In kravitz-eli/prssMixture: What the Package Does (One Line, Title Case)

The arcsine distribution is a possible non-informative prior for $\rho$ if $\rho = 0$ is not okay. This would be assuming both variances are fixed, which I think is fine in a noninformative prior.

arc_sine_dist <- function(x, a, b) {

  (pi * sqrt((x - a) * (b - x))) ^ -1
}


curve(
  arc_sine_dist(x, -1, 1), 
  from = -1, 
  to = 1, 
  lwd = 3,
  main = "PDF of Arcine Prior for Correlation",
  xlab = "rho",
  ylab = "f(rho)"
)

I can't find a closed form for the mean. I think it should be 0 so let's confirm. I manually inverted the CDF from wikipedia: https://en.wikipedia.org/wiki/Arcsine_distribution

Not correct. Not sure why

library(magrittr)

inverse_arc_sin = function(q, a, b){

  # (b - a) * sin(pi / 2 * q)^2 + a

  (a^2 - a * b - sin(pi / 2 * q)^2) / (a - b)

}
# See if plot of pdf looks reasonable
curve(inverse_arc_sin(x, -1, 1), -1, 1, lwd = 3)