Related Properties For A Family Of Inflated-parameter Discrete Distributions

The family of inflated-parameter discrete distribution is a hot topic in risk theory. As ageneralization of the classical discrete distributions, they have similar properties and internalrelation with classical discrete distributions. In this paper we mainly focus on the numericalcharacters, the lack of memory and other related properties. We also give some necessary andsufficient conditions for those distributions, two parameter Bernoulli sequence is alsodiscussed. The results of this paper improve and supplement the relevant research for thefamily of inflated-parameter discrete distribution in existing literature.This paper is divided into six chapters:The first chapter is mainly making a review of the origin and development of the familyof inflated-parameter discrete distributions, some basic properties are summarized.The second chapter is mainly discussing on the inflated-parameter geometric distributionwith numerical characters and the property of lack of memory.The third chapter studies the numerical characters of inflated-parameter Bernoullidistribution, and obtains the necessary and sufficient conditions for the inflated-parametergeometric distribution.The fourth chapter is similar to the third chapter. We discuss the numerical characters forthe inflated-parameter negative binomial distribution, then give a sufficient and necessarycondition for the inflated-parameter negative binomial distribution.The fifth chapter discusses the inflated-parameter negative binomial distribution andPoisson distribution. Numerical characters and the relationship between them are given.The sixth chapter is focus on other inflated-parameter discrete distribution. We study theproperties of inflated-parameter logarithmic series distribution and the two parameterBernoulli series distribution.