sev: The Smallest Extreme Value Distribution

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

Description

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

Usage

qsev(p, loc = 0, scale = 1)

psev(q, loc = 0, scale = 1)

dsev(x, loc = 0, scale = 1)

rsev(n, loc = 0, scale = 1)

ssev(x, loc = 0, scale = 1)

Arguments

p	Vector of probabilities
loc	Location parameter
scale	Scale parameter
q	Vector of quantiles
x	Vector of quantiles
n	Number of observations

Details

If loc is not specified, a default value of 0 is used. If scale is not specified, a default value of 1 is used.

The smallest extreme value distribution with location parameter μ and scale σ has density

f(x;μ,σ) = \frac{1}{σ}φ_{_{SEV}}≤ft(\frac{x-μ}{σ}\right),\quad -∞ < x < ∞

where φ_{_{SEV}}(z) exp[z - exp(z)] is the density of the standard LEV distribution.

Value

dsev gives the density, psev gives the distribution function, qsev gives the quantile function, and rsev generates random observations.

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

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