Either I haven’t seen this before, or forgot it, but it’s surprising because I use the sum of independent uniform variables every once in a while — the sum of two vars is a tent function, the sum of three is a smooth piecewise quadratic lump, and the sum of many tends toward a normal distribution. And the distribution is easy calculated as the convolution of the input box functions (uniform variables). Looking it up just now I learned the sum of uniform variables is called an Irwin-Hall distribution (aka uniform sum distribution).
The min of two random vars has the opposite effect as the max does in this video. And now I’m curious - if we use the function definition of min/max — the nth root of the sum of the nth powers of the arguments — there is a continuum from min to sum to max, right? Are there useful applications of this generalized distribution? Does it already have a name?
The min of two random vars has the opposite effect as the max does in this video. And now I’m curious - if we use the function definition of min/max — the nth root of the sum of the nth powers of the arguments — there is a continuum from min to sum to max, right? Are there useful applications of this generalized distribution? Does it already have a name?