################################################################
#This returns a dataframe with the columns
##Int -- cells with 0, 1, 2, etc.
##Freq -- total sample size in that count
##PoisF -- the total count expected via the Poisson distribution
##ResidF -- the residual between Freq and PoisF (count scale)
##Prop -- proportion of the sample with that integer value
##PoisD -- the proportion expected via the Poisson distribution
##ResidD -- residual between Prop and PoisD (proportion scale)
CheckPoisson <- function(counts,min_val,max_val,pred){
   freqN <- as.data.frame(table(factor(counts,levels=min_val:max_val)))
   mu <- pred #mean(counts)
   if(length(mu) == 1){
	print( paste0('mean: ', mean(counts)) )
	print( paste0('variance: ',var(counts)) )
      PoisD <- dpois(min_val:max_val,mu)
   }
   else{
      PoisD <- min_val:max_val
	  n <- length(counts)
	  for (i in 1:length(PoisD)){
	      PoisD[i] <- sum(dpois(PoisD[i],mu))/n
	  }
   } 
   freqN$PoisF <- PoisD*length(counts)
   freqN$ResidF <- (freqN$Freq  - freqN$PoisF)
   freqN$Prop <- (freqN$Freq/sum(freqN$Freq))*100
   freqN$PoisD <- PoisD*100
   freqN$ResidD <- (freqN$Prop - freqN$PoisD)
   freqN$Var1 <- as.numeric(as.character(freqN$Var1))
   names(freqN)[1] <- 'Int'
   return(freqN)   
}
################################################################

##Example use for constant over the whole sample
#set.seed(10)
#lambda <- 0.2
#x <- rpois(10000,lambda)
#CheckPoisson(x,0,max(x),mean(x))
#82% zeroes is not zero inflated -- expected according to Poisson!

##Example use if you have varying predictions, eg after Poisson regression
#n <- 10000
#ru <- runif(n,0,10)
#x <- rpois(n,lambda=ru)
#CheckPoisson(x, 0, 23, ru)


######################
#ToDo, this for negative binomial fit
######################