Double StudentRangeCDF(Double q, Int32 r, Int32 v, Int32 ci)
Cumulative probability distribution for the Studentized Range statistic.
| # | Name | Description |
|---|---|---|
| 1 | q | The quantile at which to evaluate the distribution (q>0). |
| 2 | r | Number of samples (groups), integer r>=2. |
| 3 | v | Degrees of freedom, integer v>=1. To obtain the maximum normal range distribution (v = Inf), specify this parameter larger than 25000. |
| 4 | ci | If ci = 1, the cumulative probability of the studentized range is returned. If ci > 1 (e.g. 2), the studentized maximum modulus distribution is obtained (the studentized-range CDF raised to the power ci). |
Returns: Double - the cumulative probability P(Q <= q) of the studentized range Q with r groups and v degrees of freedom (for ci=1). Returns 0 for q<=0 and NaN if r<2 or v<1.
The studentized range CDF is the probability that the range (max minus min) of r independent standard normal samples, divided by an independent root-mean-square estimate of the standard deviation on v degrees of freedom, does not exceed q:
CDF(q | r,v) = P((max_i X_i-min_i X_i)/S <= q) , S^2 ~ chi^2_v/v .
It is computed by Gauss-Legendre quadrature (algorithm AS 190). Monotone non-decreasing in q, with CDF(0)=0 and CDF tending to 1 as q tends to +infinity. Returns NaN for r<2 or v<1. Note: the maximum allowed q when v = 1 is 200; accuracy decreases as r grows, as v shrinks, and as the probability approaches 1.
References:
[1] Based on Fortran program from statlib, http://lib.stat.cmu.edu, Algorithm AS 190 Appl. Statist. (1983) Vol.32, No. 2 Incorporates corrections from Appl. Statist. (1985) Vol.34 (1) [2] Ferreira, D., et al. "Quantiles from the Maximum Studentized Range Distribution." Biometric Brazilian Journal 25.1 (2007): 117-135. http://jaguar.fcav.unesp.br/RME/fasciculos/v25/v25_n1/A8_Daniel.pdf (See qrange function)