Rajesh Singh

• M.Sc., Ph.D.
• Professor (Full) at Banaras Hindu University

The paper focus on influence of various determinants viz, General Nature (Religion, type of place of residence, State, Ethnicity, Caste, Education level of partners, justification of beating by women, alcohol consumption, type of relationship to husband before marriage), Women empowerment and Childhood Trauma influencing domestic violence and women...

In the present paper a ratio cum product type exponential class of estimators has been proposed to estimate the finite population mean of rare type or hard to reach type population. The mean square error and bias expressions of the proposed generalized class have been derived and presented up to the first order of approximation. New estimators have...

In the context of classical statistics, the estimation of the population mean is done with determinate, precise, and crisp data when auxiliary information is available. However, there are instances where dealing with uncertain, indeterminate, and imprecise data in interval form is required. To overcome this issue, Florentin Smarandache introduced n...

Improving efficiency has long been a focal challenge in sampling literature. However, simultaneously enhancing estimator efficacy and optimizing survey costs is a practical necessity across various fields such as medicine, agriculture, and transportation. In this study, we present a comprehensive family of generalized exponential estimators specifi...

This article suggests three generalized exponential estimators using an auxiliary variable for estimating population mean with some transformations. The mean squared error expressions are derived up to the first order approximation for comparing the efficiency of the proposed estimators with the existing estimators in literature. We compared the ef...

The primary objective of sample survey is to have an estimate of population parameter. The more is the available information the better is an estimate. In this study, the Exponentially Weighted Moving Average statistic is used to estimate the population mean with auxiliary information. For the purpose of estimating population mean, we have designed...

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...

This article introduces a novel class of estimators and several new novel member estimators, combining the ratio and product forms, within the framework of Adaptive Cluster Sampling (ACS) design for estimating finite population mean. Specifically designed for rare or hidden clustered populations, the new novel estimators developed from the proposed...

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 utilizing auxiliary information. Up to the first order of approximation, the equations for the bias and mean squared error of the suggested estimators a...

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 ad...

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...

This paper proposes two classes of robust ratio type estimators of finite population mean and two classes of robust ratio type estimators of finite population variance using a single auxiliary variable under the adaptive cluster sampling design. Seven robust ratio type estimators have been developed from each class. The generalized expressions of b...

The primary goal of this study is to address the limitations of classical statistics in handling ambiguous or indeterminate data. The best alternative to classical and fuzzy statistics for handling such data uncertainty is neutrosophic statistics, which is a generalization of both. A generalization of classical statistics, neutrosophic statistics a...

In survey sampling, it might happen that information on the population mean of the auxiliary variable is not available, but it can be obtained if the researcher opts for it. The sampling design to be used in such a case is the Two-Phase sampling design. This design has been studied extensively in SRSWOR, but it has not been studied when the populat...

The objective of the paper is to propose an almost unbiased ratio estimator for the finite coefficient of variation (CV). In this paper, we have proposed an exponential ratio type and log ratio type estimators for estimating population coefficient of variation. Two real data sets and one simulation study is carried out in support of the theoretical...

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 correl...

In this paper we have proposed classes of ratio-type estimators for finite population mean in presence of non-response in stratified sampling. The properties of the estimators have been discussed. We have also derived optimum choices of scalar constant to reduce the bias in the estimators which make suggested classes of estimators almost unbiased....

Log -type estimator is proposed to estimate population mean in ACS

In this article, we have proposed two new estimators to estimate the coefficient of variation (CV) incorporating transform ratio type and log type estimators of the study variable using the known information on an auxiliary variable. These estimators utilize information on logarithm transformation on both the population and sample mean of auxiliary...

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...

Various efficient estimators using single and dual auxiliary variables with different functions including log and exponential have been developed in the SRSWOR design. Since the Adaptive cluster sampling (ACS) design is relatively new, estimators using functions like log and exponential with single and dual auxiliary variables have not been explore...

This article introduces a generalized class of estimators tailored for estimating the finite population mean within the framework of Adaptive Cluster Sampling (ACS) design. The proposed class is designed to encompass numerous existing estimators as its particular cases while also introducing several new novel estimators. It should be noted that the...

Through this paper, we present some improved estimators of population mean using auxiliary variables in stratification. 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 efficient than other estimators taken in this paper. In verify...

This paper presents improved population mean estimators using auxiliary variables 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 eficient than other estimators taken in this paper. In an...

In this study, we have put forward a class of estimators for estimating population mean for the cross-sectional and time scaled surveys. It is revealed in the study conducted by [5] that the use of Exponentially weighted moving average (EWMA) statistic improves the performance of the estimators for the time scaled surveys as it makes the use of pas...

This paper introduces the basic concepts of Ranked Set Sampling (RSS) and compares RSS with Simple Random Sampling (SRS). In this paper, we have presented some improved estimators of population mean using auxiliary variables in RSS. We have derived the expressions for the bias and the mean square errors of the suggested estimators up to the first o...

In this paper, mean estimators under ranked set sampling are reviewed. In this paper, we have also presented some improved novel classes of estimators for estimating the population mean using auxiliary variable under ranked set sampling. We have derived the expressions for bias and mean squared error of the proposed estimators up to the first ord...

In this study, we have put forward a class of estimators for estimating population mean for the cross-sectional and time scaled surveys. It is revealed in the study conducted by [5] that the use of Exponentially weighted moving average (EWMA) statistic improves the performance of the estimators for the time scaled surveys as it makes the use of pas...

The use of power transformed estimator results in higher precision in the estimation as these estimators provide a lesser MSE. Such precision is much appreciated when the population under study is rare or hidden clustered as with this population, getting a representative sample is difficult and when the precision of the estimate is paramount. To de...

In this paper, we proposed two classes of estimators under two new calibration schemes for a heterogeneous population by incorporating auxiliary information of Non-Conventional Measures of dispersion which are robust against the presence of outlier in the data. Theoretical results are supported by simulation studies conducted on six bivariate popul...

In survey sampling, presence of outliers in the data collected has been one of the biggest concerns. This problem becomes severe when dealing with estimation of communicable diseases. Further, there are several cases where the population under study is hidden clustered or clumped and non-adaptive sampling designs in these cases fail to give a relia...

Classical statistics and its methods deal with randomness, but there are cases where the data at hand are indeterminate or vague or ambiguous rather than random. In such situations, estimation using classical statistical methods does not yield promising results. Fuzzy logic [1, 2] is one solution to tackle such a problem, but still, it ignores inde...

The use of multi-auxiliary variables helps in increasing the precision of the estimators, especially when the population is rare and hidden clustered. In this article, four ratio-cum-product type estimators have been proposed using two auxiliary variables under adaptive cluster sampling (ACS) design. The expressions of the mean square error (MSE) o...

This paper proposes two classes of robust ratio type estimators of finite population mean and two classes of robust ratio type estimators of finite population variance using a single auxiliary variable under the adaptive cluster sampling design. Seven robust ratio type estimators have been developed from each class. The generalized expressions of b...

In this paper three efficient exponential ratio type estimators of finite population mean in the Adaptive Cluster Sampling design have been proposed using one known auxiliary variable. The expressions of bias and mean squared error of the proposed estimators are derived up to the first order of approximation. A simulation study has been conducted o...

In this article, we suggest some novel estimators of population Coefficient of Variation (CV) of the study variable using the known information on an auxiliary variable like population mean and population variance. Up to the first order of approximation, formulas for the bias and Mean squared Errors (MSE) of the proposed estimators are obtained. Th...

In this paper, we proposed new conventional unbiased and calibration estimators for estimating finite population variance for a Mail Survey Design characterized by the presence of non-response in practice. The properties of the proposed estimators are studied theoretically and numerically. Empirical studies were conducted using two each of existing...

This paper addresses the problem of biases in variance estimators under the simultaneous influence of both measurement and non-response errors. Three classes of estimators are suggested and their properties are studied up to first order of approximation. Also, their efficiency conditions over some existing estimators are established. Resultant almo...

The initial spread of COVID-19 is highly clustered or clumped. In such a case conventional sampling designs viz., Simple random sampling without replacement, Stratified random sampling or other non-adaptive designs cannot be used to estimate the average cases of COVID-19 as the sample drawn will not be a representative one. In this article, we have...

In this manuscript, we have proposed two improved exponential ratio estimators using auxiliary information for estimating the unknown population mean in Adaptive Cluster Sampling (ACS) and have found the optimum value of a (the base of the exponent) using a numerical study. The Mean Squared Error for the two estimators has been derived up to the fi...

In this paper, we suggest an exponential type estimator for estimation of population mean for missing data under suggested imputation techniques. Family of proposed estimator is obtained for missing data. Expression for Bias and MSE's are acquired in the form of population parameters up to the terms of first order of approximation. Theoretical resu...

Estimation of population parameters plays a vital role in the area of sampling. Many authors have proposed several estimators for estimating population parameter(s) using auxiliary information. This paper has attempted to suggest a new estimator for estimating the general parameter ta,b using auxiliary information in SRSWOR. A conventional estimato...

When the data is vague or indeterminate, estimators proposed under classical statistics fail. Neutrosophic Statistics becomes the only alternative because it deals with indeterminacy. In this article, we have proposed different transformed neutrosophic ratio estimators to estimate the unknown population mean of neutrosophic data. The Mean squared e...

The paper comprises an estimator for estimating population variance using auxiliary information as median, since auxiliary information correlated with the study variable boosts the efficiencies of the estimators. Simple random sampling without replacement scheme has been applied as a technique. The proposed estimator's mean squared error is derived...

In this paper, we have proposed a regression-type compromised imput-ation methods free of unknown parameters. The properties (biases and MSEs) of the proposed class of estimators are derived up to first order approximation using Taylor series approach. Also, the conditions for which the proposed estimators are more efficient than other estimators c...

In this paper, two modified, design-based calibration ratio-type estimators are presented. The suggested estimators were developed under stratified random sampling using information on an auxiliary variable in the form of robust statistical measures, including Gini’s mean difference, Downton’s method and probability weighted moments. The properties...

In this paper, we have proposed six classes of estimators for different cases of non-response for a heterogeneous population under the stratified random sampling using auxiliary information with unknown population mean. The properties of the proposed estimators have been examined and studied for fixed sample size and the members of the proposed cla...

Use of auxiliary information is always suggested at the planning and estimation stage to make the estimators perform more efficiently.Estimation using auxiliary information is common in sampling literature but using distribution of study and auxiliary information at the estimation stage is uncommon and found useful especially when dealing with rare...

In this paper, we have proposed three classes of almost unbiased estimators for population mean under simultaneous presence of measurement and non-response error. Asymptotic properties such as Bias and MSE for the proposed classes of estimators are obtained. Numerical illustration in support of theoretical results is also given on two real data set...

In this paper, we suggest an exponential type estimator for estimating population mean under simple random sampling without replacement and also utilize this estimator for missing data under varied imputation techniques. Expressions for Bias and MSE's are acquired in the form of population parameters up to the first order of approximation. The empi...

In this manuscript, we have proposed improved estimators for estimating the finite population mean under stratified random sampling in three different situations: At first we considered the properties of the estimators under non-response, then in the next case we studied the estimators for measurement error and in the last case we examined the esti...

In this paper, we propose an exponential type estimator for finite population variance under simple random sampling without replacement using an auxiliary variable, which is highly correlated with the study variable. Mean square error of the proposed estimatoris derived up to first order of approximation. Efficiency of the proposed estimator is com...

In this manuscript, we have proposed improved estimators for estimating the finite population mean under stratified random sampling in three different situations: At first we considered the properties of the estimators under non-response, then in the next case we studied the estimators for measurement error and in the last case we examined the esti...

This paper proffers an improved estimation for population coefficient of variation using information on a single auxiliary variable. We derived the expressions for the mean squared error of the proposed estimators up to the first order of approximation. Here we have shown that our proposed estimators are more efficient than the existing estimators....

It is experienced that auxiliary information when suitably incorporated yields more efficient and precise estimates. Mishra et al. (2017) have introduced a log type estimator for estimating unknown population mean using ancillary information in simple random sampling. Here we propose an improved log-product type estimator for population variance un...

In this paper, we have proposed two log- product -type estimators and a new estimator for estimation of finite population mean under measurement error by using auxiliary information. The expressions for Bias and mean squared error of proposed estimators are evaluated up to first order of approximation. Based on theoretical results obtained, a numer...

In the sampling literature, auxiliary information is commonly used to improve estimates. Many authors have suggested estimators based on auxiliary information. However in many practical situations, instead of the existence of auxiliary variables there exist some auxiliary attributes, e.g., φ, which are highly correlated with the study variable y, s...

An alternative to simple random sampling (SRS) is the sample design known as ranked set sampling (RSS). McIntyre (1952) introduced it looking to increase the efficiency of the estimation of the population mean. The method is useful when the variable of interest is very expensive or difficult to measure but it can be easily ranked at a negligible co...

Ambati et al. (2017) proposed an estimator for estimating the unknown coefficient of dispersion under simple random sampling without replacement case. Unfortunately, the mean squared error (MSE) expression obtained by Ambati et al. (2017) was incorrect. In this paper, we have obtained correct expression of the MSE of the estimator proposed by Ambat...

This paper propounds an improved estimation of coefficient of variation utilizing information on a single auxiliary variable. The expressions for mean square errors of the proposed estimators have been derived up to first order of approximation. At one hand, among the proposed estimators, some of the estimators under optimum conditions are more eff...

Ranked Set Sampling (RSS) strategies when an Optional in Scrambling Randomized Response Modeling procedure is used, are derived. In this paper are obtained Ranked Set Sampling models for estimating unbiasedly the mean, the variance of the sensitive variable as well as of its sensitivity level W. The scrambled response modeling of Mehta et al (201...

In this paper effect of measurement error and non response error is examined on estimation of unknown population mean of study variable. We have obtained the expression of the MSE (mean square error) of the proposed estimator up to first order of approximation. We have shown theoretically and empirically that the proposed estimator performs better...

This paper suggests the generalized class of estimators, motivated by Sharma and Singh (2015), of finite population variance utilizing the known value of parameters related to an auxiliary variable such as quartile and its properties are studied in simple random sampling without replacement. The efficiency of proposed class of estimators is compare...

This paper proposed some improved class of estimators of population mean in presence of measurement error using auxiliary variable based on arithmetic mean, geometric mean and harmonic mean of the usual unbiased estimator, Salabh estimator (1977) and estimators due to Bahal and Tuteja (1991) in case of simple random sampling without replacement (SR...

In this paper, we suggest an estimator using two auxiliary variables in stratified random sampling. The propose estimator has an improvement over mean per unit estimator as well as some other considered estimators. Expressions for bias and MSE of the estimator are derived up to first degree of approximation. Moreover, these theoretical findings are...

When dealing with data provided by sensors we must deal with Big Data.That is the case in many environment applications. It is often needed to estimate the Average Derivative and the problem is concerned with non parametric regression fitting and the reliability of it is based on the point-wise consistency of an estimator of a probability density f...

Derivatives used in euotriphication research The best overall classification method is using the “Nearest Neighbor Distance”. If the most important issue is classifying correctly the potable water, the best method is the ANNMM with the m-estimate; while the behavior of f Lj provides the smaller misclassification probability when classifying the wat...

When dealing with data provided by sensors we must deal with Big Data. That is the case in many environment applications. It is often needed to estimate the Average Derivative and the problem is concerned with non parametric regression fitting and the reliability of it is based on the point-wise consistency of an estimator of a probability density...

In this article, we have proposed a generalized class of estimators, exponential class of estimators based on adaption of Sharma and Singh (2015) and Solanki and Singh (2013) and simple difference estimator for estimating unknown population mean in case of Poisson distributed population in simple random sampling without replacement. The expressions...

Yasmeen et al. (Int J Appl Comput Math 1(2), 1–10, 2015) introduced an exponential ratio cum dual to ratio type of estimator for the population mean and compared the performance of the several estimators using the derived expression of MSE. But unfortunately, the expressions of bias and MSE of their proposed estimator \(\hbox {t}_{\mathrm{n}/2\math...

This paper deals with estimation of unknown population variance of study variable (y) using auxiliary qualitative characteristic. The properties of the proposed class of estimators is studied and is supported through two real data sets.

In this paper, we proposed some new type estimators for estimating finite population mean of study variable. The mean squared error of the proposed estimators have been obtained up to the first order of approximation. Here we shown that our proposed estimators are more efficient than usual estimator. An empirical study is also carried out to demons...

This article discusses the problem of estimation of population mean in stratified sampling using information on two auxiliary variables. The expressions for the mean square error of the proposed estimator have been derived up to the first order of approximation and are compared with the existing estimators. Also, an empirical study has been carried...

In this paper we have proposed an exponential ratio type estimator of the finite population mean in presence of measurement error and non-response error. Expression of Mean Square Error has been calculated up to first order of approximation. Empirical study based on five data sets has been carried out. Theoretically and empirically we have found th...

Stochastic optimization problems are present in applications in management, engineering and medicine, as well as in environment, physical and social sciences. This chapter is concerned with studying the behavior of the estimation and approximation of the Approximation Error in different types of stochastic problems. Statistical techniques are consi...

This article deals with estimation of population mean for missing data in simple random sampling. The properties of the proposed procedure is studied up-to first order of approximation and under the optimality conditions proposed estimator outperforms other existing estimators. A numerical illustration, based on the two real data sets, highlights t...

In this paper, we proposed some new type estimators for estimating finite population mean of study variable. The mean squared error of the proposed estimators have been obtained up to the first order of approximation. Here we shown that our proposed estimators are more efficient than usual estimator. An empirical study is also carried out to demons...

In this paper we have suggested some estimators of population variance using auxiliary information based on arithmetic mean, geometric mean and harmonic mean.We have also suggested an almost unbiased estimator for estimating population variance. The expressions of mean squared error (MSE) have been derived up to the first order of approximation. It...

Some imputation techniques are suggested for estimating the population mean when the data values are missing completely at random under a simple random sample without replacement scheme. Two classes of point estimators are proposed. The bias and mean squared error expressions of the proposed point estimators are derived up to first order of approxi...

This paper suggests a generalized class of estimators for the population mean of a qualitative study variable in simple random sampling using information on an auxiliary variable. Asymptotic expressions of bias and mean square error of the proposed class of estimators have been obtained. Asymptotic optimum estimator has been investigated along with...

This article presents improved estimation of population mean using auxiliary attribute. The bias and mean square error of proposed estimators are obtained up to first order of approximation and it is shown that proposed class of estimator under optimum conditions is more efficient than the other estimators considered in this article. The theoretica...

Adapting [14] and [15], we proposed modified classes of estimators for the unknown mean of study variable when auxiliary information is available in the form of attribute. The bias and mean square error of the estimators belonging to the classes are obtained and the expressions for the optimum parameters minimizing the asymptotic mean square error...

In this paper, we suggest an estimator using two auxiliary variables in stratified random sampling following Malik and Singh [12]. The propose estimator has an improvement over mean per unit estimator as well as some other considered estimators. Expressions for bias and MSE of the estimator are derived up to first degree of approximation. Moreover,...