Suppose that we have an empirical distribution $f_X(x)$ which says $$P(X>1000) = 0.05$$ in any given unit time period. I.e. the exceedance probability of 1000 is $0.05$, so we would expect the event $X>1000$ to occur every $\frac{1}{0.05} = 20$ time periods
Suppose that now we observe using historic data of $X$ that the event $X>1000$ occurs twice in the last ten time periods. I am trying to test if this is statistically significant to question the empirical distribution which assumed that we would observe the event $X>1000$ 1 in every 20 time periods.
To put it into context, I'm looking at historical data and the time period is the number of years. The emperical distribution is for a one year time period and has $P(X>1000) = 0.05$, so we expect the event $X>1000$ to be a one-in-twenty year event. Looking at the past ten years of data, I see the event has occurred twice already, and in fact we have also observed a few 1-in-50 year events from the last ten years. I feel as though it is enough to question the emperical model, but I want to be able to say we can reject it with say a $95%$ percent confidence interval.
This answer is a bit of a stretch given such limited data. The data over the last $10$ years is likely more accurate/reliable in determining the actual distribution. However, the probability of getting two extreme $(.05)$ events in $10$ years is:
$p = \binom{10}{2}\cdot .05^2\cdot .95^8 = .074$
As $.074 > .05$, we fail to reject the null hypothesis as the result is not statistically significantly different.
A far more reliable method, assuming the distribution is normal, would be one that takes into account the mean and standard deviation of $10$ years of data instead of just $2$ extreme events.