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

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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.

Author(s)

J.K. Lindsey

See Also

dnorm for the normal or Gaussian distribution.

Examples

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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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