3.5.3.2.22 Srangecdf

Definition:

double prob = srangecdf(q, v, group) computes the probability associated with the lower tail of the distribution of the Studentized range statistic.

The externally Studentized range, q, for a sample, x_1,x_2,\cdots,x_r is defined as:

 q=\frac{\max (x_i)-\min (x_i)}{\hat{\sigma _e}}

where \hat{\sigma _e} is an independent estimate of the standard error of the x_i 's.

For a Studentized range statistic the probability integral,P(q) , for \nu degrees of freedom and r groups, can be written as:

P(q)=C\int_0^{+\infty }x^{\nu -1}e^{-\nu x^2/2}\{r\int_{-\infty }^{+\infty }\Phi (y)[\Phi (y)-\Phi (y-qx)]^{r-1}dy\}dx

where C=\frac{\nu ^{\nu /2}}{\Gamma (\nu /2)2^{\nu /2-1}}, \Phi (y)=\int_{-\infty }^y\frac 1{\sqrt{2\pi }}e^{-t^2/2}dt

Parameters:

q (input, double)
the Studentized range statistic,q.  q>0
v (input, double)
the number of degrees of freedom for the experimental error. \nu .  \nu \geq 1.0
group (input,int)
the number of groups, r.group\geq 2
prob (output, double)
the probability.