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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 abscissa, although the term is also sometimes used to refer to ...
The Landau distribution; The Laplace distribution; The Lévy skew alpha-stable distribution or stable distribution is a family of distributions often used to characterize financial data and critical behavior; the Cauchy distribution, Holtsmark distribution, Landau distribution, Lévy distribution and normal distribution are special cases.
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Well-known families in which the functional form of the distribution is consistent throughout the family include the following: Normal distribution; Elliptical distributions; Cauchy distribution; Uniform distribution (continuous) Uniform distribution (discrete) Logistic distribution; Laplace distribution; Student's t-distribution
|cdf_image= — cumulative distribution image-spec, such as: yyy.svg. |cdf_caption= — cumulative distribution image caption |cdf_image_alt= — alternative text for the image in |cdf_image= |notation= — typical designation for this distribution, for example (,). The notation should include all the distribution parameters explained in the ...
The variance-gamma distribution, generalized Laplace distribution [2] or Bessel function distribution [2] is a continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the gamma distribution. The tails of the distribution decrease more slowly than the normal distribution. It is ...
The variance gamma process has been successfully applied in the modeling of credit risk in structural models. The pure jump nature of the process and the possibility to control skewness and kurtosis of the distribution allow the model to price correctly the risk of default of securities having a short maturity, something that is generally not possible with structural models in which the ...
Cumulative distribution function for the exponential distribution Cumulative distribution function for the normal distribution. In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable, or just distribution function of , evaluated at , is the probability that will take a value less than or equal to .