Search results
Results from the WOW.Com Content Network
In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a ...
Category: Exponential family distributions. ... Print/export Download as PDF; Printable version; In other projects
The (a,b,0) class of distributions is also known as the Panjer, [1] [2] the Poisson-type or the Katz family of distributions, [3] [4] and may be retrieved through the Conway–Maxwell–Poisson distribution. Only the Poisson, binomial and negative binomial distributions satisfy the full form of this relationship.
The gamma distribution with two parameters is an exponential family but not a NEF and the chi-squared distribution is a special case of the gamma distribution with fixed scale parameter, and thus is also an exponential family but not a NEF (note that only a gamma distribution with fixed shape parameter is a NEF).
Download as PDF; Printable version; In other projects ... This is a list of exponential topics, by Wikipedia page. See also list ... Exponential family; Exponential ...
In probability theory and statistics, the Exponential-Logarithmic (EL) distribution is a family of lifetime distributions with decreasing failure rate, defined on the interval [0, ∞). This distribution is parameterized by two parameters p ∈ ( 0 , 1 ) {\displaystyle p\in (0,1)} and β > 0 {\displaystyle \beta >0} .
This family of distributions is a special or limiting case of the normal-exponential-gamma distribution. This can also be seen as a three-parameter generalization of a normal distribution to add skew; another distribution like that is the skew normal distribution, which has thinner tails.
In the univariate case, a real-valued random variable belongs to the additive exponential dispersion model with canonical parameter and index parameter , (,), if its probability density function can be written as