logisticnormal: Functions for the logistic normal distribution

In aeggers/pivotprobs: Methods for estimating the probability of ties and other important election events.

Functions for the logistic normal distribution

Description

Functions to compute the density of or generate random deviates from the logistic normal distribution.

Usage

rlogisticnormal(n, mu, sigma)

dlogisticnormal(x, mu, sigma, tol = 1e-10)

Arguments

n	Number of random vectors to generate
mu	Vector of expectations (pre-logistic transformation). One value must be zero, and it must correspond to the row/column of sigma that is also all zeros.
sigma	Matrix of covariances (pre-logistic transformation). There must be a j such that sigma[j,] and sigma[,j] are all zeros, and mu[j] must also be zero.
x	A vector containing one random deviate (i.e. one )
tol	dlogisticnormal returns zero if the sum of x is further than tol away from 1.

Details

The logistic normal distribution arises when we draw from a multivariate normal distribution and then apply the logistic transformation to the resulting draws. It has been described as the Gaussian on the unit simplex. It allows for more flexible forms of dependence among the components than the better-known Dirichlet distribution.

In this parameterization, exactly one element of the random vector must be fixed at zero, i.e. mean zero with zero variance and zero covariance with other elements of the vector. Other parameterizations leave this element out of the multivariate draw. The reason for including it here is that we can then reshuffle the parameters as we cycle through e.g. pairs of candidates.

Examples

mu <- c(.1, -.1, 0)
sigma <- rbind(c(.25, .05, 0),
               c(.05, .15, 0),
               c(0, 0, 0))
rlogisticnormal(10, mu = mu, sigma = sigma)
dlogisticnormal(rbind(c(.4, .35, .25), c(.3, .5, .2)), mu = mu, sigma = sigma)

aeggers/pivotprobs documentation built on Oct. 28, 2024, 9:46 a.m.