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This paper presents a new model for a stationary non-negative first order of integer-valued random variables based on the Pegram and thinning operators. Some fundamental and regression properties of the proposed model are discussed. Maximum likelihood estimation (MLE) by the EM algorithm is applied to estimate the parameters. Numerical studies to compare the proposed model with the thinning and Pegram models and the breakdown point of MLE for the proposed model have been conducted. Finally, a real life count data set has been used to illustrate its application. Comparison with existing models by AIC showed that the proposed model is much better and illustrates its potential usefulness in empirical modeling.

In commerce, economics, engineering and the sciences, quantitative methods based on statistical models for forecasting are very useful tools for prediction and decision. There is an abundance of papers on forecasting for continuous-time series but relatively fewer papers for time series of counts which require special consideration due to the integer nature of the data. A popular method for modelling is the method of mixtures which is known for its flexibility and thus improved prediction capability. This paper studies the coherent forecasting for a flexible stationary mixture of Pegram and thinning (MPT) process, and develops the likelihood-based asymptotic distribution. Score functions and the Fisher information matrix are presented. Numerical studies are used to assess the performance of the forecasting methods. Also, a comparison is made with existing discrete-valued time series models. Finally, the practical application is illustrated with two sets of real data. It is shown that the mixture model provides good forecasting performance.

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This paper introduces a generalization of the weighted or skewed exponential distribution. The motivation to consider this generalization stems from the interest in modelling unemployment data. The generalized skewed exponential distribution is shown to be log-concave, and as a consequence, a number of properties of the distribution are obtained. The generalized skewed exponential distribution is shown to give much better fit than the skewed exponential, Weibull, lognormal and logistic distributions for the unemployment age data.