Description Usage Arguments Details Value Author(s) References See Also Examples
Density, distribution function, quantile function, and random number generation for the Levy distribution a.k.a alpha-stable distribution with index 1/2 and skewness 1.
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x,q |
vector of quantiles |
p |
vector of probabilities |
n |
number of samples to generate |
location |
the location parameter |
scale |
the scale parameter |
use.names |
Default is TRUE |
The Levy distribution is a special case of the alpha-stable distribution.
The density for the Levy distribution has the form
√(σ/(2*π)) * (x - μ)^(-(3/2)) * \exp(-(σ/(2*(x-μ))))
where μ is the location parameter and σ is the scale parameter.
It is supported on (μ, ∞). The distribution for the Levy distribution with location 0 has the form
F(x) = 2 * (1 - Φ(√(σ/x)))
.
Quantiles are found by solving F(x) = p.
Random numbers from the Levy distribution can be generated via the transformation σ Z^{-2} + μ, where Z is drawn from the standard normal distribution.
The Levy distribution will be evaluated at each point
in x
(or p
or q
). The output
will be an array whose dimensions are the given by the
lengths of x
, location
, and scale
.
Any dimension with length 1 will be dropped.
Christopher G. Green christopher.g.green@gmail.com
Samorodnitsky, Gennady and Taqqu, Murad S. (1994) Stable Non-Gaussian Random Processes, Chapman \& Hall / CRC, Boca Raton.
There is an implementation of the PDF, etc., of the
general alpha-stable distribution in the stabledist
package; see the dstable
, pstable
,
qstable
, and rstable
functions
in that package.
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