Estimation of Sampling Distributions of the Overlapping Coefficient and Other Similarity Measures

Authored by: Madhuri S. Mulekar , Jeffrey M. Boone , Subhash Aryal

Handbook of Fitting Statistical Distributions with R

Print publication date:  October  2010
Online publication date:  April  2016

Print ISBN: 9781584887119
eBook ISBN: 9781584887126
Adobe ISBN:

10.1201/b10159-32

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Abstract

Measures of similarity are useful to quantify the extent of similarity between two populations. Their complements, known as measures of dissimilarity, are also used commonly by researchers. These measures are often used to make comparative inferences about two groups, such as describing the degree of inter-specific encounter or crowdedness of two species in their resource utilization, estimating the proportion of genetic deviates in segregating populations, determining the similarity of two different radiologists’ readings of the same x-rays, measuring racial segregation, or making inference about the comparison of survival of two groups after cancer treatment. One such similarity measure, also known as the overlap coefficient, has been used for comparing fits of statistical distributions by different methods. Due to the unknown nature of sampling distributions of these measures, however, decisions are often made using only point estimates. A study was designed using the Alabama Supercomputer to simulate distributions of estimates of four different similarity measures for several different parametric configurations for commonly used normal and exponential distributions. With the help of a distribution fitting technique, the sampling distributions were estimated to be from the family of beta distributions whose parameters were estimated using multiple regression techniques with transformations.

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