It's well known that the distribution of the sample variance $s_n^2$ of the normal distribution $\mathcal{N}(0, 1)$ is $s_n^2 \sim \frac{\chi_{n-1}^2}{n-1}$.
Suppose I have a Student distribution $t(\nu)$ with $\nu > 2$ degrees of freedom and variance 1 (i.e. scale$=\sqrt{\frac{\nu - 2}{\nu}}$). What is the distribution of the sample variance of $t(\nu)$? Does it have variance in case when $\nu \leq 4$?
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davynci
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Maybe you could adapt a method like this to the t distribution instead of the normal distribution? – K.defaoite May 22 '24 at 18:34
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1Unfortunately, it doesn't work, because Student distribution doesn't have a moment-generating function. – davynci May 25 '24 at 19:38
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But I realized, that there is a simple formula for variance of sample variance, and, yeah, it doesn't have a variance in case when $\nu \leq 4$. – davynci May 25 '24 at 19:39
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Would you mind posting it? I have never seen such a formula before – K.defaoite May 25 '24 at 21:55
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1variance of sample variance in general case – davynci May 26 '24 at 06:28