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- MakaleAçık Erişim2025A FIXED POINT APPROACH TO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS: CONVERGENCE AND DATA DEPENDENCE
Cona, Lale
Fractional calculus, which involves derivatives and integrals of non-integer order, is widely used in modeling real-world problems in science and engineering. This study focuses on solving fractional integro-differential equations using Picard's three-step iteration algorithm. We apply Picard's three-step iteration algorithm to approximate solutions and show that it converges strongly. The method is shown to be not only efficient in approximating solutions but also robust with respect to perturbations in the initial data and operators, demonstrating its data dependence. A numerical example is provided to illustrate the theoretical results and to confirm the applicability and reliability of the proposed approach.
- MakaleAçık Erişim2024A NEW LOGARITHMIC TYPE ESTIMATORS FOR ANALYSIS OF NUMBER OF AFTERSHOCKS USING POISSON DISTRIBUTION
Zaman, Tolga; Iftikhar, Soofia; Sozen, Caglar; Sharma, Prayas
Earthquake is a fierce and unavoidable natural disaster. The study of aftershocks following an earthquake provides a comprehensive understanding of seismic activity, making it an important area of research. Although it is important to mention that the use of the Poisson distributed population, to estimate the mass mean of rare events such as earthquakes, has been little studied in the literature. In this context, this study proposes a new class of logarithmic type ratio estimators for estimating the mean of a Poisson distributed population in a simple random sampling without replacement. The proposed estimators are obtained using the logarithmic transformation of the ratio estimator, and the expressions for the mean square error (MSE) are also derived to the first order of approximation. The study demonstrates that the proposed logarithmic type estimators are more efficient than the existing estimators, both theoretically and empirically. The Empirical evidence from a real data study conducted using earthquake data from Turkey confirms the superiority of the proposed estimators over the existing estimators. The study provides valuable insights for researchers and practitioners working with Poisson distributed populations and requiring ratio estimators using simple random sampling without replacement.
- MakaleAçık Erişim2024AN EFFICIENT FAMILY OF RATIO TYPE ESTIMATORS FOR SIMPLE RANDOM SAMPLING
Yadav, Subhash Kumar; Arya, Diksha; Koc, Tuba; Zaman, Tolga
The study provides an enhanced estimation of the population mean using known information on an auxiliary variable. An enhanced class of estimators is suggested for the same. The proposed estimator's bias and mean squared error (MSE) are calculated up to the first order of approximation. The optimum values of the characterizing constants are obtained by minimizing the MSE of the proposed estimator. The minimum MSE and the bias values are achieved by optimising the characterizing scalar. The MSE of the proposed estimator has also been compared both conceptually and empirically with the MSEs of competing estimators. Real and simulated data sets are adopted to verify the theoretical prerequisites for the proposed estimator's greater efficiency over competing estimators. The most efficient estimator is recommended for practical utility in different areas of applications and the suggested estimator filfills the requirement.
- MakaleAçık Erişim2023A NEW LOGARITHMIC RATIO TYPE ESTIMATOR OF POPULATION MEAN FOR SIMPLE RANDOM SAMPLING: A SIMULATION STUDY
Zaman, Tolga; Iftikhar, Soofia
This paper provides a logarithmic ratio type estimator of a finite population mean using an auxiliary variable in simple random sampling. The expression for the mean square error (MSE) of the proposed estimator and some selected estimators are calculated along with the theoretical conditions. Further the numerical comparisons and simulation study based on different probability distributions supports the claim that the proposed estimator performs better as compared to the ones used in this study.
- DergiJOURNAL OF SCIENCE AND ARTS