besselexp: Bessel exponential distribution

In keesmulder/flexcircmix: Fit Mixtures of Flexible Circular Distributions

Description

Functions for the Bessel exponential distribution. This is the conditional posterior distribution of the concentration parameter kappa of a von Mises distribution with conjugate prior. The random generation algorithm is due to Forbes and Mardia (2015).

Usage

dbesselexp(kp, eta = 1, g = -0.5, log = FALSE)

dbesselexpkern(kp, eta, g, log = FALSE)

rbesselexp(n, eta, g)

Arguments

kp	Numeric; value of kappa to evaluate.
eta	Integer; This is the posterior sample size, which is n + c where c is the number of observations contained in the conjugate prior. For uninformative, c = 0 and eta = n.
g	Numeric; Should be -R*cos(mu-theta_bar)/eta, where R is the posterior mean resultant length, and theta_bar is the posterior mean, while mu is the current value of the mean. Note that this parameter is called β_0 in Forbes and Mardia (2015).
log	Logical; Whether to return the log of the result.
n	Integer; number of generated samples.

Value

For dbesselexp and dbesselexpkern, a scalar. For rbesselexp, a vector of random variates from the distribution.

Functions

• dbesselexp: Probability density function.

• dbesselexpkern: Kernel (unnormalized version) of the pdf.

• rbesselexp: Random generation.

Examples

dbesselexp(2, 20, -.5)
plot(density(rbesselexp(100, 20, -.5)), xlim = c(0, 5))

# Plot probability density function
dbesexpfun <- Vectorize(function(x) dbesselexp(x, 20, -.5))
curve(dbesexpfun, 0, 5)

# Compare with density of random draws
plot(density(rbesselexp(1000, 20, -.5)), xlim = c(0, 5))

keesmulder/flexcircmix documentation built on May 29, 2019, 3:02 a.m.