Jordan Journal of Mathematics and Statistics

An Efficient New Ratio-Type and Ratio-Type Exponential Estimator for Population Mean in Sample Surveys

2025-06-22T18:59:11+03:00

This paper addresses the problem of estimating the finite population mean of the study variable using information on auxiliary variable in sample surveys. A class of ratio-type and ratio-type exponential formulae for estimating finite population mean is defined. The bias and mean squared error of the proposed class of estimators are obtained up to terms of order n⁻¹ under simple random sampling without replacement (SRSWOR) sampling scheme. The optimum conditions are obtained at which the mean squared error is minimum. It has been shown theoretically that at the optimum conditions, the proposed class of estimators is more efficient than the customary unbiased estimator, ratio and regression estimators. We have also obtained the condition in which the proposed class of estimators is superior to Rao’s (1991) estimator. Two numerical exemplifications are given in support of the present study.

Keywords: Population Mean; Bias; Mean squared error; Ratio-type exponential estimator.

2010 Mathematics Subject Classification. 26A25; 26A35

Developing Almost and Modified Almost Unbiased Estimators to Handle Multicollinearity Problem in Logistic Regression Model

2025-06-22T19:08:50+03:00

This paper introduces two biased estimators to avoid problems arising from multicollinearity in the logistic regression model. We investigated the theoretical excellence of the proposed estimators according to the mean square error matrix (MSE) and the scalar mean square error (MSE) criterion. We found that they have the superiority than some existing estimators. Moreover, we run the simulation study, which depended on the simulated MSE (SMSE), squared bias (SB) and generalized cross validation (GCV) as criteria to compare the estimators. The simulation results showed that the proposed estimators have the superiority than the estimators under comparison at several factors and at the same time, they work well at the high level of correlation. In addition, we investigated the behavior of the present estimators applying the real data. Under this trend, the results were consistent with the theoretical results.

Keywords: Maximum likelihood estimator; Multicollinearity; AL estimator; Mean squared error matrix.

Mathematics Subject Classification. Primary: 62J12. 26A25; 26A35

Optimal Maintenance Strategy of a System Which Deteriorates in Accordance With a Gamma Process Over a Bounded Time Horizon

2025-06-22T19:16:37+03:00

This article discusses the mean and variance of discounted total maintenance cost of a system intended to operate during the finite time interval [0, t]. We implement the age replacement strategy under the assumption that the system deteriorates in accordance with a stochastic gamma process. Laplace transforms for the mean and second moment of the total maintenance cost are obtained. We apply the result to obtain an optimal period for preventive maintenance which minimizes the mean of the discounted total maintenance cost in the time interval [0, t]. Standard deviation for the optimal period for preventive maintenance is also calculated.

Keywords: Age replacement strategy; Gamma process; Discount factor; Renewal process; Laplace transform.

2010 Mathematics Subject Classification. 90B25; 60K10

Further Results on Odd Harmonious Labeling of Graphs

2025-06-22T19:21:25+03:00

Liang and Bai proposed the notion of odd harmonious labeling of a graph in 2009. Since then, numerous papers have explored this topic. This study adds some new results to the existing literature. First, we provide a sufficient condition for an Eulerian graph to be an odd harmonious graph, which enhances the result from 2014. Furthermore, we identify several new classes of graphs that exhibit odd harmonious properties.

Keywords: disjoint union of graphs; odd harmonious labeling; path union of graphs; splitting graph; subdivided shell flower graph;
vertex union of graphs.

2010 Mathematics Subject Classification. 26A25; 26A35

New Robust Weighted Grouping Method for Multiple Models

2025-06-22T19:27:57+03:00

In this paper, three new estimation methods are proposed to fit a multiple structural measurement error model with two independent variables when all variables are subject to errors. The first two procedures are modifications of the Theil and Siegel estimators, where they involved the proposed Weighted Latent Variables method, while the third procedure is Iterative Weighted Grouping, an extension of Wald estimation that involved the Weighted Grouping method. A Monte Carlo experiment is performed to investigate the performance of the new estimators compared with the classical estimation methods; the Maximum Likelihood Estimator and Method of Moment, in terms of root mean square error and its bias. The outcomes of the simulation demonstrated that the suggested estimators are more effective than conventional estimators. In addition, real data analysis is discussed to examine the relationship between national gross domestic product, unemployment rate, and human development index, after applying the proposed estimation methods.

Keywords: Model of Measurement Error; Robust Estimators; Iterative Estimator; Human Development Index; Unemployment Rate;
National Gross Domestic Product; Monte Carlo Simulation.

2010 Mathematics Subject Classification. 26A25; 26A35

Geometrical Approach for Construction of Balanced Incomplete Block Design

2025-06-22T19:33:00+03:00

Construction of balanced incomplete block design has been a major concern in the field of combinatorial design. Different techniques have been proposed by several authors to verify the existence and non-existence of balanced incomplete block designs (BIBDs); however, there is still no general method or algorithm to solve this challenge. In this paper, we propose a projective geometry approach of order PG(N, p) to construct balanced incomplete block designs with different N-dimensions. We establish PG(2,2) and PG(3,2) orders to construct two different sets of BIBDs. It is observed that the constructed balanced incomplete block designs (BIBDs) are also symmetry balanced incomplete block designs (SBIBDs), but the reverse is not true in some cases. Hence, this approach is easier and more straightforward for constructing BIBDs and has proven to be effective in determining the existence and non-existence of balanced incomplete block designs.

Keywords: Geometry;Projective Geometry; block design; balanced design; Incomplete balanced design.

2010 Mathematics Subject Classification. 26A25; 26A35

Development of Conformable Fractional Numerical Methods of Constant Order using Fractional Power Series Theorem

2025-06-22T19:42:10+03:00

This study aims to employ novel numerical approaches for the constant-order conformable fractional derivative. By utilizing the fractional power series theorem, two innovative numerical techniques have been devised: the constant-order conformable Euler method and the constant-order conformable Runge Kutta 2-stage method. Furthermore, these techniques account for various fractional constant-order derivatives. Different models have been analyzed to demonstrate their behavior under varying constant orders, and their agreement and validation with standard Runge-Kutta and Euler methods have been confirmed. Notably, both methods hold promise for application in fractional financial models. The study includes a comparative analysis of these methods against classical derivatives, supported by tabular data showcasing the numerical outcomes.

Keywords: Conformable constant order derivative; Fractional financial model; Numerical technique; Classical derivative.

2010 Mathematics Subject Classification. 26A25; 26A35

Wrapped Generalized Akash Distribution: Properties and Applications

2025-06-22T19:46:16+03:00

Circular probability distributions are the most appropriate statistical tools to model directional data. In this paper, we introduce a new circular distribution based on the wrapping method and it is named as wrapped generalized Akash distribution. We also studied some important properties of the proposed probability distribution such as characteristic function, trigonometric moments, invariance properties etc. Further we have applied maximum likelihood procedure for the estimation of the parameters of the distribution. The proposed model is applied to real- life dataset and studied its suitability to compare with other similar circular probability distributions in the literature.

Keywords: Circular Statistics;Wrapped distribution; Generalized Akash distribution; Trigonometric moments.

2010 Mathematics Subject Classification. 26A25; 26A35

Strongly Topologically Transitive, Supermixing, and Hypermixing Maps on General Topological Spaces

2025-06-22T19:50:09+03:00

We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.

Keywords: strongly topologically transitive; supermixing; hypermixing.

2010 Mathematics Subject Classification. 37B02; 54C05

How Dependable is COVID-19 Data During First Wave? Disclosure of Inconsistencies in Daily Reportage Confirmed Cases and Deaths

2025-07-03T13:23:09+03:00

The global crisis triggered by the COVID-19 pandemic necessitated precise data monitoring and rigorous analysis efforts from worldwide health authorities and governments, particularly during the pandemic’s initial surge. This study employs Newcomb Benford’s Law specifically to identify potential anomalies in the reporting of COVID-19 data during the pandemic’s first wave. Our methodology encompasses the application of Newcomb Benford’s Law to the first digit analysis focusing on three (3) key statistics [d^∗,
α−statistic (α^∗) and ω statistic (ω^∗)] in conjunction with the Kolmogorov-Smirnov test to unveil possible inconsistencies within world continental COVID-19 data reportage. By evaluating the actual distribution of leading digits across various COVID-19 data categories
such as cumulative confirmed cases, deaths, recoveries, and active cases against the theoretical distribution proposed by Newcomb Benford’s Law, possible significant deviations were identified. We used the deviation from the Newcomb Benford’s law of anomalous numbers as a proxy for data accuracy. The findings reveal that except for the Australia/Oceania continent which exhibited pronounced deviations due to its unique data structure, the COVID-19 data from all other continents maintained a possible high level of reliability during the initial outbreak. The study concludes that while Benford’s Law is a valuable tool for anomaly detection in diverse data, its use in COVID-19 reportage data shows potential pitfalls. To enhance the effectiveness and reliability of detecting anomalies, the study advocates for integrating additional anomaly detection strategies, like density and boundary based approaches encompassing the local outlier factor and one-class SVM, alongside the Newcomb Benford analysis.

Keywords: COVID-19; Newcomb Benford’s Law; First-digits; World Continents; Kolmogorov-Smirnov test.

On the solvability of the (SSIE) (s (c) R ) B(r;s;t) ⸦ s (c) x , involving the infinite triple band matrix B (r; s; t)

2025-07-03T13:29:27+03:00

In this article, we consider the infinite triple band matrix B(r,s,t), with r, s, t ≠ 0. Then, under the condition ∆ = s² −4rt, t, −s and r > 0, we state an interesting characterization of the set ℐ^(c) _R (r,s,t) of all positive sequences x = (x_n)_n∈N, such that (s^(c)_R) _B(r,s,t) ⊂ s ^(c) _x for R >0. Then, we obtain some numerical applications, and results associated with the fine spectrum theory.
Finally, we consider the triple band matrix B (1,2s,as²) and we solve the (SSIE) (s^(c)_R) _B(1,2s,as²) ⊂ s ^(c) _x and we state some tauberian results, using the Silverman- Toeplitz theorem. These results extend those stated in [37, 8, 9].

Keywords: Matrix transformations; Silverman-Toeplitz theorem; Tauberian theorem; (SSIE); band matrix B(r,s,t).

2010 Mathematics Subject Classification. 40H05, 46A45

Numerical Approximation of Lambert W Function for Real Values by Unique Method of Quadratic Approximation

2025-07-03T13:45:14+03:00

This paper introduces a novel method for the numerical approximation of the Lambert W function, W(x) = y, in the real domain. By linearly approximating the natural logarithm, the function is transformed into a quadratic equation whose roots refine the initial approximation. Iterative solving of this equation yields high precision, with iterations determined by the desired accuracy. Two methods for positive x are proposed, the first expresses the function as (z₁ + a₁) ln(z₁ + a₁) = x, iteratively refining the approximation of z, where z₁, is the initial approximation and a₁<<z₁, while the second method is based on ln(y₁ + a₁) + y₁ + a₁ =ln(x), where y₁ is the initial approximation, and a₁<<y₁. For x between 0 and 1/e, the method is extended to approximate W(-x) =-y. Unlike Newton or Halley’s methods, this approach handles both branches without constraints on initial assumptions, covering a broad range of values.
Extensive examples and a software algorithm validate the method’s accuracy, offering a precise and flexible tool for numerical analysis.

Keywords: Lambert W Function; Natural Logarithm; Quadratic Approximation; Real Number.

2010 Mathematics Subject Classification. 26A25; 26A35

The Global Existence and Attractor for m(x)-Laplacian Equation with Nonlinear Boundary Conditions

2025-07-03T13:54:36+03:00

In this paper, we consider a doubly m(x)-Laplacian equation
∂α(v)/∂t −div(|∇v|^m(x)−2∇v)+F(v) = G, in Ω ×(0,+∞),
with nonlinear boundary conditions and initial data given. Firstly, we use the regularization method to determine the existence and uniqueness of weak solutions in the Sobolev space with variable exponents. Secondly, in the frame of the dynamical systems approach, a standard limiting process and a method to generate a series of approximation solutions are used to study the long behavior of solutions for the above problem (1.1). We formulate our problem as a dynamical system, and then, by using H¨older continuity solutions and assuming appropriate hypotheses, we prove also the existence of a global attractor in L²(Ω).

Keywords: m(x)-Laplacian; nonlinear boundary conditions; existence; uniqueness; variable exponents; global attractors.

2010 Mathematics Subject Classification. 35K55; 46E35; 35D30