Nonexistence in power and gamma density regression, sum of nonnegative terms

Abstract

When we use the power function a(c+x)b and gamma density axbe-cx to fit the data by the least squares method, we have to address the question of existence. The closure of the set of each type of these functions defined on a finite domain is determined.

We derive a way to determine the closure of a sum of nonnegative functions if the closures of the summands are available.

Keywords

• Nonexistence
• power
• gamma
• density
• regression
• nonnegative
• terms