Inverse Chi-Square Distribution (Percentile)
Determine the percentile from the lower or upper cumulative probability value of the inverse chi-squared distribution.
| \(\normalsize Inverse-chi-square\ distribution\ \frac{1}{X^2}(x,\nu)\\ (1) probability\ density\\ \hspace{30px}f(x,\nu)={\large\frac{x^{-\frac{\nu}{2}-1}e^{-\frac{1}{2\small x}}}{2^{\frac{\nu}{2}}\Gamma(\frac{\nu}{2})}}\\ (2) lower\ cumulative\ distribution\\ \hspace{30px}P(x,\nu)={\large\int_{\small 0}^{\small x}}f(t,\nu)dt\\ (3) upper\ cumulative\ distribution\\ \hspace{30px}Q(x,\nu)={\large\int_{\small x}^{\small\infty}}f(t,\nu)dt\\ \) |
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