dlaplace {greybox}

Laplace Distribution

Description

Density, cumulative distribution, quantile functions and random number generation for the Laplace distribution with the location parameter mu and the scale parameter (which is equal to Mean Absolute Error, aka Mean Absolute Deviation).

Usage

dlaplace(q, mu = 0, scale = 1, log = FALSE)

plaplace(q, mu = 0, scale = 1)

qlaplace(p, mu = 0, scale = 1)

rlaplace(n = 1, mu = 0, scale = 1)

Arguments

q

vector of quantiles.

mu

vector of location parameters (means).

scale

vector of mean absolute errors.

log

if TRUE, then probabilities are returned in logarithms.

p

vector of probabilities.

n

number of observations. Should be a single number.

Details

When mu=0 and scale=1, the Laplace distribution becomes standardized. The distribution has the following density function:

f(x) = 1/(2 scale) exp(-abs(x-mu) / scale)

Both plaplace and qlaplace are returned for the lower tail of the distribution.

Value

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

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

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

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

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

Author(s)

Ivan Svetunkov, [e-mail]

References

• Wikipedia page on Laplace distribution: https://en.wikipedia.org/wiki/Laplace_distribution.

See Also

Distributions

Examples

x <- dlaplace(c(-100:100)/10, 0, 1)
plot(x, type="l")

x <- plaplace(c(-100:100)/10, 0, 1)
plot(x, type="l")

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

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