Journal of Advanced Statistics

Download PDF (498.3 KB) PP. 136 - 145 Pub. Date: September 1, 2016

DOI: 10.22606/jas.2016.13003

• Manoj Kumar^*
  Central University of Rajasthan, Kishangarh-305817
• Sanjay Kumar Singh
  Department of Statistics and DST-CIMS, Banaras Hindu University,Varanasi-221005
• Umesh Singh
  Department of Statistics and DST-CIMS, Banaras Hindu University,Varanasi-221005

In this paper we propose a new generalized counting process with extension of exponential inter-arrival time distribution. This new model is a generalization of the exponential distribution. The computational intractability is overcome by deriving the extension of exponential count model using polynomial expansion. The hazard function of this new model is an increasing then decreasing function of time, so that the distribution displays positive then negative duration dependence. The model is applied to a real data set on inter arrival times between emissions of beta particles from a nuclear reaction. This count model can be simulated by Markov Chain Monte-Carlo (MCMC) methods, using Metropolis-Hastings algorithm. Our model has many nice features and its comparable with other existing competitive models. It has computational simplicity and there exist of moments that can be used for under-dispersed data.

Count Model, Moments, Polynomial expansion.

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