parameter estimates for tidy_burr()

[spsanderson]

library(TidyDensity)

data <- tidy_burr(.shape1 = 1, .shape2 = 2, .rate = 3)$y

blik <- function(theta,x){
  c <- exp(theta[1])
  k <- exp(theta[2])
  mu <- 0
  sigma <- exp(theta[3])
  bll <- actuar::dburr(x, c, k, mu, sigma)
  return(-sum(log(bll)))  
}

brmod <- optim(c(.shape1 = 0, 
                 .shape2 = 0, 
                 .scale = 0), 
               fn = blik,
               x = data)
> exp(brmod$par)
  .shape1   .shape2    .scale 
1.0130505 2.0605886 0.2967962