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  2. Gamma distribution - Wikipedia

    en.wikipedia.org/wiki/Gamma_distribution

    The gamma distribution is a two-parameter exponential family with natural parameters α − 1 and −1/θ (equivalently, α − 1 and −λ), and natural statistics X and ln X. If the shape parameter α is held fixed, the resulting one-parameter family of distributions is a natural exponential family.

  3. Shape parameter - Wikipedia

    en.wikipedia.org/wiki/Shape_parameter

    In probability theory and statistics, a shape parameter (also known as form parameter) [1] is a kind of numerical parameter of a parametric family of probability distributions [2] that is neither a location parameter nor a scale parameter (nor a function of these, such as a rate parameter).

  4. Generalized gamma distribution - Wikipedia

    en.wikipedia.org/wiki/Generalized_gamma_distribution

    It is a generalization of the gamma distribution which has one shape parameter (and a scale parameter). Since many distributions commonly used for parametric models in survival analysis (such as the exponential distribution , the Weibull distribution and the gamma distribution ) are special cases of the generalized gamma, it is sometimes used ...

  5. List of probability distributions - Wikipedia

    en.wikipedia.org/wiki/List_of_probability...

    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

  6. Inverse-gamma distribution - Wikipedia

    en.wikipedia.org/wiki/Inverse-gamma_distribution

    The inverse gamma distribution's probability density function is defined over the support > (;,) = (/) + ⁡ (/)with shape parameter and scale parameter. [2] Here () denotes the gamma function.

  7. Weibull distribution - Wikipedia

    en.wikipedia.org/wiki/Weibull_distribution

    A Weibull distribution is a generalized gamma distribution with both shape parameters equal to k. The translated Weibull distribution (or 3-parameter Weibull) contains an additional parameter. [ 12 ] It has the probability density function

  8. Relationships among probability distributions - Wikipedia

    en.wikipedia.org/wiki/Relationships_among...

    A beta distribution with shape parameters α = β = 1 is a continuous uniform distribution over the real numbers 0 to 1. A beta-binomial distribution with parameter n and shape parameters α = β = 1 is a discrete uniform distribution over the integers 0 to n. A Student's t-distribution with one degree of freedom (v = 1) is a Cauchy ...

  9. Nakagami distribution - Wikipedia

    en.wikipedia.org/wiki/Nakagami_distribution

    The Nakagami distribution or the Nakagami-m distribution is a probability distribution related to the gamma distribution. The family of Nakagami distributions has two parameters: a shape parameter / and a scale parameter >. It is used to model physical phenomena such as those found in medical ultrasound imaging, communications engineering ...