Volume 1, Number 1 (2023)
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Estimating the Overlapping Coefficient in the Case of Normal Distributions

Volume 1, Issue 1, January 2023     |     PP. 1-13      |     PDF (1239 K)    |     Pub. Date: November 27, 2023
DOI: 10.54647/wjm5071001    50 Downloads     863 Views  


Omar M. Eidous, Department of Statistics, Yarmouk University, Irbid, Jordan
Abeer J. Al-Shourman, Department of Statistics, Yarmouk University, Irbid, Jordan

Given that we have two independent random samples, each of which follows a normal distribution, the main objective of this paper is to estimate the overlapping Weitzman coefficient ∆. This coefficient is widely used and is defined as the area under two probability density functions. The proposed estimation technique is based on the rules of integral numerical approximation such as trapezoidal rules and Simpson's rules. Simulation results showed the effectiveness of the proposed technique over some of the methods found in the literature.

Normal Distribution; Numerical Integration Methods; Maximum Likelihood Method; Relative Bias; Relative Mean Square Error.

Cite this paper
Omar M. Eidous, Abeer J. Al-Shourman, Estimating the Overlapping Coefficient in the Case of Normal Distributions , World Journal of Mathematics . Volume 1, Issue 1, January 2023 | PP. 1-13. 10.54647/wjm5071001


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