An algorithm to test divisibility of continuous distributions, applied to the uniform distribution

Abstract

We present an algorithm to test if a continuous random variable is n-divisible. Through the algorithm, testing for divisibility is put in the format of numerical analysis amenable to computer processing. This is illustrated with the uniform distribution which is known to be non-divisible. New evidence and new proofs arising out of the insight developed with this style are given. This algorithm, along with the analytical methods should provide much needed versatility to tackle problems in this area. The fact that Bondesson [1987] works on the divisibility of the Half Cauchy Distribution gives evidence that there are many distributions which can use the combination of the analytical and the algorithmic tools to settle the divisibility issue.

Keywords:

• Divisibility
• Inverse Fourier
• Branch