R : Copyright 1998, The R Development Core Team
Version 0.63.0 Unstable (June 23, 1998)

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> ####	d|ensity
> ####    p|robability (cumulative)
> ####	q|uantile
> ####    r|andom number generation
> ####
> ####    Functions for  ``d/p/q/r''
> 
> source(paste(getenv("SRCDIR"),"all.equal.R", sep="/"))
> 
> if(!interactive()) .Random.seed <- rep(7654, 3)
> 
> ##--- Cumulative Poisson '==' Cumulative Chi^2 :
> ##--- Abramowitz & Stegun, p.941 :  26.4.21 (26.4.2)
> n1 <- 20; n2 <- 16
> for(lambda in rexp(n1))
+   for(k in rpois(n2, lambda)) {
+     tst <- all.equal(1 - pchisq(2*lambda, 2*(k+1)),
+                      sum(dpois(0:k, lambda=lambda)))
+     if(!(is.logical(tst) && tst))
+       cat("lambda=", format(lambda),".  k =",k, " --> tst=", tst,"\n")
+   }
> 
> ##--- Cumulative Binomial '==' Cumulative F :
> ##--- Abramowitz & Stegun, p.945-6;  26.5.24  AND  26.5.28 :
> n0 <- 50; n1 <- 16; n2 <- 20; n3 <- 8
> for(n in rbinom(n1, size = 2*n0, p = .4)) {
+   cat("n=",n,": ")
+   for(p in c(0,1,rbeta(n2, 2,4))) {
+     cat(".")
+     for(k in rbinom(n3, size = n,  prob = runif(1))) {
+       ## For X ~ Bin(n,p),  compute  1 - P[X > k] = P[X <= k]  in two ways :
+       tst <- all.equal(if(k==n || p==0) 1 else
+                        pf((k+1)/(n-k)*(1-p)/p, df1= 2*(n-k), df2 = 2*(k+1)),
+                        sum(dbinom(0:k, size = n, prob = p)))
+       if(!(is.logical(tst) && tst))
+         cat("n=", n,"; p =", format(p),".  k =",k, " --> tst=", tst,"\n")
+     }
+   }
+   cat("\n")
+ }
n= 46 : ......................
n= 42 : ......................
n= 36 : ......................
n= 37 : ......................
n= 34 : ......................
n= 43 : ......................
n= 41 : ......................
n= 39 : ......................
n= 34 : ......................
n= 43 : ......................
n= 37 : ......................
n= 39 : ......................
n= 41 : ......................
n= 48 : ......................
n= 43 : ......................
n= 33 : ......................
>