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Chapter 3: Problem 8

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

Short Answer

Expert verified
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

01

Formula for Skewness

The formula for the skewness of a gamma distribution is: \(2/ \sqrt{ \alpha } \). Substitute \( \alpha \) with the given parameter.
02

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.
03

Formula for Kurtosis

The formula for the kurtosis of a gamma distribution is: \(6/ \alpha \). Substitute \( \alpha \) with the given parameter.
04

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.

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