Independence of Linear Statistics with Random Coefficients and Characterizations of Geometric and Poisson Distributions

There is given a characterization of the geometric distribution by the independence of linear forms with random coefficients. The result is a discrete analog of the corresponding theorem on exponential distribution. The property of linear statistics independence is also a characterization of Poisson law. Keywords: geometric distribution; exponential distribution; Poisson distribution; linear forms; random coefficientsComment: 5 pages, no figure

Bayes, Neyman and Neyman-Bayes Inference for Queueing Systems

In this paper we will use the Bayesian inference for the parameters that appear in the queueing systems. We will estimate these parameters and we will build confidence intervals and significance tests for them, considering the parameters of the exponential Poisson and geometric distribution. We will also use the Neyman and the Neyman-Bayes inference for the exponential and Poisson distribution.parameters estimation, confidence intervals, statistical tests, Bayes

Bolshev's method of confidence limit construction

Confidence intervals and regions for the parameters of a distribution are constructed, following the method due to L. N. Bolshev. This construction method is illustrated with Poisson, exponential, Bernouilli, geometric, normal and other distributions depending on parameters

Poisson Autoregression

This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional variance, implying an interpretation as an integer valued GARCH process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model for time series is considered. Under geometric ergodicity the maximum likelihood estimators of the parameters are shown to be asymptotically Gaussian in the linear model. In addition we provide a consistent estimator of the asymptotic covariance, which is used in the simulations and the analysis of some transaction data. Our approach to verifying geometric ergodicity proceeds via Markov theory and irreducibility. Finding transparent conditions for proving ergodicity turns out to be a delicate problem in the original model formulation. This problem is circumvented by allowing a perturbation of the model. We show that as the perturbations can be chosen to be arbitrarily small, the differences between the perturbed and non-perturbed versions vanish as far as the asymptotic distribution of the parameter estimates is concerned.generalized linear models; non-canonical link function; count data; Poisson regression; likelihood; geometric ergodicity; integer GARCH; observation driven models; asymptotic theory

Model Asuransi Kendaraan Bermotor Menggunakan Distribusi Mixed Poisson

Motor vehicle insurance is a form of protection of motor vehicles owned by the insured. One of the activities in insurance companies is claim. Claim is risk of loss claim is paid by the insurance company to the insured. Analysis of motor vehicle insurance claims typically uses poisson distribution approach. Nevertheless in many cases of motor vehicle insurance claim, the value of variance greater than the mean value. In this case overdispersed has been going on the assumption poisson distribution. If the poisson distribution continued to be used when going overdispersed, so the poisson distribution is inefficient because it affects the error standard. To solve the problem can be used mixed Poisson distribution. This final project used two mixed Poisson distribution which is a mixture of gamma poison known as negative binomial distribution and poisson-exponential mixture known as a geometric distribution. Carried out on the data motor vehicle claim in PT. Jasa Asuransi Indonesia, Semarang branch year 2010 to 2011 it is estimated that of the 100 vehicle type Car policyholders aged <1 year will be 2 claims per year