Boundary conditions for similarity Index

TL;DR

This paper investigates the boundary conditions of the Bray-Curtis similarity index, identifying the numerical ranges where the formula becomes ineffective, through simulation of normally distributed data across various fields.

Contribution

It establishes the effective numerical range for the Bray-Curtis similarity index, providing guidelines for its appropriate application in different contexts.

Findings

Identified the boundary conditions where the index becomes ineffective

Simulated real-world data to determine the formula's effective range

Provided insights into the applicability of the similarity index

Abstract

The recent development, shows that the Bray-Curtis's formula for similarity Index (1957), has been applied in various fields like Ecology, Astrophysics, etc. In this paper, we found the possible boundary conditions for this evolved formula (i.e. the numerical range in which the formula becomes in-effective to give the expected result). Here we have simulated the real world data in the form of normally distributed random numbers, that directly shows the range (or conditions) at which this formula gives unambiguous similarity result.