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Chi distribution : ウィキペディア英語版
Chi distribution

|
cdf =P(k/2,x^2/2)\,|
mean =\mu=\sqrt\,\frac|
median =|
mode =\sqrt\, for k\ge 1|
variance =\sigma^2=k-\mu^2\,|
skewness =\gamma_1=\frac\,(1-2\sigma^2)|
kurtosis =\frac(1-\mu\sigma\gamma_1-\sigma^2)|
entropy =\ln(\Gamma(k/2))+\,
\frac(k\!-\!\ln(2)\!-\!(k\!-\!1)\psi_0(k/2))|
mgf =Complicated (see text)|
char =Complicated (see text)|
}}
In probability theory and statistics, the chi distribution is a continuous probability distribution. It is the distribution of the square root of the sum of squares of independent random variables having a standard normal distribution. The most familiar examples are the Rayleigh distribution with chi distribution with 2 degrees of freedom, and the Maxwell distribution of (normalized) molecular speeds which is a chi distribution with 3 degrees of freedom (one for each spatial coordinate). If X_i are ''k'' independent, normally distributed random variables with means \mu_i and standard deviations \sigma_i, then the statistic
:Y = \sqrt\right)^2}
is distributed according to the chi distribution. Accordingly, dividing by the mean of the chi distribution (scaled by the square root of ''n'' − 1) yields the correction factor in the unbiased estimation of the standard deviation of the normal distribution. The chi distribution has one parameter: k which specifies the number of degrees of freedom (i.e. the number of X_i).
==Characterization==


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「Chi distribution」の詳細全文を読む



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