Cauchy distribution (percentile)

Calculates the percentile from the lower or upper cumulative distribution function of the Cauchy distribution.

cumulative mode
 lower P upper Q
cumulative distribution
 0≦P,Q≦1
location parameter a
scale parameter b
 b＞0
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt

 $\normal Cauchy\ distribution\\[10](1)\ probability\ density\\\hspace{30}f(x,a,b)={\large\frac{1}{\pi}\frac{b}{(x-a)^2+b^2}}\\(2)\ lower\ cumulative\ distribution\\\hspace{30}P(x,a,b)={\large\int_{\small-\infty}^{\hspace{25}\small x}}f(t,a,b)dt\\(3)\ upper\ cumulative\ distribution\\\hspace{30}Q(x,a,b)={\large\int_{\small x}^{\hspace{25}\small\infty}}f(t,a,b)dt\\$

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