Ordered Probability Mass Function

TL;DR

This paper introduces the ordered probability mass function, a novel method for evaluating sequences of positive numbers by minimizing variance and distinguishing sequences statistically.

Contribution

It presents the ordered probability mass function as a new tool for sequence analysis and score evaluation, enhancing statistical differentiation.

Findings

The ordered probability mass function can identify sequences with smaller variance.

It effectively distinguishes between different sequences of positive numbers.

The method provides a new approach for score evaluation and statistical analysis.

Abstract

Suppose that in the four tests Alice's scores are 90, 95, 85, 90, and Bob's scores are 85, 95, 90, 90. How to evaluate their scores? In this paper, we introduce the concept of ordered probability mass function which can be used to find a probability mass function with smaller variance. More interestingly, we can use it to distinguish sequences of positive numbers statistically.