Browsing by Author "Anamika Kumari"

Now showing 1 - 15 of 15

Application of Neutrosophic Stratified Ranked Set Sampling: An Efficient Sampling Technique in the Estimation of Average Relative Humidity in USA
(American Scientific Publishing Group (ASPG), 2025) Vishwajeet Singh; Rajesh Kumar Singh; Anamika Kumari
The study examined the shortcomings of conventional statistical techniques in managing unclear or ambiguous data and emphasized the necessity of implementing neutrosophic statistical techniques as a more enhanced remedy. Advanced techniques like neutrosophic statistics (NS) were developed since traditional statistical methods are unable to handle the uncertainty present in ambiguous data. In order to tackle this problem, the study suggested an innovative and novel sampling method called "neutrosophic stratified ranked set sampling (NSRSS)" in addition to specialized neutrosophic estimators for precisely predicting the population mean in the proximity of uncertainty. This novel strategy adjusted ranked set sampling (RSS) techniques to allow the special features of neutrosophic data. Furthermore, the study improved the precision of estimating the population mean in uncertain situations by introducing neutrosophic estimators that use subsidiary information inside the structure of stratified ranked set sampling (SRSS). The work provided theoretical insights into the performance of these estimators by presenting comprehensive formulations of bias and mean squared error (MSE). To illustrate the efficacy of the suggested techniques, the study includes simulation studies, numerical examples conducted using the computer language R. Evaluations utilizing MSE, and percentage relative efficiency (PRE) demonstrated the higher accuracy of the suggested estimators over conventional alternatives. The findings demonstrated the NSRSS's applicability, particularly for predicting population means in situations where heterogeneity and uncertainty are prevalent. Furthermore, it was demonstrated that the estimators and technique produced interval-based findings, which provided a more accurate depiction of the uncertainty related to population parameters. The reliability of the estimators in estimating population means was greatly improved by this interval estimation in combination with a lower MSE. A significant vacuum in the field of statistical research is filled by the study's introduction of estimators and a customized sampling approach made especially for neutrosophic data. This research significantly advances statistical theory and practice by extending traditional statistical approaches to efficiently handle ambiguous data, especially for applications where exact data is few, heterogeneous, or uncertain. The empirical validation through numerical illustrations and simulations conducted in R further solidifies the practicality and robustness of the proposed techniques, reinforcing their applicability to real-world scenarios. © 2025, American Scientific Publishing Group (ASPG). All rights reserved.
Application to Road Traffic Accidents: An Almost Unbiased Estimator for Population Mean Under Ranked Set Sampling and Stratified Ranked Set Sampling
(Springer Science and Business Media B.V., 2025) Sunil Kumar Yadav; Rajesh Kumar Singh; Anamika Kumari
Ranked Set Sampling (RSS) serves as an effective and efficient alternative to Simple Random Sampling (SRS), especially when ranking items is easier than taking precise measurements. Stratified sampling is used for better estimation when the population is heterogeneous. In this work, we introduce a new family of nearly unbiased estimators for estimating the population mean under the RSS and SRSS framework. These estimators are formulated as linear combinations of three established estimators and are specifically developed to minimize bias to the first order. We analytically derive their theoretical properties, including bias and Mean Squared Error (MSE), to evaluate their statistical performance. To support our theoretical claims, we apply the proposed estimators to real-world data and perform extensive simulation experiments under varying sample sizes and correlation settings. We benchmark our estimator against existing ones such as the conventional sample mean, the exponential ratio estimator, and the logarithmic estimator. The assessment is based on key metrics like MSE and Percentage Relative Efficiency (PRE). The findings consistently show that the proposed estimator yields lower MSE and higher PRE, indicating better accuracy and efficiency under both sampling frames. Furthermore, its near-unbiased behaviour enhances its practical applicability, particularly in scenarios where ranking is more feasible than direct measurement. © The Author(s) 2025.
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.
Estimation of population mean using ranked set sampling in the presence of measurement errors
(Elsevier B.V., 2024) Abdullah Ali H. Ahmadini; Rajesh Singh; Yashpal Singh Raghav; Anamika Kumari
Ranked set sampling is widely acknowledged for its superior efficiency compared with simple random sampling. Only a small amount of work has been conducted using ranked set sampling when measurement errors are present. This study introduces innovative estimators utilizing ranked set sampling to assess the population mean when faced with both correlated and uncorrelated measurement errors. The expressions for the bias and mean squared error of the proposed estimators are derived up to the first-order approximation, revealing their superior performance compared to the other examined estimators. The efficacy of the suggested estimators in handling measurement errors was demonstrated through numerical illustration and simulation study investigations. The recommended estimators are further compared to the existing ones using the percentage relative efficiency and mean squared error, and the impact of measurement errors on the results is highlighted through the percentage computation of measurement errors. The innovative estimators suggested were formulated by judiciously incorporating ratio, exponential, and log estimators. Numerical examples involving expenditure and income, as well as simulated data generated from a normal population using R software, affirm the superior performance of the proposed estimators over existing ones such as the usual mean estimator and those proposed by Vishwakarma and Singh (2022), as evidenced by the higher percent relative efficiency and lower mean squared error. The evaluation of the percentage contribution of measurement error values confirms the impact of measurement errors on the properties of the estimators. © 2024 The Author(s)
Estimation of population mean using ranked set sampling in the presence of non-response error with numerical illustration and simulation study
(Springer Science and Business Media B.V., 2025) Anamika Kumari; Prayas Sharma; Rajesh Kumar Singh
This paper develops innovative estimators based on ranked set sampling (RSS) for estimating the population mean in the presence of non-response (NR) errors, utilizing auxiliary information. RSS is shown to be a more efficient alternative to simple random sampling (SRS), particularly under non-response conditions. The proposed estimators are evaluated against existing ratio, regression, and exponential estimators using bias, mean squared error (MSE), and percent relative efficiency (PRE). Results from empirical analysis and simulation studies demonstrate that the RSS-based estimators achieve lower MSE and higher PRE, thereby outperforming conventional methods. The study highlights the practical advantages of RSS in survey sampling and contributes to improving the robustness and accuracy of estimators under non-response error scenarios, while also suggesting directions for future research. © The Author(s) 2025.
IMPROVED ESTIMATORS OF POPULATION MEAN USING AUXILIARY VARIABLES IN RANKED SET SAMPLING
(Universidad de La Habana, 2023) Rajesh Singh; Anamika Kumari
This paper presents some improved estimators of population mean using auxiliary variables in Ranked Set Sampling. We have derived the expressions for bias and mean square errors up to the first order of approximation and shown that the proposed estimators under optimum conditions are more efficient than other estimators taken in this paper. In an attempt to verify the efficiencies of proposed estimators, theoretical results are supported by empirical study and simulation study for which we have considered two populations. © 2023 Universidad de La Habana. All rights reserved.
Modern techniques in variance estimation with auxiliary information: a logarithmic perspective
(Taylor and Francis Ltd., 2025) Poonam Singh; Prayas Sharma; Anjali P. Singh; Anamika Kumari
Variance estimation is essential to statistical analysis because it sheds light on the accuracy and dependability of estimations. The effectiveness of traditional methods is frequently increased by using linear connections between the study and auxiliary variables. Nonetheless, the connection between the research variable and auxiliary data may exhibit a nonlinear pattern, namely a logarithmic shape, in several real-world scenarios. A family of variance estimators that use logarithmic connections with auxiliary variables to increase accuracy is proposed in this study in recognition of this. Real-world situations where data show multiplicative impacts or exponential development patterns, where logarithmic modeling is more suitable than linear assumptions, are the driving force behind this approach. The usefulness of the suggested estimators is illustrated by real-world examples, including biological measures, income distribution studies, and environmental data assessments. To evaluate the performance in general, theoretical characteristics are derived, such as mean square error and bias. The superiority of the logarithmic approach over traditional techniques is further supported by numerical examples and simulations, which offer a reliable and adaptable tool for variance estimates in a variety of domains. © 2025 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.
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.
Preliminary estimators of population mean using ranked set sampling in the presence of measurement error and non-response error with applications and simulation study
(Universidade Federal de Lavras -Departamento de Estatistica, 2024) Rajesh Singh; Anamika Kumari
In order to estimate the population mean in the presence of both non-response and measurement errors that are uncorrelated, the paper presents some novel estimators employing ranked set sampling by uti-lizing auxiliary information. Up to the first order of approximation, the equations for the bias and mean squared error of the suggested estimators are produced, and it is found that the proposed estimators out-perform the other existing estimators analysed in this study. Investigations using simulation studies and numerical examples show how well the suggested estimators perform in the presence of measurement and non-response errors. The relative efficiency of the suggested estimators compared to the existing estimators has been expressed as a percentage, and the impact of measurement errors has been expressed as a percentage computation of measurement errors. © Brazilian Journal of Biometrics.
Response of N P S doses and urea foliar spray on lentil under guava (Psidium guajava) + lentil (Lens culinaris) based agri-horti system
(Indian Council of Agricultural Research, 2022) Vikash Kumar; Manoj Kumar Singh; D. Udaya Lakshmi; Aakash; Nilutpal Saikia; Anamika Kumari
An experiment was conducted at research farm of Rajiv Gandhi South Campus, Barkachha, Mirzapur situated in eastern Uttar Pradesh during winter (rabi) season of 2021-22 with the objective to study the response of nitrogen, phosphorous, sulphur doses and urea foliar spray on lentil growth attributes, yield attributes, yield and economics under guava + lentil based agri-horti system. Results revealed that the higher growth, yield attributes, yield, net monetory returns and benefit-cost ratio were recorded under N23.5+P60+S40 which was at par with N20+P50+S30. In case of varied doses of foliar spray of urea, foliar spray of 2% urea at pre-flowering stage fb 2% urea at pod initiation stage recorded significantly higher growth, yield, yield attributes and economics which was at par with foliar spray of 2% urea spray at pre-flowering stage. Moreover, between the sowing of the lentils and the harvest, the guava's growth attributes were also increased. Therefore, under rainfed conditions of Vidhyan region of eastern Uttar Pradesh, application of nitrogen, phosphorus and sulphur @20, 50 and 30 kg/ha as basal application along with foliar application (spray) of 2% urea at pre-flowering stage (45 DAS) to lentil crop was found to be better option for higher profitability under guava plantation. © 2022 Indian Council of Agricultural Research. All rights reserved.
Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling; [Algunos estimadores combinados mejorados de la media de la población en el muestreo de conjuntos clasificados estratificados]
(Universidad Nacional de Colombia, 2023) Rajesh Singh; Anamika Kumari
This paper presents improved population mean estimators using auxiliary variables in Stratified Ranked Set Sampling. We have derived the expres-sions for bias and mean square errors up to the first order of approximation and shown that the proposed estimators under optimum conditions are more efficient than other estimators taken in this paper. In an attempt to verify the efficiencies of proposed estimators, theoretical results are supported by numerical illustrations and simulation study for which we have considered two populations. © 2023, Universidad Nacional de Colombia. All rights reserved.
Some Improved Separate Estimators of Population Mean in Stratified Ranked Set Sampling
(Society of Statistics, Computer and Applications, 2024) Rajesh Singh; Anamika Kumari
This paper presents improved population mean estimators using auxiliary variable in Stratified Ranked Set Sampling. We have derived the expressions for bias and mean square errors up to the first order of approximation and shown that the proposed estimators under optimum conditions are more efficient than other estimators taken in this paper. In an attempt to verify the efficiencies of proposed estimators, theoretical results are supported by empirical study and simulation study for which we have considered two populations. © 2024, Society of Statistics, Computer and Applications. All rights reserved.
Some novel sine-type estimators for finite population mean utilizing known auxiliary information
(Springer Science and Business Media B.V., 2025) Rajesh Kumar Singh; Anamika Kumari; Shivam Dubey; Shobh Nath Tiwari
In sampling, the population mean estimate is essential because it offers a clear snapshot of the population’s average, helping with analysis and informed choices in areas such as environmental science, economics, and public health. To improve the efficiency and accuracy of estimators in estimating unknown population parameters, auxiliary information is often utilized, which typically results in reduced mean squared error (MSE) and increased percentage relative efficiency (PRE). In this paper, we modified conventional estimators and introduced some novel sine-type estimators, along with proposing a new exponential-cum-sine-type estimator to enhance finite population mean estimation with auxiliary data under simple random sampling. We compute the bias and MSE of the proposed estimator by applying first-order approximation techniques. The effectiveness and practical utility of the newly proposed estimator are validated using both real-world datasets and simulation studies. The proposed estimator proves to be consistently more efficient than both the sample mean and several competing sine-type estimators (ratio, product, regression, etc.) analyzed in this research. The results are summarized and followed by an analysis of the estimator’s practical applicability in real-world scenarios. The improved efficiency and reliability of the proposed estimator highlight its practical relevance in real-world data analysis. Its applicability across different domains underscores its potential as a robust tool for finite population mean estimation using auxiliary information. © The Author(s), under exclusive licence to Springer Nature B.V. 2025.
Understanding stunting and its determinant among children in the most populous state of India using estimation of population mean under ranked set sampling in the presence of missing data
(Routledge, 2024) Rajesh Singh; Chitra Saroj; Anamika Kumari
In real-life scenarios, encountering data with missing values is common, and if not managed carefully from the outset of a study, it can lead to significant biases in survey estimates. Various methods exist for imputing missing values in sampling procedures. Ranked set sampling (RSS) is widely recognized for its superior efficiency compared to simple random sampling. However, limited research has been conducted on ranked set sampling in the presence of missing data. This article introduces novel imputation methods designed to estimate population means in the context of missing data under RSS. These innovative estimators are developed by integrating ratio, exponential, and logarithmic estimators judiciously. Expressions for the bias and mean squared error of the proposed estimators are derived up to the first-order approximation. Through simulation studies and an application to stunting and its determinants among children in Uttar Pradesh, India’s most populous state, the effectiveness of the suggested estimators in handling missing data is demonstrated. Numerical examples involving stunting in Uttar Pradesh, as well as simulated data generated using R software, confirm the superior performance of the proposed estimators over existing methods, as evidenced by comparisons of percentage relative efficiency and mean squared error. The results are promising, indicating improvement over all existing imputation methods. Additionally, pertinent recommendations are provided for survey professionals regarding future research. © 2024 Taylor & Francis Group, LLC.