du.dist: U Shaped Distribution

In burrm/lolcat: Miscellaneous Useful Functions

U Shaped Distribution

Description

Calculate a U Shaped Distribution with support from -a to a. This is also the distribution of a harmonic oscillator.

Usage

du.dist(x, a = 1)

pu.dist(q, a = 1, lower.tail = T)

qu.dist(p, a = 1, lower.tail = T)

ru.dist(n, a = 1)

Arguments

x	Scalar - numeric - quantile.
a	Scalar - numeric - support for distribution (-a,a).
q	Scalar - numeric - quantile.
lower.tail	Scalar - logical - if true, probabilities are lower tail probabilities.
p	Scalar - numeric - probability.
n	Scalar - integer - number of observations.

Value

du.dist returns density function, pu.dist returns distribution function, qu.dist returns quantiles, and ru.dist returns random value(s).

References

Robinett, R.W. Quantum and classical probability distributions for position and momentum. Am. J. Phys. 63 (9) September 1995. pp 823-832.

Examples

## Example 1 - plot the distribution function 
# x <- seq(-1.9,1.9,.001)
# y <- du.dist(x, a=2)
# plot(x,y, type="l", col="blue", main="U Shaped Distribution", xlab="quantile", ylab="density)

burrm/lolcat documentation built on Aug. 15, 2024, 6:16 p.m.