evd (version 1.2-3)

bvneglog: The Bivariate Negative Logistic Model

Description

Density, distribution function and random generation for the bivariate negative logistic model.

Usage

dbvneglog(x, dep, mar1 = c(0, 1, 0), mar2 = mar1, log = FALSE) 
pbvneglog(q, dep, mar1 = c(0, 1, 0), mar2 = mar1) 
rbvneglog(n, dep, mar1 = c(0, 1, 0), mar2 = mar1)

Arguments

x, q

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

n

Number of observations.

dep

Dependence parameter.

mar1, mar2

Vectors of length three containing marginal parameters, or matrices with three columns where each column represents a vector of values to be passed to the corresponding marginal parameter.

log

Logical; if TRUE, the log density is returned.

Value

• dbvneglog gives the density, pbvneglog gives the distribution function and rbvneglog generates random deviates.

Details

The bivariate negative logistic distribution function with parameter $\code{dep} = r$ is $$G(z_1,z_2) = \exp\left{-y_1-y_2+ [y_1^{-r}+y_2^{-r}]^{-1/r}\right}$$ where $r > 0$ 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 $i = 1,2$, where the marginal parameters are given by $\code{mari} = (a_i,b_i,s_i)$, $b_i > 0$. If $s_i = 0$ then $y_i$ is defined by continuity. This is a special case of the bivariate asymmetric negative logistic model. The univariate marginal distributions are generalized extreme value.

Independence is obtained in the limit as $r$ approaches zero. Complete dependence is obtained as $r$ tends to infinity. The earliest reference to this model appears to be Galambos (1975, Section 4).

References

Galambos, J. (1975) Order statistics of samples from multivariate distributions. J. Amer. Statist. Assoc., 70, 674--680.

See Also

abvneglog, rbvaneglog, rgev

Examples

dbvneglog(matrix(rep(0:4,2),ncol=2), 1.2)
pbvneglog(matrix(rep(0:4,2),ncol=2), 1.2)  
rbvneglog(10, 1.2)