# Equation for Inverse Poisson CDF

I am attempting to calculate quantile probabilities. I.e., the value above which there is only a 1% chance occurrence for an arrival process.

The R code is pretty straight forward with say a lambda = 2. qpois(.99, 2, lower.tail = TRUE, log.p = FALSE)

But what is the inverse Poisson CDF equation?

• The help page for qpois explains the algorithm. It necessarily involves a numerical search. – whuber Aug 8 '17 at 14:30
• @whuber That's interesting; I'd have assumed the quickest way would would be to use the relationship with the chi-square (and hence call an inverse incomplete gamma routine). Not having worked it through I'm probably missing something obvious though. – Glen_b Aug 9 '17 at 3:16
• @glen The Gamma shape parameter is varied in the search. – whuber Aug 9 '17 at 3:47