Probability density function for the beta prime distribution (aka. inverse Beta)

Probability density function for the beta prime distribution (aka. inverse Beta)

Usage

dbetaprime(x, mu, phi, log = FALSE)

Source

Bases on Bourguignon, M., Santos-Neto, M., & de Castro, M. (2018). A new regression model for positive data (https://arxiv.org/abs/1804.07734)

Arguments

x

Value, x > 0.

mu

Mean, mu > 0.

phi

Precision, phi > 0.

log

Optional argument. If true, returns the log density.

Value

Density of the pdf given x, mu and phi.

Details

The beta prime distribution has density $$f(y) = \frac{y^{(\mu(\Phi+1)-1)} (1+y)^{(-(\mu(\Phi+1)+\Phi+2))}} {\Beta(\mu(1+\Phi), \Phi +2)}$$

With the usual beta prime parameters $$\beta = \Phi + 2, \alpha = \mu(\Phi + 1)$$

Examples

x <- seq(from = 0.1, to = 20, length.out = 1000)
plot(x, dbetaprime(x, mu = 4, phi = 2), type = "l")