Estimation Of Population Variance Research Articles

ESTIMATION OF POPULATION VARIANCE USING KNOWN COEFFICIENT OF KURTOSIS AND MEDIAN OF AN AUXILIARY VARIABLE

We have suggested an improved ratio type log estimator for population variance by using coefficient of kurtosis and median of an auxiliary variable x. The properties of proposed estimator have been derived

Calibration estimation of population variance under stratified successive sampling in presence of random non response

This paper considers the problem of estimation of population variance of the study character in stratified successive sampling over two occasions under random non-response. Utilizing information available on a highly positively correlated auxiliary variable, a logarithmic type estimator is proposed and its properties, including bias and mean square error, are discussed. Calibration techniques have been applied for determining the optimum strata weight. Empirical studies have been carried out using both real and simulated data to show the efficiency of our proposed estimator over standard estimator, and suitable recommendations have been put forward to the survey statisticians for applications in real life problems.

An Improved Mathematical Model Applying Practicable Algorithms

In this article, we have considered the problem of estimation of population variance on two occasion successive sampling. A class of estimators of population variance has been proposed and its asymptotic properties have been discussed. The proposed class of estimators is compared with the sample variance estimator when there is no matching from the previous occasion. Numerical illustrations are also given in support of the present study.

Generalized regression cum ratio estimators of population variance in two phase sampling

This study suggested the generalized regression cum ratio estimators for estimating the population variance of the variable under study. The bias and mean squared error of the suggested estimator are derived under simple random sampling without replacement (SRSWOR) scheme. Empirical study has been performed with the three natural data sets which are having the dissimilar correlation among the study variable and the auxiliary variables. The proposed estimators are more efficient than the usual unbiased estimator, Isaki (1983) and Jhajj & Walia (2011) at all type of correlated populations.

ESTIMATION OF POPULATION VARIANCE IN LOG – PRODUCT TYPE ESTIMATORS UNDER DOUBLE SAMPLING SCHEME

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 under double sampling. Properties of the estimators are studied both mathematically and numerically.

A composite class of estimators to deal with the issue of variance estimation under the situations of random non-response in two-occasion successive sampling

Missing data often creates complications in data analysis for any type of scientific investigations. The non response is the source of missing data and it is an unavoidable phenomenon in survey sampling. This problem becomes more severe in the case of repeated surveys because of its repetitious nature. The missing data due to random causes which we call as random non-response is an important issue which needs to be dealt with a more cautious approach. To address these thoughts, this study is an attempt to reduce the adverse impact of random non response in the estimation of population variance on the current occasion in two-occasion successive sampling. A composite class of estimators for estimation of population variance on the current occasion has been proposed and its properties are deeply examined. An empirical study is carried out to show the efficacious performances of the proposed class of estimators over an estimator defined for the complete response situation. Suitable recommendations are made to the survey practitioners for their real-life practical applications.

An efficient estimator for population variance using parameters of an auxiliary variable

In this work a fresh attempt has been made to search for more efficient estimator for population variance of the study variable by making use of known parameters of an auxiliary variable. There are examples in the literature where authors have used irrelevant auxiliary information such as individual quartiles which have no bearing on variance estimation. In this short paper, we use the known parameters of auxiliary variable in the form of inter quartile range and correlation coefficient with the main variable under consideration. Both of these parameters are clearly relevant to this context. The expressions for the bias and MSE for the intended estimator have been derived using Taylor approximation. A comparison of estimators has been made through numerical computations using natural populations.

Enhancing the efficiency of the ratio-type estimators of population variance with a blend of information on robust location measures

Numerous ratio-type estimators of the population variance are proposed in the existing literature based on different characteristics of the study as well as the auxiliary variable. However, mostly the existing estimators are based on the conventional measures of the population characteristics and their efficiency is dubious in the presence of outliers in the data. This study presents improved families of variance estimators under simple random sampling without replacement assuming that the information on some robust non-conventional location parameters of the auxiliary variable is known besides the usual conventional parameters. The bias and mean square error of the proposed families of estimators are obtained and the efficiency conditions are derived mathematically. The theoretical results are supplemented with the numerical illustrations by using real datasets which indicates the supremacy of the suggested families of estimators.

Searching efficient estimator of population variance using tri-mean and third quartile of auxiliary variable

This paper concerns with the estimation of population variance of study variable using tri-mean and third quartile of the auxiliary variable. In this study, the sampling properties, bias and mean squared error of the proposed estimator are demonstrated. The justification of the performance of the proposed estimator under SRSWOR has been made with reference to the competing estimators of population variance, the sample variance, Isaki (1983) estimator, the estimator due to Upadhyaya and Singh (1999), Kadilar and Cingi (2006) estimators, Subramani and Kumarapandiyan (2012) estimators, Khan and Shabbir (2013) estimator and Maqbool and Javaid (2017) estimator of population variance. Based on data provided by Murthy (1967), it has been demonstrated that the proposed estimator has shown a significant improvement over all competing estimators of population variance.

Estimation of Population Variance Under an Imputation Method in Two-Phase Sampling

In this paper, an attempt has been made to reduce the negative effect of random non-response in the estimation procedure of population variance in two-phase sampling. A difference-type imputation method has been considered to reduce the wrong impact of random non-response in the two-phase sampling. To build efficient estimation strategies, information on two auxiliary characters has been used in the estimation of population variance and describes the effectiveness of the proposed estimators; dominant performances of the suggested estimators are compared with the well-known estimators of the population variance under the complete response. Results are explained through empirical studies which are followed by suitable recommendations.

Searching efficient estimator of population variance using tri-mean and third quartile of auxiliary variable

Searching efficient estimator of population variance using tri-mean and third quartile of auxiliary variable

English

English

DEVELOPMENT OF CHAIN-TYPE EXPONENTIAL ESTIMATORS FOR POPULATION VARIANCE IN TWO-PHASE SAMPLING DESIGN IN PRESENCE OF RANDOM NON-RESPONSE

Abstract In this paper, an investigation has been carried out to deal with a unified approach of estimation procedures of population variance in two-phase sampling design under missing at random non-response mechanism circumstances. Using two auxiliary variables, we have developed different chain-type exponential estimators of finite population variance for two different set-ups and studied their properties under the different assumption of random non-response considered by Tracy and Osahan (1994). The comparisons of the proposed estimators have been made with some contemporary estimators of population variance under the similar realistic conditions. Numerical illustrations are presented to support the theoretical results. Results are analysed and suitable recommendations are put forward to the survey statisticians.

Fuzzy nonparametric estimation of capability index $$\textit{C}_{pk}$$ C pk

Process capability indices have been widely used in the manufacturing industry to measure the potential performance. This paper proposes a nonparametric approach for estimating the proportion of non-conforming items and capability index $$C_{pk}$$ , when sample observations and specification limits of a process are reported as imprecise numbers. In this approach, first the $$\alpha $$ -pessimistic values of the imprecise observations were first applied to determine an unbiased estimator for population variance and optimal bandwidth. Thereafter, the fuzzy proportion of non-conforming items based on kernel distribution function was obtained. Finally, the fuzzy proportion of non-conforming items was applied to obtain the membership function of fuzzy nonparametric capability index $${\widetilde{C}}_{pk}$$ . Moreover, the proposed nonparametric methods are examined to compare with some other existing parametric methods and their performance will be cleared via some numerical examples and some comparison studies.

On the estimation of population variance using auxiliary attribute in absence and presence of non-response

In this article we proposed a new class of estimators for estimating the finite population variance using available auxiliary attribute in absence and presence of non-response problem. Properties such as bias and mean square error of the proposed class are derived up to the first order of approximation. The proposed class is more efficient than the Singh et al. (1988), Shabbir and Gupta (2007), Singh and Solanki (2013a), usual sample variance and regression estimators.

Improved Estimator of Population Variance Using Measure of Dispersion of Auxiliary Variable

This research study is designed to obtain a more precise class of estimators of a population variance by taking advantage of relation between auxiliary variable and study variable. Here a class of new modified ratio type estimators of population variance by using coefficient of variation (CV), standard deviation, mean and median of auxiliary variable. Further empirical study is made to compare bias and mean square error (MSE) of proposed estimators with the existing estimators. Expressions for bias and MSE are obtained. Few secondary data sets are used to check the efficiency of proposed estimators of population variance.

Estimate of Population Variance by Introducing Gini’s Mean Difference as Auxiliary Information

Estimate of Population Variance by Introducing Gini’s Mean Difference as Auxiliary Information

Robust Estimators for Estimation of Population Variance Using Linear Combination of Downton’s Method and Deciles as Auxiliary Information

Robust Estimators for Estimation of Population Variance Using Linear Combination of Downton’s Method and Deciles as Auxiliary Information

Exponential Estimators of Finite Population Variance Using Transformed Auxiliary Variables

This study is based on the proposal of generalized exponential estimator for finite population variance using two transformed auxiliary variables. The expressions for mean square errors and the minimum values for the optimized constants are obtained. The conditions are obtained for which the proposed estimator are better than existing estimators. The result of empirical and simulation study indicates that the suggested estimator is efficient than existing estimators for population variance.

An improved generalized class of estimators for population variance using auxiliary variables

This paper proposed an improved generalized class of estimator for estimating population variance using auxiliary variables based on simple random sampling without replacement. The expression of me...