SDistribution function

S Distribution

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

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.

Returns

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.

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.

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)

See Also

Distributions

Author(s)

Ivan Svetunkov, ivan@svetunkov.com