Probability density function for the generalized_normal distribution
Usage
dgeneralized_normal(x, mu, sigma, beta, log = FALSE)
Arguments
- x
Value, unbound
- mu
Mean, unbound
- sigma
Scale, sigma > 0
- beta
shape, beta > 0
- log
Optional argument. If true, returns the log density.
Value
Density of the pdf given x, mu and sigma
Details
The generalized_normal distribution has density
$$f(y | \mu, \sigma, \beta) = \frac{\beta}{2 \beta \Gamma(1/\beta)}exp(-|z|^\beta)$$
Where z is the linear transformation
$$z(y, \mu, \sigma) = \frac{y - \mu}{\sigma}$$
Examples
x <- seq(from = -5, to = 10, length.out = 1000)
plot(x, dgeneralized_normal(x, mu = 1, sigma = 1, beta = 0.5), type = "l")
