|Probability density function |Cumulative distribution function
where is Euler's constant In probability theory and statistics,
the Lévy distribution, named after Paul Lévy, is a continuous
probability distribution for a non-negative random variable. In
spectroscopy this distribution, with frequency as the dependent
variable, is known as a van der Waals profile.[note 1] It is a
special case of the inverse-gamma distribution. It is one of the
few distributions that are stable and that have probability
density functions that can be expressed analytically, the others
being the normal distribution and the Cauchy distribution. All
three are special cases of the stable distributions, which do
not generally have a probability density function which can be
expressed analytically. The probability density function of the
Lévy distribution over the domain is where is the complementary
error function. The shift parameter has the effect of shifting
the curve to the right by an amount , and changing the support
to the inte