dordbeta {ordbetareg}

Probability Density Function for the Ordered Beta Distribution

Description

This function will return the density of given variates of the ordered beta distribution conditional on values for the mean (mu), dispersion (phi) and cutpoints governing the ratio of degenerate (discrete) to continuous responses.

Usage

dordbeta(x = 0.9, mu = 0.5, phi = 1, cutpoints = c(-1, 1), log = FALSE)

Arguments

x

Variates of the ordered beta distribution (should be in the [0,1] interval).

mu

Value of the mean of the distribution. Should be in the \(0,1\) interval (cannot be strictly equal to 0 or 1). If length is greater than 1, should be of length x.

phi

Value of the dispersion parameter. Should be strictly greater than 0. If length is greater than 1, should be of length x.

cutpoints

A vector of two numeric values for the cutpoints. Second value should

log

where to return the log density be strictly greater than the first value.

Value

Returns a vector of length x of the density of the ordered beta distribution conditional on mu and phi.

Examples

# examine density (likelihood) of different possible values
# given fixed values for ordered beta parameters

x <- seq(0, 1, by=0.01)

x_dens <- dordbeta(x, mu = 0.3, phi=2, cutpoints=c(-2, 2))

# Most likely value for x is approx 1
# Note discontinuity in density function between continuous/discrete values
# density function is a combined PMF/PDF, so not a real PDF
# can though be used for MLE

plot(x_dens, x)

# discrete values should be compared to each other:
# prob of discrete 0 > prob of discrete 1

x_dens[x==0] > x_dens[x==1]