Count data that exhibit over dispersion (variance of counts is larger than its mean) are commonly analyzed using discrete distributions such as negative binomial, Poisson inverse Gaussian and other models. The Poisson...Count data that exhibit over dispersion (variance of counts is larger than its mean) are commonly analyzed using discrete distributions such as negative binomial, Poisson inverse Gaussian and other models. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial and the Poisson inverse Gaussian have variance larger than the mean and therefore are more appropriate to model over-dispersed count data. As an alternative to these two models, we shall use the generalized Poisson distribution for group comparisons in the presence of multiple covariates. This problem is known as the ANCOVA and is solved for continuous data. Our objectives were to develop ANCOVA using the generalized Poisson distribution, and compare its goodness of fit to that of the nonparametric Generalized Additive Models. We used real life data to show that the model performs quite satisfactorily when compared to the nonparametric Generalized Additive Models.展开更多
On the basis of a well-established binomial structure and the socalled Poisson-Lindley distribution,a new two-parameter discrete distribution is introduced.Its properties are studied from both the theoretical and prac...On the basis of a well-established binomial structure and the socalled Poisson-Lindley distribution,a new two-parameter discrete distribution is introduced.Its properties are studied from both the theoretical and practical sides.For the theory,we discuss the moments,survival and hazard rate functions,mode and quantile function.The statistical inference on the model parameters is investigated by the maximum likelihood,moments,proportions,least square,and weighted least square estimations.A simulation study is conducted to observe the performance of the bias and mean square error of the obtained estimates.Then,applications to two practical data sets are given.Finally,we construct a new flexible count data regression model called the binomial-Poisson Lindley regression model with two practical examples in the medical area.展开更多
文摘Count data that exhibit over dispersion (variance of counts is larger than its mean) are commonly analyzed using discrete distributions such as negative binomial, Poisson inverse Gaussian and other models. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial and the Poisson inverse Gaussian have variance larger than the mean and therefore are more appropriate to model over-dispersed count data. As an alternative to these two models, we shall use the generalized Poisson distribution for group comparisons in the presence of multiple covariates. This problem is known as the ANCOVA and is solved for continuous data. Our objectives were to develop ANCOVA using the generalized Poisson distribution, and compare its goodness of fit to that of the nonparametric Generalized Additive Models. We used real life data to show that the model performs quite satisfactorily when compared to the nonparametric Generalized Additive Models.
文摘On the basis of a well-established binomial structure and the socalled Poisson-Lindley distribution,a new two-parameter discrete distribution is introduced.Its properties are studied from both the theoretical and practical sides.For the theory,we discuss the moments,survival and hazard rate functions,mode and quantile function.The statistical inference on the model parameters is investigated by the maximum likelihood,moments,proportions,least square,and weighted least square estimations.A simulation study is conducted to observe the performance of the bias and mean square error of the obtained estimates.Then,applications to two practical data sets are given.Finally,we construct a new flexible count data regression model called the binomial-Poisson Lindley regression model with two practical examples in the medical area.
