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Laplace. In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location parameter) spliced together along the ...
Distribution (number theory) – function on finite sets which is analogous to an integralPages displaying wikidata descriptions as a fallback. Distribution on a linear algebraic group – Linear function satisfying a support condition. Green's function – Impulse response of an inhomogeneous linear differential operator.
Definitions Generation and parameters Let be a standard normal variable, and let and be two real numbers, with >.Then, the distribution of the random variable = + is called the log-normal distribution with parameters and .These are the expected value (or mean) and standard deviation of the variable's natural logarithm, not the expectation and standard deviation of itself.
A normal and a Cauchy distribution The following example is adapted from Hampel, who credits John Tukey. Consider the mixture distribution defined by F(x) = (1 − 10 −10) (standard normal) + 10 −10 (standard Cauchy). The mean of i.i.d. observations from F(x) behaves "normally" except for exorbitantly large samples, although the mean of F(x) does not even exist.
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. where is the Gamma function and is the Fox H-function. [1] In probability theory, statistics and econometrics, the Burr Type XII distribution or simply the Burr distribution [2] is a continuous probability distribution for a non-negative random variable. It is also known as the Singh–Maddala distribution [3] and is one of a number of ...
CF. PGF. In probability theory and statistics, the beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers arising when the probability of success in each of a fixed or known number of Bernoulli trials is either unknown or random. The beta-binomial distribution is the binomial ...
