翻訳と辞書
Words near each other
・ "O" Is for Outlaw
・ "O"-Jung.Ban.Hap.
・ "Ode-to-Napoleon" hexachord
・ "Oh Yeah!" Live
・ "Our Contemporary" regional art exhibition (Leningrad, 1975)
・ "P" Is for Peril
・ "Pimpernel" Smith
・ "Polish death camp" controversy
・ "Pro knigi" ("About books")
・ "Prosopa" Greek Television Awards
・ "Pussy Cats" Starring the Walkmen
・ "Q" Is for Quarry
・ "R" Is for Ricochet
・ "R" The King (2016 film)
・ "Rags" Ragland
・ ! (album)
・ ! (disambiguation)
・ !!
・ !!!
・ !!! (album)
・ !!Destroy-Oh-Boy!!
・ !Action Pact!
・ !Arriba! La Pachanga
・ !Hero
・ !Hero (album)
・ !Kung language
・ !Oka Tokat
・ !PAUS3
・ !T.O.O.H.!
・ !Women Art Revolution


Dictionary Lists
翻訳と辞書 辞書検索 [ 開発暫定版 ]
スポンサード リンク

Spitzer's identity : ウィキペディア英語版
Spitzer's formula
In probability theory, Spitzer's formula or Spitzer's identity gives the joint distribution of partial sums and maximal partial sums of a collection of random variables. The result was first published by Frank Spitzer in 1956. The formula is regarded as "a stepping stone in the theory of sums of independent random variables".
==Statement of theorem==

Let ''X''1, ''X''2, ... be independent and identically distributed random variables and define the partial sums ''S''''n'' = ''X''1 + ''X''2 + ... + ''X''''n''. Define ''R''''n'' = max(0,''S''1,''S''2,...,''S''''n''). Then〔
::\sum_^\infty \phi_n(\alpha,\beta)t^n = \exp \left(\sum_^\infty \frac \left( u_n (\alpha) + v_n(\beta) -1 \right) \right )
where
::\begin
\phi_n(\alpha,\beta) &= \operatorname E(\exp\left(i(\alpha R_n + \beta(R_n-S_n)\right ))\\
u_n(\alpha) &= \operatorname E(\exp \left(S_n^+\right )) \\
v_n(\beta) &= \operatorname E(\exp \left(\beta S_n^-\right ))
\end
and ''S''± denotes (|''S''| ± ''S'')/2.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Spitzer's formula」の詳細全文を読む



スポンサード リンク
翻訳と辞書 : 翻訳のためのインターネットリソース

Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.