In the present paper, we propose a new method to determine the minimum Hellinger distance estimator of stationary Gaussian univariate processes with long-range dependence. Under some assumptions which ensure some probabilistic properties, we establish strong consistency and asymptotic distribution properties of this estimator.

This paper develops the theory of the Gegenbauer AutoRegressive Fractionally Integrated Seasonal Moving Average (GARFISMA) process with alpha-stable innovations.We establish its conditions for causality and invertibility. This is a finite parameter process which exhibits high variability, long memory, cyclical, and seasonality in financial, hydrological data studies, and more. We perform some simulations to illustrate the behavior of our process.

Data on the demand for medical care is usually measured by a number of different counts. These count data are most often correlated and subject to high proportions of zeros. However, excess zeros and the dependence between these data can jointly affect several utilization measures.In this paper, the zero-inflated bivariate Poisson regression model (ZIBP) was used to analyze health-care utilization data. First, the asymptotic properties of the maximum likelihood estimator (MLE) of this model were investigated theoretically.Then, a simulation study is conducted to evaluate the behaviour of the estimator in finite samples. Finally, an application of the ZIBP model to health care demand data is provided by way of illustration.

Data on the demand for medical care is usually measured by a number of different counts. These count data are most often correlated and subject to high proportions of zeros. However, excess zeros and the dependence between these data can jointly affect several utilization measures.In this paper, the zero-inflated bivariate Poisson regression model (ZIBP) was used to analyze health-care utilization data. First, the asymptotic properties of the maximum likelihood estimator (MLE) of this model were investigated theoretically. Then, a simulation study is conducted to evaluate the behaviour of the estimator in finite samples. Finally, an application of the ZIBP model to health care demand data is provided by way of illustration.