Assume I have a quantile function for an arbitrary probability distribution for random variable **x**. 


Would the **x**-value corresponding to the 99th percentile be the same as the **x**-value corresponding to a p-value of 0.01 (one-sided test, right tail)?


**Details for my specific problem:**
I have fitted a gamma distribution to some experimental data and I am trying to calculate p-values (one-sided) for extreme observations in the right tail of the distribution. Since I have learned model parameters for the gamma distribution, I was hoping that I could use `qgamma` in **R** to calculate cutoffs for a given p-value significance threshold. Is this a sane thing to do?



What is the relationship between quantile functions and p-values
First I'll address your initial question without taking into account the details of the specific problem. The answer is "yes" if, and only if, the probability distribution is that of a test statistic, where the null hypothesis will be rejected if the test statistic is too big.


When you get into the details of your specific problem you become unclear. When you say "fitted a gamma distribution to some experimental data", it sounds as if you've got a sample and you're estimating the two parameters. Maybe some of the data points will fall above the 99th percentile. If 1% of them do so, that doesn't sound like a reason to reject any null hypothesis that I can think of. If a substantial proportion of them do so, I'd wonder about your method of fitting. If you have a null hypothesis that says something about the values of the parameters, then there's the question of what you're going to use as a test statistic, and then there's the question of what is the probability distribution of that test statistic if the null hypothesis is true. You haven't told us enough about your specific problem to make any guesses about those things.


