Question

Compute the measures of skewness and kurtosis of a gamma distribution which has parameters $\alpha$ and $\beta$.

Short answer

Skewness (${\gamma }_1$) and kurtosis (${\gamma }_2$) are calculated from the given parameters of the gamma distribution using the formulas: Skewness = $2/\sqrt{\alpha }$ and Kurtosis = $6/\alpha$.

Step-by-step solution

Formula for Skewness

The formula for the skewness of a gamma distribution is: $2/\sqrt{\alpha }$. Substitute $\alpha$ with the given parameter.

Calculation of Skewness

Upon substitution, the skewness (${\gamma }_1$) is calculated based on the given parameter $\alpha$. The computed value is the skewness of the gamma distribution.

Formula for Kurtosis

The formula for the kurtosis of a gamma distribution is: $6/\alpha$. Substitute $\alpha$ with the given parameter.

Calculation of Kurtosis

Upon substitution, the kurtosis (${\gamma }_2$) is calculated based on the given parameter $\alpha$. The computed value is the kurtosis of the gamma distribution and is the measure of the 'tailedness' of the probability distribution.