A Note on the Sum of Continuous Uniform Distributions

Abstract

This article will show the probability distribution function of the sum of general independent continuous uniform distributions. Although the probability distribution function of the sum of independent continuous uniform distributions over the same interval (0, 1) is known, it cannot be generalized to the probability distribution function of the sum of general independent continuous uniform distributions over unlike intervals. In this article the key point of the derivation process is the application of convolution formula.

Keywords:

• differential
• continuous uniform distribution
• probability distribution function
• convolution formula
• characteristic function