翻訳と辞書 Words near each other ・ Compound of two great icosahedra ・ Compound of two great inverted snub icosidodecahedra ・ Compound of two great retrosnub icosidodecahedra ・ Compound of two great snub icosidodecahedra ・ Compound of two icosahedra ・ Compound of two inverted snub dodecadodecahedra ・ Compound of two small stellated dodecahedra ・ Compound of two snub cubes ・ Compound of two snub dodecadodecahedra ・ Compound of two snub dodecahedra ・ Compound of two snub icosidodecadodecahedra ・ Compound of two truncated tetrahedra ・ Compound option ・ Compound pier ・ Compound Poisson distribution ・ Compound Poisson process ・ Compound presentation ・ Compound prism ・ Compound probability distribution ・ Compound refractive lens ・ Compound S ・ Compound semiconductor ・ Compound shutter ・ Compound spirit of ether ・ Compound squeeze ・ Compound steam engine ・ Compound subject ・ Compound TCP ・ Compound term processing ・ Compound turbine Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Compound Poisson process ： ウィキペディア英語版 Compound Poisson process A compound Poisson process is a continuous-time (random) stochastic process with jumps. The jumps arrive randomly according to a Poisson process and the size of the jumps is also random, with a specified probability distribution. A compound Poisson process, parameterised by a rate $\backslash lambda\; >\; 0$ and jump size distribution ''G'', is a process $\backslash$ given by :$Y(t)\; =\; \backslash sum\_^\; D\_i$ where, $\backslash$ is a Poisson process with rate $\backslash lambda$, and $\backslash$ are independent and identically distributed random variables, with distribution function ''G'', which are also independent of $\backslash .\backslash ,$ When $D\_i$ are non-negative integer-valued random variable, then this compound Poisson process is named stuttering Poisson process which has the feature that two or more events occur in a very short time . ==Properties of the compound Poisson process== Using conditional expectation, the expected value of a compound Poisson process can be calculated using a result known as Wald's equation as: :$\backslash ,E(Y(t))\; =\; E(E(Y(t)|N(t)))\; =\; E(N(t)E(D))\; =\; E(N(t))E(D)\; =\; \backslash lambda\; t\; E(D).$ Making similar use of the law of total variance, the variance can be calculated as: :$$ \begin \operatorname(Y(t)) &= E(\operatorname(Y(t)|N(t))) + \operatorname(E(Y(t)|N(t))) \\ &= E(N(t)\operatorname(D)) + \operatorname(N(t)E(D)) \\ &= \operatorname(D)E(N(t)) + E(D)^2 \operatorname(N(t)) \\ &= \operatorname(D)\lambda t + E(D)^2\lambda t \\ &= \lambda t(\operatorname(D) + E(D)^2) \\ &= \lambda t E(D^2). \end Lastly, using the law of total probability, the moment generating function can be given as follows: :$\backslash ,\backslash Pr(Y(t)=i)\; =\; \backslash sum\_\; \backslash Pr(Y(t)=i|N(t)=n)\backslash Pr(N(t)=n)$ :$$ \begin E(e^) & = \sum_i e^ \Pr(Y(t)=i) \\ & = \sum_i e^ \sum_ \Pr(Y(t)=i|N(t)=n)\Pr(N(t)=n) \\ & = \sum_n \Pr(N(t)=n) \sum_i e^ \Pr(Y(t)=i|N(t)=n) \\ & = \sum_n \Pr(N(t)=n) \sum_i e^\Pr(D_1 + D_2 + \cdots + D_n=i) \\ & = \sum_n \Pr(N(t)=n) M_D(s)^n \\ & = \sum_n \Pr(N(t)=n) e^ \\ & = M_(\ln(M_D(s))) \\ & = e^. \end 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「Compound Poisson process」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.