# rhenery: Random generation under the Henery (or Harville) softmax... In ohenery: Modeling of Ordinal Random Variables via Softmax Regression

## Description

Given base probabilities, and Henery gamma coefficients, performs random generation, using R's built in rand seed, of the final outcome of a race for each participant.

## Usage

 1 rhenery(mu, gamma = NULL) 

## Arguments

 mu a vector of the probabilities of taking first place. gamma a vector of the gamma coefficients. Should have length one less than mu, but if longer the unused elements are ignored. If shorter, we reserve the right to either throw an error or extend out the last gamma element. If not given, the coefficients are assumed to be all one, which is the Harville model.

## Details

Given vectors μ and γ, first computes

π_{1,i} = \frac{μ_i^{γ_1}}{∑_j μ_j^{γ_1}},

then assigns a 1 to participant i with probability π_{1,i}. The ‘winning’ participant is then removed from consideration, and the process is repeated using the remaining μ and γ vectors.

Typically one has that μ_i = \exp{η_i}, for some ‘odds’, η_i.

When the γ are all one, you recover the Harville softmax model.

## Value

A vector, of the same length as the probabilities, giving the entry of each horse. Note that the expected value of this returned thing makes sense, it is not the finished rank ordering of a race.

## Author(s)

Steven E. Pav shabbychef@gmail.com

rsm