Gamma distribution
The gamma distribution is a continuous probability distribution over positive values, characterized by shape and scale or rate parameters.
Ensemble Methods for Machine Learning
A gamma distribution is a continuous probability distribution on positive values commonly used to model waiting times or right-skewed magnitudes.
- How it is used
- Models continuous, positive, right-skewed regression targets such as insurance claim amounts.
- How deep it goes
- Explains support, tail behavior, surrogate likelihood, GLM formulation, and alternatives, but does not derive the gamma density.
- Examples
- Uses insurance claims, long-tailed positive targets, and bike-sharing counts to contrast gamma with Tweedie modeling.
- What you can do after
- Apply it via gamma regression, LightGBM, or XGBoost when targets are positive, continuous, and right-skewed.
Read how Ensemble Methods for Machine Learning explains gamma distribution →
Math and Architectures of Deep Learning
A probability distribution over positive continuous values, here mentioned as the univariate distribution previously used in Bayesian parameter estimation.
- How it is used
- Uses gamma distributions as conjugate priors and posteriors for Gaussian precision when variance is unknown.
- How deep it goes
- Defines the density and derives posterior parameters and the MAP mode, while deferring the gamma function’s full introduction to an appendix.
- Examples
- Works through Gaussian precision estimation with known mean and supplies PyTorch posterior-update code.
- What you can do after
- Apply it via PyTorch to compute a gamma posterior and MAP estimate for Gaussian precision from observed data.
Read how Math and Architectures of Deep Learning explains gamma distribution →
Related concepts
- posterior probabilityproduces · A posterior probability or distribution expresses the probability assigned to an event, hypothesis, or unknown quantity conditional on observed evidence and prior information.
- conjugacykind of · Conjugacy is the property whereby a prior distribution and a specified likelihood yield a posterior distribution in the same family as the prior.
- Wishart distributioncontrasts with · The Wishart distribution is a probability distribution over symmetric positive-semidefinite matrices, commonly used to model covariance-matrix estimates.
- normal-gamma distributionimplemented by · A joint probability distribution over a mean parameter and a precision parameter, defined here as the product of a normal distribution and a gamma distribution.
- precisionuses · The inverse of variance in a probabilistic model, treated here as the parameter whose conjugate prior is gamma when the mean is known.
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