Some Important Conclusions Of Exponential Distribution And Geometric Distribution

Exponential distribution is commonly used on electronic components,and its properties are recognized deeply due to abundance of practice of reliability en gineering and queuing theory. Geometric distribution has already been applied to in more fields,and it played quite an important role,especially in some fields such as information engineering,electronic engineering,control theory and econom ics.Moreover,exponential distribution and geometric distribution have many simil ar properties.So study of its properties is a meaningful research direction,and t he study has theoretical value and practical value,and the study will make it applied more widely in applied probabilistic model such as reliability mathemati cs.This paper studies the properties of exponential distribution and geometric di stribution,by comparing exponential distribution and geometric distribution,on the basis of previous achievements.This paper obtains some important conclusions, a nd the main work is as follows.Firstly,we solve the mutual transformation relationship between exponential d istribution and geometric distribution,and between weibull distribution and discrete weibull distribution. Because of this,we first study properties of exponential distr ibution,then give corresponding properties of geometric distribution,and prove them.Secondly,we obtain a conditional distribution of exponential distribution and geometric distribution respectively,and the two distributions are additive under th e condition. Subsequently,we study analysis of exponential distribution.We make a conclu sion that an exponential distribution is sum of an exponential distribution and th e other random variable.On the basis, we discuss analysis of erlang distribution.T hen we study analysis of geometric distribution by the same method,and similar conclusions are given.,and analysis of pascal distribution is also discussed.Then we discuss moment of exponenti distribution and geometric distributio n,and obtain recurrence formula of moment of exponenti distribution and geome tric distribution.Lastly,we study order statistics of exponential distribution and geometric dis tribution. Several important conclusions of exponential distribution are first giv en,then order statistics of geometric distribution is studied by similar method.But several different conclusions are obtained,as its application,we give maximum lik elihood estimation of the parameter in geometric distribution based on censored s amples.