pvii: The Pearson Type VII (PVII) Distribution

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

Density and random generation functions for the Pearson Type VII (PVII) distribution.

Usage

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dpvii(x, mean, scale, shape, log=FALSE)
rpvii(n, mean, scale, shape)

Arguments

x

a numeric vector of observations.

mean

mean parameter (real number).

scale

scale parameter (positive real number).

shape

shape parameter (positive real number).

log

logical; if TRUE, density is given as the log-density.

n

number of observations to simulate.

Details

The PVII distribution, a generalization of the t-distribution, arises when the inverse of the variance of a normal random variable is itself a random variable with the gamma distribution. See Sun et al. (2010) for details. See mvpvii for the multivariate density which easily reduces to the univariate version.

Value

For dpvii, a vector of densities. For rpvii, a vector of length n representing a sample from the PVII distribution with the specified parameters.

Author(s)

Daniel Dvorkin

References

Sun, J., Kaban, A., and Garibaldi, J.M. (2010) Robust mixture clustering using Pearson Type VII distribution. Pattern Recognition Letters 31(16), 2447–2454.

See Also

mvpvii for the multivariate version; thetahat for parameter estimation.

Examples

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set.seed(123)
mu <- 1
Sigma <- 3
alpha <- 2
x <- rpvii(5, mu, Sigma, alpha)
x
# [1]  1.8452349 -0.2040292 -2.1309664  0.4013371  2.0181986
dpvii(x, mu, Sigma, alpha)
# [1] 0.23112248 0.17824559 0.02719683 0.26484673 0.20555914


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