Browsing by Author "Florentin Smarandache"

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Construction Of Almost Unbiased Estimator For Population Mean Using Neutrosophic Information
(University of New Mexico, 2025) Rajesh Kumar Singh; Anamika Kumari; Florentin Smarandache; Shobh Nath Tiwari
In classical statistics, the population mean is estimated using determinate, crisp data value when auxiliary information is known. These estimates can often be biased. The main objective of this study is to introduce the neutrosophic estimator with the minimum mean squared error (MSE) for the unknown value of the population mean as well as overcome the limitations of classical statistics when dealing with ambiguous or indeterminate data. Neutrosophic statistics was introduced by Florentin Smarandache. It is a generalisation of classical statistics that addresses ambiguous, unclear, vague, and indeterminate data. In this study, we have proposed neutrosophic almost unbiased estimator that use known neutrosophic auxiliary parameters to estimate the neutrosophic population mean of the primary variable. Equations for bias and mean squared error are calculated for the suggested estimators up to the first order of approximation. The proposed estimator performs better than the other existing estimators with respect to the MSE and percent relative efficiency (PRE) criteria. The estimator with the highest PRE or lowest MSE is advised for practical utility in various kinds of application areas. The theoretical conclusions are validated by the empirical analysis, which made use of the real data sets. © 2025, University of New Mexico. All rights reserved.
Construction Of Almost Unbiased Estimator for Population Median Using Neutrosophic Information
(University of New Mexico, 2025) Rajesh Kumar Singh; Anamika Kumari; Florentin Smarandache; Sunil Kumar Yadav
This paper introduces the development of an almost unbiased estimator for estimating the unknown population median of the primary variable. The proposed estimator leverages neutrosophic auxiliary information and employs simple random sampling without replacement (SRSWOR). In order to establish the efficacy of the proposed method, we derive the mathematical formulations for the mean square error (MSE), bias, and the minimum MSE of the estimator, providing approximations up to the first order. These derivations allow for a comprehensive analysis of the estimator's performance and its suitability for accurate population median estimation. To validate the theoretical results, we conduct an empirical study using two real-world datasets, ensuring that the proposed estimator's behavior aligns with theoretical predictions in practical scenarios. The study shows that the proposed estimator remains nearly unbiased, with minimal bias when approximated to the first order. This result further demonstrates that the estimator performs robustly across various data conditions. In comparison to existing estimators, the proposed estimator outperforms the others in terms of efficiency, as evidenced by the MSE and PRE values derived. The proposed method not only minimizes bias but also provides more accurate population median estimates with reduced estimation error, making it a more reliable tool in the context of uncertain or incomplete data, where traditional estimators might fall short. By bridging the gap between classical estimation techniques and modern methods that account for uncertainty, the proposed estimator offers a significant advancement in the field of statistical estimation, particularly in real-world applications involving uncertain datasets. The findings presented in this study contribute to the growing body of knowledge in statistical estimation, particularly in the use of neutrosophic information for enhancing estimator accuracy. Furthermore, the results provide a valuable foundation for future research aimed at developing more efficient and reliable statistical estimators for a variety of practical applications. © 2025, University of New Mexico. All rights reserved.
Generalized robust-type neutrosophic ratio estimators of pharmaceutical daily stock prices
(Elsevier, 2023) Rajesh Singh; Florentin Smarandache; Rohan Mishra
When the data are vague or indeterminate, methods of estimation under classical statistics fail; in such a case, neutrosophic statistics becomes the only alternative as it not only deals with randomness but with indeterminacy as well. In survey sampling, the data collected usually consist of outliers, making estimators inefficient. Hence in this chapter, we have proposed generalized robust-type neutrosophic ratio estimators to estimate the population mean of finite neutrosophic data. The expressions of bias and mean-squared error have been derived up to the first order of approximation and presented. A simulation study on a real neutrosophic population (the daily stock price of Moderna Inc.) has been conducted to assess the performance of the proposed estimator over some existing estimators. The results show that the proposed estimators result in better estimation. © 2023 Elsevier Inc. All rights reserved.
Improved exponential estimator for population variance using two auxiliary variables
(2011) Rajesh Singh; Pankaj Chauhan; Nirmala Sawan; Florentin Smarandache
In this paper, exponential ratio and exponential product type estimators using two auxiliary variables are proposed for estimating unknown population variance S 2 y . Problem is extended to the case of two-phase sampling. Theoretical results are supported by an empirical study.
Improvement in estimating population mean using two auxiliary variables in two-phase sampling
(2011) Rajesh Singh; Pankaj Chauhan; Nirmala Sawan; Florentin Smarandache
This study proposes improved chain-ratio type estimator for estimating population mean using some known values of population parameter(s) of the second auxiliary character. The proposed estimators have been compared with two-phase ratio estimator and some other chain type estimators. The performances of the proposed estimators have been supposed with a numerical illustration.
New Modification of Ranked Set Sampling for Estimating Population Mean: Neutrosophic Median Ranked Set Sampling with an Application to Demographic Data
(Springer Science and Business Media B.V., 2024) Anamika Kumari; Rajesh Singh; Florentin Smarandache
The study addressed the limitations of classical statistical methods when dealing with ambiguous data, emphasizing the importance of adopting neutrosophic statistics as a more effective alternative. Classical methods falter in managing uncertainty inherent in such data, necessitating a shift towards methodologies like neutrosophic statistics. To address this gap, the research introduced a novel sampling approach called “neutrosophic median ranked set sampling” and incorporated neutrosophic estimators tailored for estimating the population mean in the presence of ambiguity. This modification aims to address the inherent challenges associated with estimating the population mean when dealing with neutrosophic data. The methods employed involved modifying traditional ranked set sampling techniques to accommodate neutrosophic data characteristics. Additionally, neutrosophic estimators were developed to leverage auxiliary information within the framework of median-ranked set sampling, enhancing the accuracy of population mean estimation under uncertain conditions. The methods employed involved modifying traditional ranked set sampling techniques to accommodate neutrosophic data characteristics. Bias and mean squared error equations for the suggested estimators were provided, offering insights into their theoretical underpinnings. To illustrate the effectiveness and practical applications of the proposed methodology and estimators, a numerical demonstration and simulation study have been conducted using the R programming language. The key results highlighted the superior performance of the proposed estimators compared to existing alternatives, as demonstrated through comprehensive evaluations based on mean squared error and percentage relative efficiency criteria. The conclusions drawn underscored the effectiveness of the neutrosophic median ranked set sampling approach and suggested estimators in estimating the population mean under conditions of uncertainty, particularly when utilizing neutrosophic auxiliary information and validated real-life applicability. The methodology and estimators presented in the study were shown to yield interval-based results, providing a more realistic representation of uncertainty associated with population parameters. This interval estimation, coupled with minimum mean squared error considerations, enhanced the efficacy of the estimators in determining population mean values. The novelty of the work lies in its introduction of a tailored sampling approach and estimators designed specifically for neutrosophic data, filling a significant gap in the literature. By extending classical statistics to accommodate ambiguity, the study offers a substantial advancement in statistical methodology, particularly in domains where precise data is scarce and uncertainty is prevalent. Furthermore, the empirical validation through numerical demonstrations and simulation studies using the R programming language adds robustness to the proposed methodology and contributes to its practical applicability. © The Author(s) 2024.
Some ratio type estimators under measurement errors
(2011) Mukesh Kumar; Rajesh Singh; Ashish K. Singh; Florentin Smarandache
This article addresses the problem of estimating the population mean using auxiliary information in the presence of measurement errors. A comparative study is made among the proposed estimators, the mean per unit estimator and the ratio estimator in the presence of measurement errors. © IDOSI Publications, 2011.