Discretization Of Mixed Poisson Distribution And Exponential Distribution:Properties And Parameter Estimations

Researchers obtain new probability models by using different techniques such as compounding,discretization,transmutation etc.in order to illustrate a phenomenon in the form of mathematical expressions.Recently discretization of continuous probability distributions has also received attention from researchers from past decades.Discretized statistical models form a basic field of study to handle discrete lifetime data and also count data in a wide variety of disciplines such as biological and medical sciences,phys-ical sciences,engineering,agriculture and so on.In this paper we obtain a new discrete lifetime model called discretization of mixed Poisson distribution and exponential dis-tribution using the general approach to discrete their mixture with some weight.A few important basic properties and parameter estimations are discussed.Chapter 1 introduces the research background and significance,describing the methods and current situation of discretizing continuous distributions.In chapter 2 the mixed Poisson distribution and exponential distribution is developed with its distri-butional properties and reliability characteristics,especially the changes under different parameters of the index of dispersion and failure rate function.Chapter 3 gives the point estimations of the proposed distribution,including the maximum likelihood estimation and the moment estimation.It also proves the exis-tence,consistency and asymptotic normality of the estimates under the large sample.Apart from this,it simulates the maximum likelihood estimation and shows the ex-cellent qualities by the mean squared error and standard deviation.One-parameter confidence intervals and two-parameter confidence regions are shown in the form of numerical simulation results and Simulation times-Coverage rate figures in chapter 4.While in chapter 5,applications of the proposed distribution in modeling real life data and comparison with other existing discrete distributions from the aspects of AIC and BIC are presented.In the final chapter a conclusion is drawn.