greybox (version 0.6.4)

dbcnorm: Box-Cox Normal Distribution

Description

Density, cumulative distribution, quantile functions and random number generation for the distribution that becomes normal after the Box-Cox transformation. Note that this is based on the original Box-Cox paper.

Usage

dbcnorm(q, mu = 0, sigma = 1, lambda = 0, log = FALSE)
pbcnorm(q, mu = 0, sigma = 1, lambda = 0)
qbcnorm(p, mu = 0, sigma = 1, lambda = 0)
rbcnorm(n = 1, mu = 0, sigma = 1, lambda = 0)

Arguments

q

vector of quantiles.

mu

vector of location parameters (means).

sigma

vector of scale parameters.

lambda

the value of the Box-Cox transform parameter.

log

if TRUE, then probabilities are returned in logarithms.

p

vector of probabilities.

n

number of observations. Should be a single number.

Value

Depending on the function, various things are returned (usually either vector or scalar):

• dbcnorm returns the density function value for the provided parameters.

• pbcnorm returns the value of the cumulative function for the provided parameters.

• qbcnorm returns quantiles of the distribution. Depending on what was provided in p, mu and sigma, this can be either a vector or a matrix, or an array.

• rbcnorm returns a vector of random variables generated from the bcnorm distribution. Depending on what was provided in mu and sigma, this can be either a vector or a matrix or an array.

Details

The distribution has the following density function:

f(y) = y^lambda-1 1/sqrt(2 pi) exp(-((y^lambda-1)/lambda -mu)^2 / (2 sigma^2))

Both pbcnorm and qbcnorm are returned for the lower tail of the distribution.

In case of lambda=0, the values of the log normal distribution are returned. In case of lambda=1, the values of the normal distribution are returned with mu=mu+1.

All the functions are defined for non-negative values only.

References

• Box, G. E., & Cox, D. R. (1964). An Analysis of Transformations. Journal of the Royal Statistical Society. Series B (Methodological), 26(2), 211<U+2013>252. Retrieved from https://www.jstor.org/stable/2984418

Examples

# NOT RUN {
x <- dbcnorm(c(-1000:1000)/200, 0, 1, 1)
plot(c(-1000:1000)/200, x, type="l")

x <- pbcnorm(c(-1000:1000)/200, 0, 1, 1)
plot(c(-1000:1000)/200, x, type="l")

qbcnorm(c(0.025,0.975), 0, c(1,2), 1)

x <- rbcnorm(1000, 0, 1, 1)
hist(x)

# }