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LevyDistribution

LevyDistribution
represents a Lévy distribution with location parameter and dispersion parameter .
  • The probability density for value in a Lévy distribution is proportional to .  »
  • The Lévy distribution LevyDistribution is a special case of the inverse gamma distribution with and . »
  • LevyDistribution allows to be any real number and to be any positive real number.
Probability density function:
Cumulative distribution function:
Mean and variance of a Lévy distribution are infinite:
Median:
Probability density function:
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Cumulative distribution function:
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Mean and variance of a Lévy distribution are infinite:
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Median:
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Generate a set of pseudorandom numbers that are Lévy distributed:
Compare its histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare a density histogram of the sample with the PDF of the estimated distribution:
Moments of order do not exist:
Generalized moments exist for order :
Hazard function:
Quantile function:
Find the full width at half-maximum of the van der Waals spectral profile:
Compute the location of the maximum:
Solve for the half-maximum points:
Find the width:
The frequency of the emitted particle is more likely to be greater than the mode:
Parameter influence on the CDF for each :
Lévy distribution is closed under translation and scaling by a positive factor:
Lévy distribution is closed under addition:
Relationships to other distributions:
Lévy distribution is a special case of type 5 PearsonDistribution:
Lévy distribution is a transformation of a NormalDistribution:
With scale:
Lévy distribution is a StableDistribution:
LevyDistribution is not defined when is not a real number:
LevyDistribution is not defined when is not a positive real number:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
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