# Studentized range distribution (percentile) Calculator

## Calculates the percentile from the lower or upper cumulative distribution function of the studentized range distribution.

 cumulative mode lower Pupper Q cumulative distribution sample size for range r degrees of freedom ν ---------------------------------------------------------------------------------------- number of groups whose maximum range is considered c
 The accuracy of the algorithm decreased as r increased, v decreased.Reference)Ferreira, D., et al. "Quantiles from the Maximum Studentized Range Distribution." Biometric Brazilian Journal 25.1 (2007): 117-135.$\normal studentized\ range\ distribution\\[10]\hspace{5} lower\ cumulative\ distribution\\\hspace{30} F(q,r,\nu)=P(Q\leq q) = {\large\int_{\small 0}^{\hspace{25}\small \infty}} \left [ H \left ( q \sqrt{u} \right ) \right ]^{c}\hspace{2} \large \frac{\nu^{\frac{\nu}{2}} e^{-\frac{u \nu}{2}} u^{\frac{\nu}{2}-1}}{2^{\frac{\nu}{2}} \Gamma \left( \frac{\nu}{2} \right)} du \\[10]\hspace{30} H(q,r) = r {\large\int_{\small -\infty}^{\hspace{25}\small \infty}} \theta (y)\left[ \Phi (y) - \Phi(y-q) \right]^{r-1} dy \\[10]\hspace{30} \theta (y) = \large \frac{1}{\sqrt{2 \pi}} e^{\frac{-y^2}{2}} \\[10]\hspace{30} \Phi(y) = {\large\int_{\small -\infty}^{\hspace{25}\small y}} \theta (t) dt\\[10] \\[10]\normal q\ :\ vector\ of\ quantiles, \\[10]r\ :\ sample\ size\ for\ range,\\[10]\nu\ :\ degrees\ of\ freedom,\\[10]c\ :\ number\ of\ groups$

Studentized range distribution (percentile)
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