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rmutil (version 1.1.4)

Box-Cox: 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 $$ f(y) = \frac{1}{\sqrt{2 \pi \sigma^2}} \exp(-((y^\nu/\nu-\mu)^2/(2 \sigma^2)))/ (1-I(\nu<0)-sign(\nu)*pnorm(0,\mu,sqrt(\sigma)))$$ where \(\mu\) is the location parameter of the distribution, \(\sigma\) is the dispersion, \(\nu\) is the family parameter, \(I()\) is the indicator function, and \(y>0\).

\(\nu=1\) 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)
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.

See Also

dnorm for the normal or Gaussian distribution.

Examples

Run this code
# NOT RUN {
dboxcox(2, 5, 5, 2)
pboxcox(2, 5, 5, 2)
qboxcox(0.1, 5, 5, 2)
rboxcox(10, 5, 5, 2)
# }

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