A CHARACTERIZATION OF GAMMA DISTRIBUTION BY INDEPENDENT PROPERTY

  • 투고 : 2008.09.25
  • 심사 : 2009.02.13
  • 발행 : 2009.03.31

초록

Let {$X_n,\;n{\geq}1}$ be a sequence of independent identically distributed(i.i.d.) sequence of positive random variables with common absolutely continuous distribution function(cdf) F(x) and probability density function(pdf) f(x) and $E(X^2)<{\infty}$. The random variables $\frac{X_i{\cdot}X_j}{(\Sigma^n_{k=1}X_k)^{2}}$ and $\Sigma^n_{k=1}X_k$ are independent for $1{\leq}i if and only if {$X_n,\;n{\geq}1}$ have gamma distribution.

키워드

참고문헌

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