Gamma Distribution Calculator

Use Gamma Distribution Calculator to find the probability density and lower and upper cumulative probabilities for Gamma distribution with parameter $\alpha$ and $\beta$.

Gamma Distribution Calculator
Location Parameter $\alpha$:
Scale Parameter $\beta$
Value of x
Probability density : f(x)
Probability X less than x: P(X < x)
Probability X greater than x: P(X > x)

How to use Gamma Distribution Calculator?

Step 1 - Enter the location parameter (alpha)

Step 2 - Enter the Scale parameter (beta)

Step 3 - Enter the Value of x

Step 4 - Click on “Calculate” button to calculate gamma distribution

Step 5 - Calculate Probability Density

Step 6 - Calculate Probability X less x

Step 7 - Calculate Probability X greater than x

Definition of Gamma Distribution

A continuous random variable $X$ is said to have a gamma distribution with parameter $\alpha$ and $\beta$ if its p.d.f. is given by $$f(x; \alpha,\beta) = \frac{1}{\beta^\alpha \Gamma(\alpha)} x^{\alpha-1}e^{-x/\beta}; x>0; \alpha, \beta>0$$

The parameter $\alpha$ is the scale parameter and $\beta$ is the shape parameter of gamma distribution.

Mean of Gamma Distribution

The mean or expected value of gamma random variable is

$E(X)= \dfrac{\beta}{\alpha}$

Variance of Gamma distribution

The variance of gamma random variable is

$V(X) = \dfrac{\beta}{\alpha^2}$.

Harmonic Mean of Gamma Distribution

The harmonic mean of gamma random variable is


Mode of Gamma distribution

The mode of gamma random variable is


M.G.F. of Gamma Distribution

The moment generating function of gamma random variable is

$M_X(t)=\bigg(1-\dfrac{t}{\alpha}\bigg)^{-\beta}, t<\alpha$

I hope you like Gamma Distribution Calculator. Click on Theory to read more about Gamma distribution,graph of gamma distribution,M.G.F and C.G.F of gamma distribution.

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