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Journal of Mathematics and Statistics Studies
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This is an Open Access Journal

Open Access journal
ISSN (Online) 2709-4200
Published by Al-Kindi Center for Research and Development

[14 journals]

Simulation-Based Study on Extreme Ranked Set Sampling from Rician
Distribution
- Authors: Said Al Hadhrami; Shima Al Aamri, Rya Al Habsi, Sumaya Al Ghafri , Shima Al Mayyahi
  Abstract: The RSS approach is a useful method of sampling that reduces the cost and improves the representativeness of the population. It provides more efficient estimators than the competitors based on SRS. However, using RSS could be a difficult task to observe all the ranks. Thus, using only the extreme ranks eases the task and reduces the error in ranking. Samawi et al. (1996) proposed the method of Extreme Ranked Set Sampling (ERSS) to reduce errors in ranking and showed that the method gives an unbiased estimate of the population mean in the case of symmetric populations and it provides a more efficient estimator than SRS. However, the estimator of this method is biased when the distribution is skewed. Many researchers have considered ERSS, investigated several estimators, and studied their properties. In this paper, we adopt the ERSS technique when the samples are drawn from the Rician distribution. Several estimators have been studied, including arithmetic mean, geometric mean, harmonic mean, quadratic mean, median, variance, mean deviation, skewness, and kurtosis. Computer simulations were used to check the properties of these estimators and compared with the corresponding estimators using SRS. Some estimators based on ERSS are more efficient than the corresponding estimators from SRS, but some others are not.
  PubDate: Wed, 07 Aug 2024 00:00:00 +000
Degenerate Sturm-Liouville Problem for Second-Order Differential Operators
on Star-Graph
- Authors: Z. M. Abdiakhmetova; Najibullah Zahid, Feroz Sheakib, Ghulam Hazrat Aimal Rasa
  Abstract: In this paper, we present a comprehensive study of second-order differential operators on a star-graph geometric graph considering a star graph with three edges and a common vertex. We investigate the Dirichlet problem for a Sturm-Liouville operator defined on this network-type manifold. The Sturm-Liouville problem is formulated as a system of ordinary differential equations (1) on the individual edges, subject to the boundary conditions (2) and (3) at the common vertex. We assume that the condition holds, ensure the non-degeneracy of the boundary conditions by using a synthetic approach. We fully describe and solve the Dirichlet problem for the given second-order differential operator on the star graph. The key results include the characterization of the spectral parameter the construction of the matrix A composed of the boundary condition coefficients, and the analysis of the minors of A. The findings of this work contribute to the understanding of second-order differential operators on network-type manifolds and provide a framework for addressing similar problems on more complex geometric graphs. The insights gained from this study have potential applications in various fields, such as: quantum mechanics, control theory, and network analysis.
  PubDate: Thu, 25 Jul 2024 00:00:00 +000

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