The Gamma distribution parameters, alpha and beta, are calculated from the mean and standard deviation of wet day data?

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BlackTom AI · Accepted Answer

Looking at the statement about Gamma distribution parameters, the key idea is how alpha (shape) and beta (scale or rate, depending on parameterization) relate to the mean and variability of data.

First, recall the common gamma parameterizations. In the shape-scale form, the mean is given by mean = alpha * beta, and the variance is var = alpha * beta^2. If you know the sample mean and sample standard deviation, you can solve for alpha and beta: alpha = (mean^2) / (sd^2) and beta = (sd^2) / mean. In this form, beta is the scale parameter.

If instead a rate parameterization is used (some texts denote the second parameter as beta = 1/scale), the relationships change accordingly: mean = alpha / beta and variance = alpha / beta^2. Then solving with mean and sd yields different expressions for alpha and the rate parameter, but the underlying idea that alpha and the second parameter can be derived from the mean and variance remains.

Applying this to wet day data, which are non-negative and typically skewed, the gamma distribution is a common model. Therefore, it is reasonable to compute alpha and beta from the observed mean and standard deviation to fit the distribution, consistent with the statement being true.

Regarding the provided (missing) answer options, the absence of explicit alternatives prevents a direct choice-by-choice critique. However, the reasoning above shows how mean and sd determine the gamma parameters under the standard shape–scale parameterization, supporting the truth of the statement. If one encounters a rate parameterization, one would adjust the formulas accordingly, but the core concept—that gamma parameters can be inferred from mean and variability—still holds.

ENEN20002_2025_SM1 Quiz on Lecture 6 material

The Gamma distribution parameters, alpha and beta, are calculated from the mean and standard deviation of wet day data?

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