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The gamma distribution is the maximum entropy probability distribution (both with respect to a uniform base measure and a base measure) for a random variable X for which E[X] = kθ = α/β is fixed and greater than zero, and E[ln X] = ψ(k) + ln θ = ψ(α) − ln β is fixed ( ψ is the digamma function ). [1]
Calculus, mathematical analysis, statistics, physics. In mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers.
The generalized gamma distribution is a continuous probability distribution with two shape parameters (and a scale parameter ). 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 ...
CF. In probability theory and statistics, the inverse gamma distribution is a two-parameter family of continuous probability distributions on the positive real line, which is the distribution of the reciprocal of a variable distributed according to the gamma distribution. Perhaps the chief use of the inverse gamma distribution is in Bayesian ...
normal-gamma. 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. [2]
t. e. The likelihood function (often simply called the likelihood) is the joint probability mass (or probability density) of observed data viewed as a function of the parameters of a statistical model. [1] [2] [3] Intuitively, the likelihood function is the probability of observing data assuming is the actual parameter.
The Fréchet distribution, also known as inverse Weibull distribution, [2] [3] is a special case of the generalized extreme value distribution. It has the cumulative distribution function. where α > 0 is a shape parameter. It can be generalised to include a location parameter m (the minimum) and a scale parameter s > 0 with the cumulative ...
The K-distribution is an example of a non-standard distribution that can be defined as a product distribution (where both components have a gamma distribution). Gamma and Pareto distributions. The product of n Gamma and m Pareto independent samples was derived by Nadarajah. See also. Algebra of random variables