*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...

Numerous researches have been carried out to explain the relationship between the count data y and numbers of covariates x through a generalized linear model (GLM). This paper proposes a hierarchical Bayesian LASSO solution using six different prior models to the negative binomial regression. Latent variables Z have been introduced to simplify the GLM to a standard linear regression model. The ...

In actuarial hteramre, researchers suggested various statistical procedures to estimate the parameters in claim count or frequency model. In particular, the Poisson regression model, which is also known as the Generahzed Linear Model (GLM) with Poisson error structure, has been x~adely used in the recent years. However, it is also recognized that the count or frequency data m insurance practice...

Rate differences are an important effect measure in biostatistics and provide an alternative perspective to rate ratios. When the data are event counts observed during an exposure period, adjusted rate differences may be estimated using an identity-link Poisson generalised linear model, also known as additive Poisson regression. A problem with this approach is that the assumption of equality of...

Quasi-Poisson and negative binomial regression models have equal numbers of parameters, and either could be used for overdispersed count data. While they often give similar results, there can be striking differences in estimating the effects of covariates. We explain when and why such differences occur. The variance of a quasi-Poisson model is a linear function of the mean while the variance of...