bisa: The Birmbaum-Saunders Distribution

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

Description

Density, distribution function, quantile function and random generation for the BISA distribution with location loc and scale scale.

Usage

qbisa(p, shape, scale = 1)

pbisa(q, shape, scale = 1)

dbisa(x, shape, scale = 1)

rbisa(n, shape, scale = 1)

Arguments

p	Vector of probabilities
shape	Shape parameter
scale	Scale parameter
q	Vector of quantiles
x	Vector of quantiles
n	Number of observations

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

dbisa gives the density, pbisa gives the distribution function, qbisa gives the quantile function, and rbisa generates random observations.

The length of the result is determined by n for rbisa, 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.