Research Article
On Inference of Weitzman Overlapping Coefficient ∆(X,Y) in the Case of Two Normal Distributions
Omar Mohammad Eidous*
,
Salam Khaled Daradkeh
Issue:
Volume 10, Issue 2, April 2024
Pages:
14-22
Received:
9 July 2024
Accepted:
5 August 2024
Published:
20 August 2024
Abstract: The Weitzman overlapping coefficient ∆(X,Y) is the most important and widely used overlapping coefficient, which represents the intersection area between two probability distributions. This research proposes a new general technique to estimate ∆(X,Y) assuming the existence of two independent random samples following normal distributions. In contrast to some studies in this scope that place some restrictions on the parameters of the two populations such as the equality of their means or the equality of their variances, this study did not assume any restrictions on the parameters of normal distributions. Two new estimators for ∆(X,Y) were derived based on the proposed new technique, and then the properties of the estimator resulting from taking their arithmetic mean was studied and compared with some corresponding estimators available in the literature based on the simulation method. An extensive simulation study was performed by assuming two normal distributions with different parameter values to cover most possible cases in practice. The parameter values were chosen taking into account the exact value of ∆(X,Y), which taken to be small (close to zero), medium (close to 0.5) and large (close to 1). The simulation results showed the effectiveness of the proposed technique in estimating ∆(X,Y). By comparing the proposed estimator of ∆(X,Y) with some existing corresponding estimators, its performance was better than the performances of the other estimators in almost all considered cases.
Abstract: The Weitzman overlapping coefficient ∆(X,Y) is the most important and widely used overlapping coefficient, which represents the intersection area between two probability distributions. This research proposes a new general technique to estimate ∆(X,Y) assuming the existence of two independent random samples following normal distributions. In contras...
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Research Article
Boundary Domain Integral Equations for Variable Coefficient Mixed BVP in 2D Unbounded Domain
Eshetu Seid Ahimed*
Issue:
Volume 10, Issue 2, April 2024
Pages:
23-32
Received:
26 July 2024
Accepted:
20 August 2024
Published:
30 August 2024
Abstract: In this paper, the direct segregated Boundary Domain Integral Equations (BDIEs) for the Mixed Boundary Value Problems (MBVPs) for a scalar second order elliptic Partial Differential Equation (PDE) with variable coefficient in unbounded (exterior) 2D domain is considered. Otar Chkadua, Sergey Mikhailov and David Natroshvili formulated both the interior and exterior 3D domain of the direct segregated systems of BDIEs for the MBVPs for a scalar second order elliptic PDE with a variable coefficients. On the other hand Sergey Mikhailov and Tamirat Temesgen formulated only the interior 2D domain of the direct segregated systems of BDIEs for the MBVPs for a scalar second order divergent elliptic PDE with a variable coefficients. However, in this paper we formulated the exterior 2D domain of the direct segregated systems of BDIEs for the MBVPs for a scalar second order divergent elliptic PDE with a variable coefficients. The aim of this work is to reduce the MBVPs to some direct segregated BDIEs with the use of an appropriate parametrix (Levi function). We examine the characteristics of corresponding parametrix-based integral volume and layer potentials in some weighted Sobolev spaces, as well as the unique solvability of BDIEs and their equivalence to the original MBVPs. This analysis is based on the corresponding properties of the MBVPs in weighted Sobolev spaces that are proved as well.
Abstract: In this paper, the direct segregated Boundary Domain Integral Equations (BDIEs) for the Mixed Boundary Value Problems (MBVPs) for a scalar second order elliptic Partial Differential Equation (PDE) with variable coefficient in unbounded (exterior) 2D domain is considered. Otar Chkadua, Sergey Mikhailov and David Natroshvili formulated both the inter...
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