Interference on Overlapping Coefficients in Two Exponential Populations

Abstract

Three measures of overlap, namely Matusita's measure ρ , Morisita's measure λ and Weitzman's measure Δ are investigated in this article for two exponential populations with different means. It is well that the estimators of those measures of overlap are biased. The bias is of these estimators depends on the unknown overlap parameters. There are no closed-form, exact formulas, for those estimators variances or their exact sampling distributions. Monte Carlo evaluations are used to study the bias and precision of the proposed overlap measures. Bootstrap method and Taylor series approximation are used to construct confidence intervals for the overlap measures.

On Inference of Overlapping Coefficients in TwoLomaxPopulations Using Different Sampling Methods

“…The OV L measures are used in many useful applications including, clinical trials (see, Mizuno et al, 2005), and in a comparison of income distributed by race (Weitzman, 1970). Recently, many authors utilized the OV L measures, see Bradley and Piantadosi (1982), Inman and Bradley (1989), Clemons (1996), Reiser and Faraggi (1999), Clemons and Bradley (2000), Mulekar and Mishra (2000), AlSaidy, Samawi and Al-Saleh (2005), Schmid and Schmidt (2006), and Al-Saleh and Samawi (2007).…”

Notes on the overlap measure as an alternative to the Youden index: How are they related?

“…Let X 1 and X 2 be 2 diagnostic marker measurements for diseased and healthy subjects that are assumed to follow exponential densities with means θ H and θ D , respectively. Let , the continuous version of the proposed overlap measure, as derived by Al‐Salah and Samawi, can then be expressed as a function of R as follows: Now, using ∣ J ∣ = max c {| F H ( c ) − F D ( c )| } = ∣ F H ( c op ) − F D ( c op )∣, we obtain and Simplifying gives …”

“…Let X 1 and X 2 be 2 diagnostic marker measurements for diseased and healthy subjects that are assumed to follow exponential densities with means θ H and θ D , respectively. LetR ¼ θ H θ D , the continuous version of the proposed overlap measure, as derived by Al-Salah and Samawi, 19 can then be expressed as a function of R as follows:…”

Overlap Coefficients Based on Kullback-Leibler of Two Normal Densities: Equal Means Case

“…The overlap coefficient have been used for two exponential populations with different means (Al-Saleh andSamawi 2007 andDhaker et al 2017), and Mulekar and Andrade (Mulekar and Andrade, 2017) established a necessary condition to obtain valid values of Weitzman's Measure for normal densities and extend the result to lognormal, exponential, Weibull, and Pareto densities. Sibil and Seemon (Sibil and Seemon, 2019) constructed of the confidence interval of the overlap coefficient under one way random models.…”