There’s no new content here, just a little editing and more formal language. But now it can be referenced in a scholarly publication.
More random inequalities
I recently had a project that needed to compute random inequalities comparing common survival distributions (gamma, inverse gamma, Weibull, log normal) to uniform distributions. Here’s a report of the results.
Random inequalities between survival and uniform distributions
This tech report develops analytical solutions for computing Prob(X > Y) where X and Y are independent, X has one of the distributions mentioned above, and Y is uniform over some interval. The report includes R code to carry out the analytic expressions. It also includes R code to estimate the same inequalities by sampling for complementary validation.
Here are some other tech reports and blog posts on random inequalities.