Gamma Distribution Calculator
Compute gamma distribution probabilities and quantiles for waiting times, Bayesian priors, and reliability analysis with interactive charts.
The gamma distribution generalizes the exponential by modeling the time until the k-th event in a Poisson process. With its shape and rate parameters, it covers a wide family of right-skewed distributions used in reliability engineering, Bayesian statistics, and queueing theory.
This calculator lets you evaluate probabilities over intervals, find quantiles, and see how the shape parameter transitions the distribution from exponential-like to nearly symmetric.
Launch the Gamma Distribution workspace to plot the curve, inspect PDF/CDF behavior, and compute quantiles and interval probabilities.
Open Interactive Interval ProbabilityHow is the gamma distribution related to exponential?
The exponential distribution is a special case of the gamma with shape parameter equal to 1. The gamma with integer shape k models the sum of k independent exponential random variables.
What are common uses of the gamma distribution?
It models aggregate waiting times, insurance claim sizes, rainfall amounts, and serves as a conjugate prior for the Poisson rate parameter in Bayesian analysis.
What is the difference between shape-rate and shape-scale parameterization?
Shape-rate uses parameters (α, β) where β is the rate. Shape-scale uses (α, θ) where θ = 1/β is the scale. Both describe the same family; this calculator uses the parameterization shown in the controls.