gammalike

Gammalike is an informal descriptor used in probability and statistics to refer to distributions or models whose shape or mathematical form resembles the gamma distribution. It is not a formal named distribution, but a heuristic label indicating positive support, a unimodal and right-skewed profile, and a flexible shape controlled by parameters. The term signals that a variable behaves similarly to a gamma-distributed variable in key respects, though the exact distribution may differ.

In formal terms, many gammalike models belong to the generalized gamma family, whose density can be written as f(x) = (p/Γ(k)) λ^k x^{kp - 1} exp(-λ x^p) for x > 0, with parameters k > 0, p > 0, λ > 0. The gamma distribution is the special case p = 1. Other related distributions, such as the Erlang and chi-square, share the same positive support and shape characteristics and are often described as gammalike due to their close connection to the gamma form. The Weibull distribution is also related as part of the broader generalized gamma family under certain parameterizations.

Applications of gammalike models arise in modeling lifetimes, waiting times, and other positive-valued data, as well as in Bayesian analysis where gamma-type priors are common. Because gammalike is an informal label, practitioners typically specify the exact distribution or family being used to avoid ambiguity.

See also: Gamma distribution, Generalized gamma distribution, Exponential family, Positive-valued distributions.