Search results
Results from the WOW.Com Content Network
The Gamma distribution is parameterized by two hyperparameters ,, which we have to choose. By looking at plots of the gamma distribution, we pick = =, which seems to be a reasonable prior for the average number of cars. The choice of prior hyperparameters is inherently subjective and based on prior knowledge.
In Bayesian inference, the gamma distribution is the conjugate prior to many likelihood distributions: the Poisson, exponential, normal (with known mean), Pareto, gamma with known shape σ, inverse gamma with known shape parameter, and Gompertz with known scale parameter. The gamma distribution's conjugate prior is: [28]
The Poisson distribution may be useful to model events such as: ... that gamma distribution is the only prior that induces linearity of the conditional mean ...
The Gamma distribution, which describes the time until n consecutive rare random events occur in a process with no memory. The Erlang distribution, which is a special case of the gamma distribution with integral shape parameter, developed to predict waiting times in queuing systems; The inverse-gamma distribution; The generalized gamma distribution
The traditional negative binomial regression model is based on the Poisson-gamma mixture distribution. This model is popular because it models the Poisson heterogeneity with a gamma distribution. Poisson regression models are generalized linear models with the logarithm as the (canonical) link function, and the Poisson distribution function as ...
A mixed Poisson distribution is a univariate discrete probability distribution in stochastics. It results from assuming that the conditional distribution of a random variable, given the value of the rate parameter, is a Poisson distribution , and that the rate parameter itself is considered as a random variable.
If X 1 and X 2 are Poisson random variables with means μ 1 and μ 2 respectively, then X 1 + X 2 is a Poisson random variable with mean μ 1 + μ 2. The sum of gamma (α i, β) random variables has a gamma (Σα i, β) distribution. If X 1 is a Cauchy (μ 1, σ 1) random variable and X 2 is a Cauchy (μ 2, σ 2), then X 1 + X 2 is a Cauchy (μ ...
In probability theory and statistics, the normal-gamma distribution (or Gaussian-gamma distribution) is a bivariate four-parameter family of continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean and precision .