gammashaped

Gammashaped is an adjective used to describe objects, distributions, or functions whose form resembles the gamma distribution's probability density function. The gamma distribution is a two-parameter family of continuous distributions defined for positive values, often used to model positively skewed data. It is specified by a shape parameter k > 0 and a scale parameter θ > 0. Its density is f(x; k, θ) = x^{k-1} e^{-x/θ} / (θ^k Γ(k)) for x > 0.

For different values of k, the gamma-shaped curve changes: when k > 1 the distribution is unimodal with a single peak; when 0 < k < 1 it is strictly decreasing; when k = 1 it becomes the exponential distribution. The mean is kθ, the variance is kθ^2, and the mode is (k - 1)θ for k ≥ 1.

Gammashaped objects or models are common in fields dealing with positive, right-skewed data, such as waiting times, rainfall, lifetimes, or claim sizes. In practice, the gamma distribution is also used as a conjugate prior for precision parameters in Bayesian normal models, and as an Erlang special case when k is an integer.

While gammashaped emphasizes resemblance to the gamma form, many empirical distributions may be approximated as gamma-shaped for analytical convenience.