What is the mean of a gamma distribution?

For shape α and rate β, mean = α / β. Used in modeling waiting times and sizes.

How relates to exponential?

Gamma with α=1 is exponential distribution.

Gamma Mean - Perform scientific calculations with precision and accuracy.

Mean & Variance

Shape (α)

Rate (β)

The Gamma distribution is a continuous probability distribution defined by two positive parameters:

Shape (α): Also known as $k$. It defines the shape of the distribution.
Rate (β): Also known as $1/\theta$ (where $\theta$ is the scale). It defines the spread.

Mean (μ) = α / β
Variance (σ²) = α / β²

For Gamma(k, θ) (shape k, scale θ), the mean is k θ and variance is k θ².

k=3, θ=2 → mean = 6, variance = 12.

Rate form?
Using rate λ, mean = k/λ.

Applications?
Waiting times and reliability models.

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