Question

Compute the measures of skewness and kurtosis of a gamma distribution that has parameters \(\alpha\) and \(\beta\).

Short answer

The skewness of the gamma distribution is given by \(2 / \sqrt{\alpha}\) whereas the kurtosis is represented by \(6 / \alpha\). Provided with the values of \(\alpha\) and \(\beta\), simple substitution to these formulas accounts for the final results.

Step-by-step solution

Understanding the gamma distribution parameters

The gamma distribution has two parameters which are \(\alpha\) and \(\beta\). These parameters define the shape of the distribution. In this particular exercise, you are given these parameters.

Calculating Skewness

The skewness of a gamma distribution is calculated as \(2 / \sqrt{\alpha}\). Simply substitute your given value of \(\alpha\) into this formula. Ensure to correctly execute the square root function and the division operation in this step.

Calculating Kurtosis

The kurtosis of a gamma distribution can be calculated using the formula \(6 / \alpha\). This is quite straightforward. Substitute your given value of \(\alpha\) into this formula and perform the division operation. This will give you the kurtosis.