R/hCBellB.R

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

hCBellB<-function (x, a, b, k, lambda, log = FALSE,log.p = FALSE, lower.tail = TRUE) 
{
G=(1-((1+(x/a)^b))^(-k))
g=k*((1+(x/a)^b))^(-k-1) *b*x^(b-1)*a^(-b)

  pdf <- x
  pdf[log == FALSE] <- lambda*g*exp(lambda*G)*exp(exp(lambda*G)-1)/(exp(exp(lambda)-1)-1)
  pdf[log == TRUE] <- log(lambda)+log(g)+(lambda*G)+(exp(lambda*G)-1)-log((exp(exp(lambda)-1)-1))

  
  cdf <- x
  cdf[log.p == FALSE & lower.tail == TRUE] <-  (exp(exp(lambda*G)-1)-1)/(exp(exp(lambda)-1)-1)        
  cdf[log.p == TRUE & lower.tail == TRUE]  <-  log(exp(exp(lambda*G)-1)-1)-log(exp(exp(lambda)-1)-1)  
  cdf[log.p == FALSE & lower.tail == FALSE] <- (exp(exp(lambda)-1)-exp(exp(lambda*G)-1))/((exp(exp(lambda)-1)-1))  
  cdf[log.p == TRUE & lower.tail == FALSE] <-  log(exp(exp(lambda)-1)-exp(exp(lambda*G)-1))-log((exp(exp(lambda)-1)-1))
  
  hrf<-pdf/(1-cdf)
  return(hrf)
}