R/dBellBX.R

In BGFD: Bell-G and Complementary Bell-G Family of Distributions

dBellBX<-function (x, a,lambda, log = FALSE)
{
  G=(1-exp(-x^2))^a
g=2*a*x*exp(-x^2)*(1-exp(-x^2))^(a-1)
  pdf <- x
  pdf[log == FALSE] <-lambda*g*exp(lambda*(1-G))*exp(-exp(lambda)*(1-exp(-lambda*G)))/(1-(exp(-exp(lambda)+1)))
  pdf[log == TRUE] <-log(lambda)+log(g)+(lambda*(1-G))-exp(lambda)*(1-exp(-lambda*G))-log((1-(exp(-exp(lambda)+1))))
  return(pdf)
}