ds {greybox}

S Distribution

Description

Density, cumulative distribution, quantile functions and random number generation for the S distribution with the location parameter mu and a scaling parameter scale.

Usage

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

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

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

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

Arguments

q

vector of quantiles.

mu

vector of location parameters (means).

scale

vector of scaling parameter (which are equal to ham/2).

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 ham=2, the S distribution becomes standardized with scale=1 (this is because scale=ham/2). The distribution has the following density function:

f(x) = 1/(4 scale^2) exp(-sqrt(abs(x-mu)) / scale)

The S distribution has fat tails and large excess.

Both ps and qs are returned for the lower tail of the distribution.

Value

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

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

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

• qs 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.

• rs returns a vector of random variables generated from the S 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]

See Also

Distributions

Examples

x <- ds(c(-1000:1000)/10, 0, 1)
plot(x, type="l")

x <- ps(c(-1000:1000)/10, 0, 1)
plot(x, type="l")

qs(c(0.025,0.975), 0, 1)

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