The Research About The Moments Of A Kind Of Special Discrete Distribution

The moments of distribution plays an important role in Statistics, which applies in life science, biology, physic science and so on. Probability distribution includes discrete distribution and continuous distribution. The original moments and inverse moments are researched in this thesis.Firstly, the original moments are researched, using Combinatorics method. Expanding the moments of some frequent distribution with Stirling number of second kind, and then the result is represented in general situation. Secondly, summarizing the results about the inverse moments of discrete distribution. Mainly introducing asymptotic expansion for the inverse moments of binomial and poisson distribution, and the recurrence relation for the inverse moments of binomial.