asynorm {dirttee} R Documentation

## The asymmetric normal distribution.

### Description

Density, distribution function, quantile function and random generation for the asymmetric normal distribution with the parameters mu, sigma and tau.

### Usage

dasynorm(x, mu = 0, sigma = 1, tau = 0.5)
pasynorm(q, mu = 0, sigma = 1, tau = 0.5)
qasynorm(p, mu = 0, sigma = 1, tau = 0.5)
rasynorm(n, mu = 0, sigma = 1, tau = 0.5)


### Arguments

 q vector of quantiles. mu location parameter and mode of the distribution. sigma comparable to the standard deviation. Must be positive. tau asymmetry parameter. x vector of locations. p vector of probabilities. n number of observations. If length(n) > 1, the length is taken to be the number required.

### Details

The asymmetric normal distribution has the following density
f(x) = (2\sqrt{\tau(1-\tau)/\pi}/\sigma)/(\sqrt{1-\tau} + \sqrt{\tau)}\exp(-|(\tau - (x <= \mu))|*(x - \mu)^2/\sigma^2) The cdf is derived by integration of the distribution function by using the integrate function.

### Value

dasynorm gives the density, pasynorm gives the distribution function, qasynorm gives the quantile function, and rasynorm generates random deviates.

Corresponds to the normal distribution for \tau = 0.5.

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

### Examples


hist(rasynorm(1000))

qg <- qasynorm(0.1, 1, 2, 0.5)

pasynorm(qg, 1, 2, 0.5)

ax <- c(1:1000)/100-5
plot(ax,dasynorm(ax), type = 'l')


[Package dirttee version 1.0.1 Index]