rmutil (version 1.1.4)

Two-Sided Power: Two-Sided Power Distribution

Description

These functions provide information about the two-sided power distribution with location parameter equal to m and shape equal to s: density, cumulative distribution, quantiles, and random generation.

The two-sided power distribution has density $$ f(y) = s(\frac{y}{m})^{s-1}, y<=m$$ $$ f(y) =s(\frac{1-y}{1-m})^{s-1}, y>=m$$ where \(\mu\) is the location parameter of the distribution and \(\sigma\) is the shape, and \(0<y<1\).

For \(\sigma=1\), this is the uniform distribution and for \(\sigma=2\), it is the triangular distribution.

Usage

dtwosidedpower(y, m, s=2, log=FALSE)
ptwosidedpower(q, m, s=2)
qtwosidedpower(p, m, s=2)
rtwosidedpower(n, m, s=2)

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 shape parameters.

log

if TRUE, log probabilities are supplied.

References

van Dorp, J.R. and Kotz, S. (2002) A novel extension of the triangular distribution and its parameter estimation. The Statistician 51, 63-79.

See Also

dbeta for the beta distribution and dsimplex for the simplex distribution, other distributions for proportions between zero and one.

Examples

# NOT RUN {
dtwosidedpower(0.3, 0.5, 3)
ptwosidedpower(0.3, 0.5, 3)
qtwosidedpower(0.1, 0.5, 3)
rtwosidedpower(10, 0.5, 3)
# }