Exponential Ratio Estimators Research Articles

A new modified estimator of population variance in calibrated survey sampling

In survey statistics, estimating and reducing population variation is crucial. These variations can occur in any sampling design, including stratified random sampling, where stratum weights may increase the variance of estimators. Calibration techniques, which use additional auxiliary information, can help mitigate this issue. This paper examines three calibration-based estimators—calibration variance, calibration ratio, and calibration exponential ratio estimators—within the framework of stratified random sampling. The study generates data from normal, gamma, and exponential distributions to test these estimators. Results demonstrate that the proposed calibration estimators offer more accurate estimates of population variance and outperform existing methods in estimating population variance under stratified random sampling, providing more accurate and reliable estimates.

Modified exponential ratio estimator for ranked set sampling in the presence of tie information and application on COVID-19 real data

In this article, we develop the isotonic ratio mean estimator proposed by Kocyigit and Kadilar (2020) within the case of tie information in the Ranked Set Sampling (RSS). In addition, we take into consideration the population size being large and small. We offer a generalized exponential ratio estimator using the modified isotonic estimator for this situation. Simulation results show that the proposed estimator is more efficient than the estimators in the literature. In the real data study, the 34 regions of China since China is the country where the pandemic started are taken as a small population, and the data of 212 countries on a world scale is taken as a large population, then the estimators are calculated. In the real data study, the proposed estimator gives better results than the existing estimators thus the results in the simulation study are similar to the real data study.

Estimating A Finite Population Mean Under Two-Phase Sampling Using Exponential Ratio Estimator

Estimation of population parameters such as population mean, and population total has been a major concern in Sample Survey Theory. In sampling theory, researchers employ auxiliary information to improve precision and validity of estimators. This study applies two-phase sampling in estimation of a finite population mean using modified exponential ratio estimator. Two-phase sampling was used since it leverages on the information collected in the first phase, along with auxiliary variables, to guide the selection of a more targeted and efficient second-phase sample, resulting in increased precision for the estimates of interest. Study results showed that the proposed modified exponential ratio estimator produced a smaller Bias and MSE than Shabbir and Gupta (2007), and Singh and Solanki (2013). Further, the proposed estimator produced a higher relative efficiency as compared to Shabbir and Gupta (2007), and Singh and Solanki (2013).

Modified Classes of Stratified Exponential Ratio Estimators of Population Mean with Equal Optimal Efficiency

This paper introduces new classes of exponential ratio estimators for population mean and derives expressions for their biases and mean square errors (MSEs) under the large sample approximation. Asymptotic optimum estimator and its approximate MSE are derived for each class of estimators. Their properties are studied and some special members of their families are identified. Analytically, the proposed classes of estimators have been shown to have equal optimal efficiency under certain prescribed conditions. It is observed that the proposed classes of estimators fare better than the regression estimator and all the modified existing estimators under review with appreciable efficiency gains.

A simulation based optimization of factor-type exponential estimators in sample surveys with coefficients of variation and kurtosis

In the context of sample surveys, this article presents factor-type exponential ratio estimators as a technique for estimating population means. These estimators use supplementary information for an auxiliary variable, such as coefficients of variation and coefficients of kurtosis. The research includes a range of alpha values from −1 to +1 to improve estimate.Following that, the study rigorously develops formulas for both bias and mean square error for the suggested estimators. Up to the first degree of large sample approximation, these formulas are produced. The empirical findings we present are renowned in that they show that the suggested estimators consistently beat existing exponential estimators with significantly lower mean squared errors.We calculate the suggested estimator’s percent relative efficiency in comparison to the traditional mean estimator to put a number on how effective it is. We show persuasive proof of the significant improvement offered by our estimators over existing exponential estimators by a complete numerical illustration and a rigorously conducted simulations exercise. Summary:We present factor-type exponential ratio estimators for estimating population means in sample surveys. Key points:We take into account auxiliary information, different alpha values, and various correlation circumstances. Objective:We want to improve population mean estimation precision. Method:To assess our estimators, we use numerical examples and simulations. Results:Our estimators typically outperform competitors, with smaller mean squared errors. Advantage:We demonstrate their robustness and efficiency in improving population mean estimate through rigorous simulations.

On Some New Exponential Ratio Estimator of Population Mean in Two Phase Sampling

In this paper, we suggest employing the exponential ratio estimator to estimate the mean of the study variable using a two-phase sample strategy with two modified auxiliary variables. Several researchers discussed the properties of the estimators they proposed and discovered that the estimators in their studies were relatively efficient. The estimators previously studied are listed chronologically in the appendix to this paper. In two phase sampling, the estimator's mean square errors and relative efficiencies are calculated using auxiliary variable information. To assess the properties of our proposed estimator, we noticed that it has a lower mean square error (MSE) than the classical ratio estimator and some other exponential ratio estimators. The estimator is more useful than other estimators in solving real-world issues, notably in engineering, environmental science, management, and biological sciences. The proposed estimator has been applied to real-world data sets such as BRICS, Son's Head Measurement, Number of Hospital Beds, Sale Price of Residence, Ambient Pressure (AP), and Heating Load. In survey research, our suggested estimator has also been demonstrated to be more effective.

Exponential ratio estimator of the median: An alternative to the regression estimator of the median under stratified sampling

This article develops statistical inference about the population median under the stratified sampling method. An exponential class of ratio estimators of the median was suggested using the combination of scalars and known supplementary information on the population median. Mean square error and bias expressions were derived theoretically and also the AOE (asymptotic optimum estimator) conditions were obtained with its mean square error and bias expressions. From both the empirical evidence and analytical approach evaluations of the AOE with other obtainable members of the suggested class of estimators show that the AOE performs better than its competitors in the literature and is also the alternative to the regression estimator of the median under a stratified random sampling scheme.

RATIO ESTIMATORS FOR POPULATION VARIANCE IN ADAPTIVE CLUSTER SAMPLING

To estimate the variance for rare and cluster population has been the main problemin survey sampling. Three ratio type estimators were proposed for population variance utilizing thesingle auxiliary variable assuming the transformed population for adaptive cluster sampling, inpresented study. The expressions for the mean square error and bias of the proposed estimator werederived. The proposed estimatorswere used to estimate the finite population variance in adaptivecluster sampling. The simulationswereperformedon a real life data to reveal and evaluate the efficiencyof the estimators. The results showed that the proposed exponential ratio estimator was more efficientcompared to the usual sample variance estimator and the proposed ratio type variance estimators inadaptive cluster sampling, assuming given conditions. Hence, exponential ratio estimators wererecommended to estimate the population variance in adaptive cluster sampling.

Information theory approach to ranked set sampling and new sub-ratio estimators

In this study, we introduce a new approach to the mean estimators in ranked set sampling. The amount of information carried by the auxiliary variable is measured with the Shannon entropy method on populations and samples and to use this information in the estimator, the basic ratio and the generalized exponential ratio estimators are modified as sub-ratio estimators to use only the information on the sample. Without using the required population parameter for ratio estimators, we propose new sub-ratio type estimators using only the auxiliary variable for ranking in the implementation of the ranked set sampling method. The mean squared errors and bias formulas of the proposed estimators are obtained and it is shown that the proposed estimators are more efficient than the classic mean estimator and ratio estimator of RSS under the certain theoretical conditions. Simulation and real data studies also show that the proposed estimators always give better results than the mean estimators of ranked set sampling and it is observed that the relative efficiencies of the proposed estimators increase depending on the magnitude of the entropy, the correlation between the auxiliary and the study variables, and the set sizes.

OPTIMUM SEPARATE RATIO -TYPE EXPONENTIAL ESTIMATOR FOR COMPUTATION OF POPULATION MEAN IN STRATIFIED RANDOM SAMPLING

In this manuscript, we study the problem of separate type exponential ratio estimator for estimation of population mean with their properties. The MSE and Bias up to the first degree of approximation for the suggested estimator are computed. The suggested estimator is proven to be more efficient than estimators mentioned in the literature under stratified random technique. An empirical investigation was done to assess the suggested estimator. Also, the percent relative efficiency is to be remarkable for the proposed estimator.

Generalized Exponential Ratio Estimator of Population Mean Using Two Auxiliary Variables in Simple Random Sampling with an Application to Agricultural Data

Generalized Exponential Ratio Estimator of Population Mean Using Two Auxiliary Variables in Simple Random Sampling with an Application to Agricultural Data

On use of subsampling of the non-respondents for estimation of distribution function

In this study, we propose a general class of estimators of the finite population distribution function (DF) using two auxiliary variables under subsampling of non-respondents. We use the Hansen and Hurwitz [1] pioneered model in our subsampling technique. Layout of response and non-response classes are discussed in various tables in detail. Expressions for the biases and mean square errors (MSEs) of the estimators are obtained up to first order of approximation. We also obtain the conditions by comparing the proposed estimator with existing estimators. Three real data sets are used to support the theoretical findings. In our findings, it is observed that the proposed class of estimators is more efficient as compared to all other existing estimators including the usual mean estimator, ratio estimator, exponential-ratio estimator, traditional difference estimator, Rao [2] difference estimator, Kumar et al. [3] estimator and many other recent difference type estimators by using the criterion of MSE.

Measuring Performance of Ratio-Exponential-Log Type General Class of Estimators Using Two Auxiliary Variables

In this paper, a ratio-exponential-log type general class of estimators is proposed in estimating the finite population mean using two auxiliary variables when population parameters of the auxiliary variables are known. From the proposed estimator, some special estimators are identified as members of the proposed general class of estimators. The mean square error (MSE) expressions are obtained up to the first order of approximation. This study finds that the proposed general class of estimators outperforms as compared to the conventional mean estimator, usual ratio estimators, exponential-ratio estimators, log-ratio type estimators, and many other competitor regression type estimators. Four real-life applications are used for efficiency comparison.

Exponential ratio and product type estimators of the mean in stratified two-phase sampling

In this study, we propose exponential ratio estimators in the stratified two-phase sampling utilizing an auxiliary attribute. The expressions for the mean squared error of these exponential-type estimators under two different cases are derived and theoretical comparisons are made with competing estimators. We show that the proposed estimators have a lower mean square error than the simple mean estimator, usual stratified two-phase sampling ratio, and product estimators, usual exponential ratio and product estimators for the stratified two-phase sampling under the obtained conditions in theory. In addition, these theoretical results are supported with the aid of a numerical example.

Ratio estimators for ranked set sampling in the presence of tie information

In this article, we study the situation of observations whose ranks cannot be determined for the auxiliary variable in the Ranked Set Sampling (RSS) method. Therefore, we examine the case of tie information for ratio estimators of the population mean. We propose a new exponential ratio estimator using the modified isotonic estimator for this situation. Simulation results show that the proposed estimator is more efficient than the other estimators in literature. In addition, when we examine the recent COVID-19 pandemic situation, we see that the data is suitable for this structure. We can also see from the real data that the proposed estimator gives better results.

Some Exponential Type Predictive Estimators of Finite Population Mean in Two-Phase Sampling

This study is designed for predictive estimation of finite population mean in two phase sampling using two auxiliary variables. Two phase exponential ratio type estimator and exponential chain ratio type estimator are proposed under predictive approach suggested by Bahl & Tuteja (1991). The expressions of bias and mean square error of both suggested estimators have been carried out for theoretical comparison. The numerical study on real life data sets as well as simulation study has been conducted to examine the performance of suggested estimators. Finally, it is demonstrated that the suggested exponential ratio estimators are more efficient than competitive estimators in support of numerical and simulation study as well.

An efficient exponential estimator of the mean under stratified random sampling

ABSTRACT Stratification of population is a probability sampling design used to increase the precision of estimation. An efficient exponential ratio estimator allows estimating the population mean in stratified random sampling using an auxiliary variable. Its expected bias, expected mean square error, and minimum mean square error are expressed. The conditions for which the estimator is more efficient are obtained. The proposed estimators under stratified random sampling have a lower mean square error than the ratio and the exponential estimators.

A new improved difference-cum-exponential ratio type estimator in systematic sampling two auxiliary variables

A difference-cum-exponential ratio type estimator was proposed for estimating the finite population mean using two auxiliary variables under systematic sampling. Expressions for the biases and mean square errors (MSEs) were derived up to first order of approximation. It was observed that the proposed estimator is more efficient than the usual sample mean estimator, traditional ratio estimator, exponential-ratio estimator and many other recently proposed difference type estimators in terms of MSEs. Four datasets were used for efficiency comparisons.

Efficient estimation combining exponential and ln functions under two phase sampling

In this study, we propose the combination of exponential and ln ratio type estimator to estimate the mean of Y (Study Variable) by incorporating two auxiliary variables in two phase sampling scheme. Under simple random sampling without replacement, the illustration for mean square error and mathematical comparisons are presented. Several approaches are available in literature to estimate the study variable by using information on the variable of interest. The performance of our proposed estimator is compared with other ratio type estimators theoretically and empirically. It is observed that ratio and exponential ratio estimators considered by various researchers and usual unbiased estimator is less efficient than our proposed estimator. An efficiency comparison is also given using five data sets and simulation studies for checking the merits of our proposed estimator and outcomes are sound and moderately illuminating in comparison to different estimators.

Novel family of exponential estimators using information of auxiliary attribute

In this article, we propose a family of exponential ratio estimators for the estimation of the population mean of the study variable using the information of the population proportion possessing the certain attributes. We obtain the mean squared error (MSE) equations for all proposed ratio exponential estimators and find theoretical conditions that make the proposed estimators more efficient than the Naik and Gupta (1996) estimator and the ratio exponential estimator suggested by Singh et al. (2007). In addition, these conditions are supported by an application with original data sets.