### Gamma Distribution

A continuous random variable X is said to have a generalised gamma distribution with parameter Î± and Î² if its probability density fumction is defined as,

Where Î± and Î² are two parameter and Î±,Î²>0. Gamma distribution is a continuous probability distribution.

### Properties of Gamma distribution

- Gamma distribution has two parameter Î± and Î².
- Mean of Gamma distribution (variate) is Î±/Î².
- Variance of Gamma distribution (variate) is Î±/ Î²
^{2}. - Characteristic function of gamma distribution is .
- Moment generating function of gamma distribution is .
- The measure of skewness Î²
_{1}=. - Measure of kurtosis, Î²
_{2}= . These measures show that gamma distribution is positively skewed and leptokurtic. - If the value of Î²=1; mean= variance, if Î²>1; mean<variance and if Î²<1; mean>variance.

## 0 Comments