evd (version 1.2-3)

mvlog: The Multivariate Logistic Model

Description

Distribution function and random generation for the multivariate logistic model.

Usage

pmvlog(q, dep, d = 2, mar = c(0, 1, 0)) 
rmvlog(n, dep, d = 2, mar = c(0, 1, 0))

Arguments

q

A vector of length d or a matrix with d columns, in which case the distribution is evaluated across the rows.

n

Number of observations.

dep

Dependence parameter.

d

Dimension.

mar

A vector of length three containing marginal parameters for every univariate margin, or a matrix with three columns where each column represents a vector of values to be passed to the corresponding marginal parameter on every univariate margin

Value

• pmvlog gives the distribution function and rmvlog generates random deviates.

Details

Let $z = (z_1,z_2,\ldots,z_d)$. The d dimensional multivariate logistic distribution function (Gumbel, 1960) with parameter $\code{dep} = r$ is $$G(z) = \exp\left[-(y_1^{1/r}+\ldots+y_d^{1/r})^r\right]$$ where $0 < r \leq 1$ and $$y_i = {1+s_i(z_i-a_i)/b_i}^{-1/s_i}$$ for $1+s_i(z_i-a_i)/b_i > 0$ and $i = 1,\ldots,d$. Different parameters on each margin are not implemented, so $\code{mar} = (a_i,b_i,s_i)$ for every $i$. If $s_i = 0$ then $y_i$ is defined by continuity. This is a special case of the multivariate asymmetric logistic model. The univariate marginal distributions are generalized extreme value.

References

Gumbel, E. J. (1960) Distributions des valeurs extremes en plusieurs dimensions. Publ. Inst. Statist. Univ. Paris, 9, 171--173. Kotz, S. and Balakrishnan, N. and Johnson, N. L. (2000) Continuous Multivariate Distributions, vol. 1. New York: John Wiley & Sons, 2nd edn. Stephenson, A. G. (2002) Simulating multivariate extreme value distributions of logistic type. To be published - available on request.

See Also

rbvlog, rmvalog, rgev

Examples

pmvlog(matrix(rep(0:4,5), ncol=5), .7, d = 5)
pmvlog(rep(4,5), .7, d = 5)
rmvlog(10, .7, d = 5)