# Studentized range distribution Calculator

## Calculates the lower and upper cumulative distribution functions of the studentized range distribution.

 percentile q sample size for range r degrees of freedom ν ---------------------------------------------------------------------------------------- number of groups whosemaximum 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.$\normal studentized\ range\ distribution\\[10]\hspace{5} lower\ cumulative\ distribution\\\hspace{30} F(q,r,\nu)=P(Q\leq q) = {\large\int_{\small 0}^{\hspace{25}\small \infty}} \left [ H \left ( q \sqrt{u} \right ) \right ]^{c}\hspace{2} \large \frac{\nu^{\frac{\nu}{2}} e^{-\frac{u \nu}{2}} u^{\frac{\nu}{2}-1}}{2^{\frac{\nu}{2}} \Gamma \left( \frac{\nu}{2} \right)} du \\[10]\hspace{30} H(q,r) = r {\large\int_{\small -\infty}^{\hspace{25}\small \infty}} \theta (y)\left[ \Phi (y) - \Phi(y-q) \right]^{r-1} dy \\[10]\hspace{30} \theta (y) = \large \frac{1}{\sqrt{2 \pi}} e^{\frac{-y^2}{2}} \\[10]\hspace{30} \Phi(y) = {\large\int_{\small -\infty}^{\hspace{25}\small y}} \theta (t) dt\\[10] \\[10]\normal q\ :\ vector\ of\ quantiles, \\[10]r\ :\ sample\ size\ for\ range,\\[10]\nu\ :\ degrees\ of\ freedom,\\[10]c\ :\ number\ of\ groups$

Sending completion

To improve this 'Studentized range distribution Calculator', please fill in questionnaire.
Male or Female ?
Male Female
Age
Under 20 years old 20 years old level 30 years old level
40 years old level 50 years old level 60 years old level or over
Occupation
Elementary school/ Junior high-school student
High-school/ University/ Grad student A homemaker An office worker / A public employee
Self-employed people An engineer A teacher / A researcher
A retired people Others
Useful?
Very Useful A little Not at All
Purpose of use?