priornu: Discretized Juarez-Steel and Villa-Walker priors on degrees...
In twopiece: The family of two piece distributions

Description Usage Arguments Details Value References Examples

priornuJS evaluates the Juarez-Steel prior, priornuVW the Villa-Walker prior (in the particular case of location parameter equal to 0). In both cases the prior is discretized, i.e. only consider integer values for the degrees of freedom.

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priornuJS(nu,k=2.78,numax=30)

priornuVW(nu,numax=30)

`nu`	Values of the degrees of freedom
`k`	Parameter of the Juazer-Steel prior, see details
`numax`	Maximum value of nu, i.e. nu is restricted to take values between 1 and numax

The Juarez-Steel prior is proportional to k*nu/(nu+k)^3.

The Villa-Walker prior is proportional to

(log(nu+1)-log(nu))/2 + lbeta(0.5,(nu+1)/2) - lbeta(0.5,nu/2) - 0.5*(nu+1)*int1 + 0.5*(nu+2)*int2

where f1= E(log(1+x^2/nu)), f2= E(log(1+x^2/(nu+1))) and x follows a standard t with nu degrees of freedom.

Vector with prior probabilities evaluated at nu

M.A. Juarez and M.F.J. Steel. Model-based clustering of non-Gaussian panel data based on skew-t distributions. Journal of Business and Economic Statistics, 28(1):52-66, 2010

C. Villa and S. Walker. Objective prior for the number of degrees of freedom of a t distribution. Bayesian analysis, 9(1):197-200, 2014.

library(twopiece)

nuseq <- 1:30
plot(nuseq, priornuJS(nuseq,k=1.2,numax=30), ylab='Prior density', xlab=expression(nu), cex.lab=1.2)
points(nuseq, priornuVW(nuseq,numax=30), col='grey', pch=16)
legend('topright',c('Juarez-Steel (k=1.2)','Villa-Walker'),pch=c(1,16),col=c('black','grey'), cex=1.25)