Box-Cox {rmutil} R Documentation

## Box-Cox Distribution

### Description

These functions provide information about the Box-Cox distribution with location parameter equal to `m`, dispersion equal to `s`, and power transformation equal to `f`: density, cumulative distribution, quantiles, log hazard, and random generation.

The Box-Cox distribution has density

f(y) = 1/sqrt(2 pi s^2) exp(-((y^f/f - mu)^2/(2 s^2)))/ (1-I(f<0)-sign(f)*pnorm(0,m,sqrt(s)))

where m is the location parameter of the distribution, s is the dispersion, f is the family parameter, I() is the indicator function, and y>0.

f=1 gives a truncated normal distribution.

### Usage

```dboxcox(y, m, s=1, f=1, log=FALSE)
pboxcox(q, m, s=1, f=1)
qboxcox(p, m, s=1, f=1)
hboxcox(y, m, s=1, f=1)
rboxcox(n, m, s=1, f=1)
```

### 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 dispersion parameters. `f` vector of power parameters. `log` if TRUE, log probabilities are supplied.

### Author(s)

J.K. Lindsey

`dnorm` for the normal or Gaussian distribution.
```dboxcox(2, 5, 5, 2)