**Soft maximum**

I had a request to turn my blog posts on the soft maximum into a tech report, so here it is:

Basic properties of the soft maximum

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.

I had my students implement a 2-arg softmax procedure while learning Scheme a homework or two ago, and then consider how to make it variable arity. They noticed that different implementations give different answers, but remarkably similar.

John,

The first line of the second page of the soft maximum paper says ‘This report call’ instead of ‘This report calls’. Love the blog though!

Nick