Gamma distribution ================== The probability density function of the gamma distribution :math:`\mathcal{G}(\alpha, \beta)` with shape parameter :math:`\alpha > 0` and rate parameter :math:`\beta > 0`, for :math:`x\in (0, \infty)`, is given by .. math:: f(x; \alpha, \beta) = \frac{\beta^{\alpha} x^{\alpha-1} e^{-\beta x}}{\Gamma(a)}, and the cumulative distribution function is .. math:: F(x; \alpha, \beta) = P(\alpha, \beta x), where :math:`P(\alpha, \beta x)` is the regularized lower incomplete gamma function. Using this parametrization of the gamma distribution, the expected value and variance are .. math:: \mathrm{E}[X] = \frac{\alpha}{\beta}, \quad \mathrm{Var}[X] = \frac{\alpha}{\beta^2}. This parametrization is commonly used in Bayesian statistics, where the gamma function is used as a conjugate prior distribution for various distribution such as the exponential, Pareto and Poisson distribution. .. autoclass:: cprior.cdist.GammaModel :members: :inherited-members: :show-inheritance: .. autoclass:: cprior.cdist.GammaABTest :members: :inherited-members: :show-inheritance: .. autoclass:: cprior.cdist.GammaMVTest :members: :inherited-members: :show-inheritance: