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- 2013-10-12
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8#
发表于 2013-4-28 07:25
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I don’t know why, but for some reason it’s important to me to know what the chi^2, F, and t distributions actually are:
*The chi^2 distribution with k degrees of freedom is the distribution of the sum of the squares of k independent, identically distributed standard normal random variables.
*The F distribution with n degrees of freedom in the numerator and d degrees of freedom in the denominator is the distribution of the ratio of the mean of the squares of n independent, identically distributed standard normal random variables to the mean of the squares of d other independent, identically distributed standard normal random variables, in other words F ~ (chi^2/n)/(chi^2/d) where the chi^2 are independent and have n and d degrees of freedom respectively.
*If a random variable has the t distribution, then its square has the F distribution with a single degree of freedom in the numerator. In other words, t^2 ~ z^2/(chi^2/d) or t ~ z/sqrt(chi^2/d) where t and chi^2 each have d degrees of freedom, and z is standard normal.
I freaked about the F distribution on Level I, but now it doesn’t seem so bad to me. I don’t remember how much of this information is included in the readings, but I learned it from Wikipedia and various textbooks and it helps me understand and remember where to apply these distributions. |
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