ABSTRACT
The main concern of this paper is providing a flexible discrete model that captures every kind of dispersion (equi-, over- and under-dispersion). Based on the balanced discretization method, a new discrete version of Burr-Hatke distribution is introduced with the partial moment-preserving property. Some statistical properties of the new distribution are introduced, and the applicability of proposed model is evaluated by considering counting series. A new integer-valued autoregressive (INAR) process based on the mixing Pegram and binomial thinning operators with discrete Burr-Hatke innovations is introduced, which can model contagious data properly. The different estimation approaches of parameters of the new process are provided and compared through the Monte Carlo simulation scheme. The performance of the proposed process is evaluated by four data sets of the daily death counts of the COVID-19 in Austria, Switzerland, Nigeria and Slovenia in comparison with some competitor INAR(1) models, along with the Pearson residual analysis of the assessing model. The goodness of fit measures affirm the adequacy of the proposed process in modeling all COVID-19 data sets. The fundamental prediction procedures are considered for new process by classic, modified Sieve bootstrap and Bayesian forecasting methods for all COVID-19 data sets, which is concluded that the Bayesian forecasting approach provides more reliable results.
ABSTRACT
In this paper, we concentrate on the statistical properties of Gamma-X family of distributions. A special case of this family is the Gamma-Weibull distribution. Therefore, the statistical properties of Gamma-Weibull distribution as a sub-model of Gamma-X family are discussed such as moments, variance, skewness, kurtosis and Rényi entropy. Also, the parameters of the Gamma-Weibull distribution are estimated by the method of maximum likelihood. Some sub-models of the Gamma-X are investigated, including the cumulative distribution, probability density, survival and hazard functions. The Monte Carlo simulation study is conducted to assess the performances of these estimators. Finally, the adequacy of Gamma-Weibull distribution in data modeling is verified by the two clinical real data sets.Mathematics Subject Classification: 62E99; 62E15.