臺灣博碩士論文加值系統

設 F 是分佈函數並且 {m1,m2,m3...} 是 F 的矩。矩問題就是想知道是否 {m1,m2,m3...} 決定分佈函數 F。一般來說，矩的序列不一定都能決定分佈函數。所以，對於分佈函數是 moment-determinate 的條件被研究。我們得到一個關於離散之分佈函數的結果。

Let F be a distribution function and {m1,m2,m3...} be its moments. The moment problem is to know whether the moments {m1,m2,m3...} determine the distribution function F. In general, the sequence of moments does not always determine the distribution function. So the conditions for a distribution function to be moment-determinate are investigated. We get a result concerning the discrete distribution function.

1 Introduction.............................................1
2 Conditions for moment-determinacy..............................4
3 A special case for the discrete distribution function...............9

[1] A.N. Shiryaev (1996), Probability, Springer-Verlag, New York.
[2] Gwo Dong Lin (1997), On the moment problems, Statistics & Probability Letters 35, 85-90.
[3] Kai Lai Chung (1974), A course in probability theory, Academic Press, New York & London.
[4] Patrick Billingsley (1995), Probability and Measure, John Wiley, New York.