Some Characterization Results Based on Certain Conditional Expectations
碩士 === 國立高雄大學 === 統計學研究所 === 94 === Given two independent non-degenerate positive random variables $X$ and $Y$, Lukacs (1955) proved that $X/(X+Y)$ and $X+Y$ are independent if and only if $X$ and $Y$ are gamma distributed with the same scale parameter. In this work, under the assumption $X/U$ and $...
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ndltd-TW-094NUK053370062016-06-17T04:16:01Z http://ndltd.ncl.edu.tw/handle/74196557922605159629 Some Characterization Results Based on Certain Conditional Expectations 關於某些條件期望值的刻劃 Chia-hua Liu 劉嘉樺 碩士 國立高雄大學 統計學研究所 94 Given two independent non-degenerate positive random variables $X$ and $Y$, Lukacs (1955) proved that $X/(X+Y)$ and $X+Y$ are independent if and only if $X$ and $Y$ are gamma distributed with the same scale parameter. In this work, under the assumption $X/U$ and $U$ are independent, and $X/U$ has a ${\mathcal Be}(p,q)$ distribution, we characterize the distribution of $(U,X)$ by the condition $E(h(U,X)|X)=b$, where $h$ is allowed to be an exponential function or trigonometric function of $U-X$. Among others, we prove if $q=1$, and for some positive integer $n$, $E(\sum_{i=1}^n e^{i(U-X)}|X)=b$, where $b$ is a constant, then the distribution of $(U,X)$ can be determined. Some other related results are also presented. Wen-Jang Huang 黃文璋 2006 學位論文 ; thesis 23 en_US |
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碩士 === 國立高雄大學 === 統計學研究所 === 94 === Given two independent non-degenerate positive random variables $X$ and $Y$, Lukacs (1955) proved that $X/(X+Y)$ and $X+Y$ are independent if and only if $X$ and $Y$ are gamma distributed with the same scale parameter.
In this work, under the assumption $X/U$ and $U$ are independent, and $X/U$ has a ${\mathcal Be}(p,q)$ distribution, we characterize the distribution of $(U,X)$ by the condition $E(h(U,X)|X)=b$, where $h$ is allowed to be an exponential function or trigonometric function of $U-X$. Among others, we prove if $q=1$, and for some positive integer $n$, $E(\sum_{i=1}^n e^{i(U-X)}|X)=b$, where $b$ is a constant, then the distribution of $(U,X)$ can be determined. Some other related results are also presented.
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Wen-Jang Huang |
author_facet |
Wen-Jang Huang Chia-hua Liu 劉嘉樺 |
author |
Chia-hua Liu 劉嘉樺 |
spellingShingle |
Chia-hua Liu 劉嘉樺 Some Characterization Results Based on Certain Conditional Expectations |
author_sort |
Chia-hua Liu |
title |
Some Characterization Results Based on Certain Conditional Expectations |
title_short |
Some Characterization Results Based on Certain Conditional Expectations |
title_full |
Some Characterization Results Based on Certain Conditional Expectations |
title_fullStr |
Some Characterization Results Based on Certain Conditional Expectations |
title_full_unstemmed |
Some Characterization Results Based on Certain Conditional Expectations |
title_sort |
some characterization results based on certain conditional expectations |
publishDate |
2006 |
url |
http://ndltd.ncl.edu.tw/handle/74196557922605159629 |
work_keys_str_mv |
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1718306624346521600 |