beta4: The Four Parameter Beta Distribution

In teachingApps: Apps for Teaching Statistics, R Programming, and Shiny App Development

Description

Density, distribution function, quantile function and random generation for the four parameter Beta distribution with minimum value min and scale scale.

Usage

dbeta4(x, min, max, shape1, shape2, gap = 0)

pbeta4(q, min, max, shape1, shape2, gap = 0)

qbeta4(p, min, max, shape1, shape2)

rbeta4(n, min, max, shape1, shape2, seed = 42)

Arguments

x	Vector of quantiles
min	The minumum value on which the distribution is defined
max	The maximum value on which the distribution is defined
shape1	Shape parameter
shape2	Shape parameter
gap	Spacing from min and max
q	Vector of quantiles
p	Vector of probabilities
n	Number of observations
seed	A numeric value for the seed of the random number generator

Details

If shape is not specified, a default value of 1 is used.

The Birmbaum-Saunders distribution with shape β and scale θ has density

f(x;θ,β) = \frac{√{\frac{x}{θ}}+√{\frac{θ}{x}}}{2β x}φ_{_{NOR}(z)},\quad x ≥ 0

where φ_{_{NOR}}(z) is the density of the standard normal distribution and

z = \frac{1}{β}≤ft(√{\frac{x}{θ}}-√{\frac{θ}{x} } \right)

.

Value

dbeta4 gives the density, pbeta4 gives the distribution function, qbeta4 gives the quantile function, and rbeta4 generates random observations.

The length of the result is determined by n for rbeta4, and is the maximum of the lengths of the numerical arguments for the other functions.

The numerical arguments other than n are recycled to the length of the result.

Source

Birnbaum, Z. W.; Saunders, S. C. (1969), "A new family of life distributions", Journal of Applied Probability, 6 (2): 319–327, JSTOR 3212003, doi:10.2307/3212003

teachingApps documentation built on July 1, 2020, 5:58 p.m.