ′′(z) = p (1−pz)2 = (f ′(z))2, respectively, and f j(0) = 0 for j ≥ 1, therefore d dzm f j(z) ∣∣ z=0 = 0 for j > m and thus (2) is true for j > m. When n = j = 1, we have d n dzn f j(z) ∣∣ z=0 = f ′ k(0) = p, ∑n j′=1 F (n, j ′) j! (j−j′!) [f ′(z)]nf j−j ′ (z) ∣∣∣ z=0 = p, and F (n, j)j!pn = p, therefore, (2...