# Simplex: Simplex Distribution In rmutil: Utilities for Nonlinear Regression and Repeated Measurements Models

 Simplex R Documentation

## Simplex Distribution

### Description

These functions provide information about the simplex distribution with location parameter equal to `m` and shape equal to `s`: density, cumulative distribution, quantiles, and random generation.

The simplex distribution has density

f(y) = exp(-((y-m)/(m(1-m)))^2/(2y(1-y)s))/sqrt(2 pi s(y(1-y))^3)

where m is the location parameter of the distribution and s is the shape, and 0<y<1.

### Usage

```dsimplex(y, m, s, log=FALSE)
psimplex(q, m, s)
qsimplex(p, m, s)
rsimplex(n, m, s)
```

### Arguments

 `y` vector of responses. `q` vector of quantiles. `p` vector of probabilities `n` number of values to generate `m` vector of location parameters. `s` vector of shape parameters. `log` if TRUE, log probabilities are supplied.

### Author(s)

J.K. Lindsey

`dbeta` for the beta distribution and `dtwosidedpower` for the two-sided power distribution, other distributions for proportions between zero and one.

### Examples

```dsimplex(0.3, 0.5, 1)
psimplex(0.3, 0.5, 1)
qsimplex(0.1, 0.5, 1)
rsimplex(10, 0.5, 1)
```

rmutil documentation built on Oct. 29, 2022, 1:08 a.m.