MODELLING ZERO-INFLATED COUNT DATA WITH A SPECIAL CASE OF THE GENERALISED POISSON DISTRIBUTION

A one-parameter version of the generalised Poisson distribution provided by Consul and Jain (1973) is considered in this paper. The distribution is unimodal with a zero vertex and over-dispersed. A generalised linear model related to this distribution is also presented. Its parameters can be estimated by using a Fisher-Scoring algorithm which is equivalent to iteratively reweighted least squares. Due to its flexibility and capacity to describe highly skewed data with an excessive number of zeros, the model is suitable to be applied in insurance settings as an alternative to the negative binomial and zero-inflated model.

Improving Estimation Accuracy in Non\-randomized Response Questioning Methods by Multiple Answers

When private or stigmatizing characteristics are included in sample surveys, direct questions result in low cooperation of the respondents. To increase cooperation, indirect questioning procedures have been established in the literature. Nonrandomized response methods are one group of such procedures and have attracted much attention in recent years. In this article, we consider four popular nonrandomized response schemes and present a possibility to improve the estimation precision of these schemes. The basic idea is to require multiple indirect answers from each respondent. We develop a Fisher scoring algorithm for the maximum likelihood estimation in the presented new schemes and show the better efficiency of the new schemes compared with the original designs.

Improving Estimation Accuracy in Nonrandomized Response Questioning Methods by Multiple Answers

When private or stigmatizing characteristics are included in sample surveys, direct questions result in low cooperation of the respondents. To increase cooperation, indirect questioning procedures have been established in the literature. Nonrandomized response methods are one group of such procedures and have attracted much attention in recent years. In this article, we consider four popular nonrandomized response schemes and present a possibility to improve the estimation precision of these schemes. The basic idea is to require multiple indirect answers from each respondent. We develop a Fisher scoring algorithm for the maximum likelihood estimation in the presented new schemes and show the better efficiency of the new schemes compared with the original designs.

Evidence for Autoregressive Conditional Heteroskedastic errors in growth traits of beef cattle

Evidence is presented for "generalized autoregressive conditional heteroskedasticity" processes (GARCH(1,1)), in the residuals of beef cattle growth traits. This process can account for differences in variance at different time points, with the advantage of using a parsimonious parametrization. Data used were 10271 birth weights (BW), 19992 weaning weights (WW) and 9717 weight at 18 months (FW), from five herds registered in the national evaluation of the Brangus breed in Argentina. The residuals calculated from the 2005 genetic evaluation were regressed on Julian dates by least squares. From a second set of residuals out of the linear regression model, Maximum Likelihood estimation via the Fisher scoring algorithm was used to estimate the GARCH(1,1) parameters. Eight out of fifteen one-sided Lagrange multiplier statistics significantly (P < 0.05) rejected the hypothesis of null GARCH(1,1) parameters in the genetic evaluation residuals. Incorporating these effects in genetic evaluation is feasible due to the diagonal covariance matrix induced by the process on each trait, which simplifies building the mixed model equations.