Authors

• Gholamreza Hesamian ¹
• Farid Bahrami ²

¹ Department of Statistics, Payame Noor University, Tehran, Iran.

² Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran.

Abstract

This paper considers an extension of probability space based on interval random variables. In this approach, first, a notion of interval random variable is introduced. Then, based on a family of continuous distribution functions with interval parameters, a concept of probability space of an interval random variable is proposed. Then, the mean and variance of an interval random variable are introduced. The presented theoretical results will be illustrated with some lemmas. Some numerical examples will be used to show the performance of the proposed method.

Keywords

• Interval mean
• interval parameter
• interval random variable
• probability space
• variance of an interval random variable