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)
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.
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.