A New Difference-Cum-Exponential Type Estimator of Finite Population Mean in Simple Random Sampling

Abstract

Auxiliary information is frequently used to improve the accuracy of the estimators when estimating the unknown population parameters. In this paper, we propose a new difference-cum-exponential type estimator for the finite population mean using auxiliary information in simple random sampling. The expressions for the bias and mean squared error of the proposed estimator are obtained under first order of approximation. It is shown theoretically, that the proposed estimator is always more efficient than the sample mean, ratio, product, regression and several other existing estimators considered here. An empirical study using 10 data sets is also conducted to validate the theoretical findings.Key words: Ratio estimator, Auxiliary Variable, Exponential type estimator, Bias, MSE, Efficiency. ResumenInformación auxiliar se utiliza con frecuencia para mejorar la precisión de los estimadores al estimar los parámetros poblacionales desconocidos. En este trabajo, se propone un nuevo tipo de diferencia-cum-exponencial estimador de la población finita implicar el uso de información auxiliar en muestreo aleatorio simple. Las expresiones para el sesgo y el error cuadrático medio del estimador propuesto se obtienen en primer orden de aproximación. Se muestra teóricamente, que el estimador propuesto es siempre más eficiente que la media de la muestra, la relación de, producto, regresión y varios otros a Professor.

On the Optimal Search for Efficient Estimators of Population Mean in Simple Random Sampling in the presence of an Auxiliary Variable

“…Significantly, the range of values of the regulating parameter δ obtained through appropriate mathematical proof and solving a formulated nonlinear programming model are used to obtain the Asymptotic Optimal Estimators for the proposed family, which are shown with their Mean Square Errors in Table 2. This approach shows advancement over the works of [43] and [31], whose choice of parameters were given intuitively without any concrete mathematical backup. From Table 2, it has also been observed that Asymptotic Optimal Estimators (AOE) include some existing estimators of [28] and [24].…”

“…Recent works have built on both the modifications of the classical ratio or regression and the exponential ratio estimators to obtain improved efficiencies in simple random sampling. These works include [24], [10], [58], [31], [35], [35], [42], [6], [7], [8]. These works showed some improvements over the Regression estimator.…”

Difference-Type-Exponential Estimators Based on Dual Auxiliary Information Under Simple Random Sampling

“…Several authors have used ratio, product and regression-type estimators to estimate population mean when both study and auxiliary variables are directly observable. For detail, see the following references: Kadilar and Cingi [2][3], Gupta and Shabbir [4], Grover and Kaur [5][6], Singh and Solanki [7], Haq and Shabbir [8], Shabbir et al [9], Ekpenyong and Enang [10], Khan et al [11], Solanki and Singh [12], Srisodaphol et al [13], Singh and Pal [14], Singh et al [15], Irfan et al [16][17], Javed et al [18] etc. This section gives a brief introduction of traditional estimators i.e.…”

A New Exponential Type Estimator for the Population Mean in Simple Random Sampling

“…Population 2. Source Shabbir, Haq, and Gupta (2014): The study variable Y is the level of apple production (in 1000 tons) and the auxiliary variable X is the number of apple trees in 104 villages in 1999. Population 3.…”