Gamma Distribution formulas

Question

Why I am finding two formulas for the gamma distribution

The one in my textbook is {1/(beta)^alpha*gamma(alpha)} * x^alpha-1 * exp(-x/beta)

The one I found on the internet is {beta^alpha/gamma(alpha)}* x^alpha-1 * exp(-beta*x)

(I have plotted these graphs for specific values of alpha and beta, they are not similar ) are they two different?? if not can you tell why?

Thanks in advance

Hi and welcome to Math.SE. For future questions, it would be preferable to use MathJax for mathematical expressions. You can get started here, and a more complete reference can be found here. — user3733558, Apr 09 '21 at 21:38

score 1 · Accepted Answer · answered Apr 09 '21 at 21:21

1

As Wikipedia tells us, Gamma distribution can be formulated in terms of shape $k$ and scale $\theta$, or in terms of shape $\alpha=k$ and rate $\beta = 1/\theta$.

Although, it is atypical to call denote scale with $\beta$, it happens sometimes. Both formulas are the same if you let $\beta \to \beta^{-1}$

answered Apr 09 '21 at 21:21

Vasily Mitch

10,129

I got it, thank you! – Arghadeep Modak Apr 09 '21 at 21:32

Gamma Distribution formulas

1 Answers1