The gamma distribution depends on two parameters, a>0 and b>0; the value of the density function at x ≥ 0 is gammad(a,b,x) = xa−1e−bxba/Γ(a). If you enter
for example, you will get
The cumulative distribution function for the gamma distribution with parameters a and b at a value x is gammad_cdf(n,x) = Prob(X ≤ x). It turns out that gammad_cdf(n,x) = igamma(a, bx, 1) where igamma is the incomplete gamma function; igamma(a,x,1) = ∫0x e−tta−1dt/Γ(a). If you enter
you will get
If you give gammad_cdf an extra argument, you will get the probability that the random variable lies between two values; gammad_cdf(a,b,x,y) = Prob(x ≤ X ≤ y). If you enter
you will get
The inverse distribution function for the gamma distribution with parameters a and b is computed with gammad_icdf(a,b,h); recall that this will return the value x with gammad_cdf(a,b,x) = h. If you enter
you will get