Dr.Aamir Sanaullah - Academia.edu (original) (raw)
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Papers by Dr.Aamir Sanaullah
This paper suggests a general class of exponential ratio and product type estimators for estimati... more This paper suggests a general class of exponential ratio and product type estimators for estimating finite population mean in single phase sampling. The expression for the mean square error (MSE) and bias of the first and second order approximation of the proposed class of estimators are given. The properties of the proposed estimators have been analyzed for independent units under simple random sampling without replacement (SRSWOR). It has been shown that the proposed ratio and product exponential type estimators are more efficient than Simple random sampling, classical ratio, Bhal, Tutaja [1] and Solanki et al. [2].
In this paper some improved exponential ratio-type estimators have been proposed for estimating t... more In this paper some improved exponential ratio-type estimators have been proposed for estimating the finite populations mean using auxiliary information on two auxiliary variables in double sampling. The properties of the proposed estimators have been analyzed for independent and dependent samples case under simple random sampling without replacement (SRSWOR). An empirical study is carried out to demonstrate the performance of proposed estimators over Noorul-Amin and Hanif (
In this paper some improved exponential ratio-type estimators have been proposed for estimating t... more In this paper some improved exponential ratio-type estimators have been proposed for estimating the finite populations mean using auxiliary information on two auxiliary variables in double sampling. The properties of the proposed estimators have been analyzed for independent and dependent samples case under simple random sampling without replacement (SRSWOR). An empirical study is carried out to demonstrate the performance of proposed estimators over Noor-ul-Amin and Hanif (2012), Singh et al. (2008), Singh and Vishvakarma (2007), and Classical Ratio Estimator.
A new class of improved estimators for estimating finite population mean has been proposed using ... more A new class of improved estimators for estimating finite population mean has been proposed using full information on two auxiliary variables in single and two-phase sampling. Expressions of Mean Square error and Bias for the proposed estimators under simple random sampling without replacement (SRSWOS) have been derived. An empirical comparison of proposed class with respect to usual unbiased estimator with some well-known estimators in single and double sampling has also been made. Empirical study confirmed that the proposed class of estimators is the class of more efficient estimators under percent relative efficiency (PRE) criterion.
In this paper a class of improved estimators has been proposed for estimating population mean in ... more In this paper a class of improved estimators has been proposed for estimating population mean in two phase (double) sampling when only partial information is available on either of two auxiliary variables. Under simple random sampling (SRWOR), expressions of mean square error and bias have been derived to make comparison of suggested class with wide range of other estimators. Empirical study has also been given using five different natural populations. Empirical study confirmed that the suggested class of improved estimators is more efficient under percent relative efficiency (PRE) criterion.
Pakistan Journal of Statistics, Feb 16, 2015
Brazilian Journal of Probability and Statistics
In this paper, some generalized exponential chain-ratio and chain-product estimators have been pr... more In this paper, some generalized exponential chain-ratio and chain-product estimators have been proposed for estimating the finite population mean under the stratified two-phase random sampling method for two different cases under non-response case when information on only secondary auxiliary variable is available. The expressions for the bias and mean square error (MSE) of proposed estimators have been derived for two different situations under non-response case. The proposed class of generalized exponential estimators has been compared in theory with the adapted forms of Hansen-Hurwitz, ratio and product estimators to the stratified two-phase sampling method. An empirical study has also been given to demonstrate the performances of the estimators.
Pakistan Journal of Statistics
In this paper, generalized exponential estimators have been proposed for estimating the finite po... more In this paper, generalized exponential estimators have been proposed for estimating the finite population mean of study variable using information on two auxiliary variables in the presence of non-response under stratified two-phase random sampling. The expressions for the bias and mean square error (MSE) of proposed estimators have been derived in two different situations of non-response. Theoretical comparisons of proposed estimators have been made with modified forms of Hansen and Hurwitz’s (1946), ratio and product estimators to the stratified two-phase sampling method. An empirical study has also been carried out to demonstrate the performances of proposed estimators.
Pakistan Journal of Statistics
Koyuncu and Kadilar (2009) proposed a family of ratio-type estimators for population mean using a... more Koyuncu and Kadilar (2009) proposed a family of ratio-type estimators for population mean using auxiliary information in simple random sampling. Srivastava and Garg (2009) proposed a general class of ratio estimator for estimating population mean using auxiliary variablein two-stage sampling. In this paper, motivated by Srivastava and Garg (2009) and Koyuncu and Kadilar (2009) we have proposed a general class of estimators for population mean for three different cases in two-stage sampling design. The mean square error (MSE) and bias expressions have been obtained in a general form up to the first order of approximation for the three cases. It has also been shown that for each of the three cases in two-stage sampling, minimum MSE of this class is asymptotical equal to the MSE of regression estimator. An empirical study has also been carried out, in order to demonstrate the performance of proposed general class of estimators for three cases in two-stage sampling design. KEYWORDS Auxi...
Journal of statistical theory and practice
In survey sampling, the improved estimators for the population mean of study variable have been o... more In survey sampling, the improved estimators for the population mean of study variable have been obtained using the transformations of auxiliary variables. In this context, Srivenkatramana [20] established a transformation using the mean of non-sampled observations. Mohanty and Sahoo [7] introduced linear transformation of auxiliary variable using the extreme value of auxiliary variable from the population. In this study, a linear transformation to the auxiliary variable has been introduced by combining the concepts of Srivenkatramana [20] and Mohanty and Sahoo [7]. The transformation is based on the assumption of prior knowledge of population extreme values of auxiliary variable and the mean of non-sampled observations of auxiliary variable. The usual ratio and product, exponential ratio and product estimators have developed using the proposed transformation. The mean square errors and biases have been obtained, up to first order of approximation. Theoretical comparison of proposed ...
This study presents the exponential type estimators under double sampling design using the inform... more This study presents the exponential type estimators under double sampling design using the information from two auxiliary variables. This paper deals with the nested samples and non-nested samples. The estimators in each case of double sampling are discussed for partial information and full information situation. The optimum properties and special cases of the estimators are discussed. An empirical study is conducted to examine the efficiency of the proposed estimators with respect to some estimators available in literature. 1. INTRODUCTION The precision of the estimators can be improved by using the auxiliary information. The ratio type and product type estimators are suggested for positive and negative correlation between study variable and auxiliary variable, respectively. The ratio or regression estimators are preferable when the linear relationship between study variable and auxiliary variable is strong enough, whereas, exponential estimators are suggested when the linear relat...
Revista Colombiana de Estadística, 2014
In this paper, generalized exponential-type estimator has been proposed for estimating the popula... more In this paper, generalized exponential-type estimator has been proposed for estimating the population variance using mean auxiliary variable in singlephase sampling. Some special cases of the proposed generalized estimator have also been discussed. The expressions for the mean square error and bias of the proposed generalized estimator have been derived. The proposed generalized estimator has been compared theoretically with the usual unbiased estimator, usual ratio and product, exponential-type ratio and product, and generalized exponential-type ratio estimators and the conditions under which the proposed estimators are better than some existing estimators have also been given. An empirical study has also been carried out to demonstrate the efficiencies of the proposed estimators.
Applied Mathematics and Computation, 2014
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.
International Journal of Applied and Computational Mathematics, 2015
In this study, two-phase sampling is considered for estimating the population variance of study v... more In this study, two-phase sampling is considered for estimating the population variance of study variable taking two auxiliary variables. The proposed generalized estimator and class of estimators are the exponential function of auxiliary variables. The mean square errors and biases equations have been obtained for the proposed estimators. The conditions for which proposed estimators are more efficient as compared to other estimators have been discussed. The empirical study showed that proposed estimators are more efficient as compared to the unbiased sample variance estimator, double sampling version of Isaki and Singh et al. (2011) generalized estimator.
This paper suggests a general class of exponential ratio and product type estimators for estimati... more This paper suggests a general class of exponential ratio and product type estimators for estimating finite population mean in single phase sampling. The expression for the mean square error (MSE) and bias of the first and second order approximation of the proposed class of estimators are given. The properties of the proposed estimators have been analyzed for independent units under simple random sampling without replacement (SRSWOR). It has been shown that the proposed ratio and product exponential type estimators are more efficient than Simple random sampling, classical ratio, Bhal, Tutaja [1] and Solanki et al. [2].
In this paper some improved exponential ratio-type estimators have been proposed for estimating t... more In this paper some improved exponential ratio-type estimators have been proposed for estimating the finite populations mean using auxiliary information on two auxiliary variables in double sampling. The properties of the proposed estimators have been analyzed for independent and dependent samples case under simple random sampling without replacement (SRSWOR). An empirical study is carried out to demonstrate the performance of proposed estimators over Noorul-Amin and Hanif (
In this paper some improved exponential ratio-type estimators have been proposed for estimating t... more In this paper some improved exponential ratio-type estimators have been proposed for estimating the finite populations mean using auxiliary information on two auxiliary variables in double sampling. The properties of the proposed estimators have been analyzed for independent and dependent samples case under simple random sampling without replacement (SRSWOR). An empirical study is carried out to demonstrate the performance of proposed estimators over Noor-ul-Amin and Hanif (2012), Singh et al. (2008), Singh and Vishvakarma (2007), and Classical Ratio Estimator.
A new class of improved estimators for estimating finite population mean has been proposed using ... more A new class of improved estimators for estimating finite population mean has been proposed using full information on two auxiliary variables in single and two-phase sampling. Expressions of Mean Square error and Bias for the proposed estimators under simple random sampling without replacement (SRSWOS) have been derived. An empirical comparison of proposed class with respect to usual unbiased estimator with some well-known estimators in single and double sampling has also been made. Empirical study confirmed that the proposed class of estimators is the class of more efficient estimators under percent relative efficiency (PRE) criterion.
In this paper a class of improved estimators has been proposed for estimating population mean in ... more In this paper a class of improved estimators has been proposed for estimating population mean in two phase (double) sampling when only partial information is available on either of two auxiliary variables. Under simple random sampling (SRWOR), expressions of mean square error and bias have been derived to make comparison of suggested class with wide range of other estimators. Empirical study has also been given using five different natural populations. Empirical study confirmed that the suggested class of improved estimators is more efficient under percent relative efficiency (PRE) criterion.
Pakistan Journal of Statistics, Feb 16, 2015
Brazilian Journal of Probability and Statistics
In this paper, some generalized exponential chain-ratio and chain-product estimators have been pr... more In this paper, some generalized exponential chain-ratio and chain-product estimators have been proposed for estimating the finite population mean under the stratified two-phase random sampling method for two different cases under non-response case when information on only secondary auxiliary variable is available. The expressions for the bias and mean square error (MSE) of proposed estimators have been derived for two different situations under non-response case. The proposed class of generalized exponential estimators has been compared in theory with the adapted forms of Hansen-Hurwitz, ratio and product estimators to the stratified two-phase sampling method. An empirical study has also been given to demonstrate the performances of the estimators.
Pakistan Journal of Statistics
In this paper, generalized exponential estimators have been proposed for estimating the finite po... more In this paper, generalized exponential estimators have been proposed for estimating the finite population mean of study variable using information on two auxiliary variables in the presence of non-response under stratified two-phase random sampling. The expressions for the bias and mean square error (MSE) of proposed estimators have been derived in two different situations of non-response. Theoretical comparisons of proposed estimators have been made with modified forms of Hansen and Hurwitz’s (1946), ratio and product estimators to the stratified two-phase sampling method. An empirical study has also been carried out to demonstrate the performances of proposed estimators.
Pakistan Journal of Statistics
Koyuncu and Kadilar (2009) proposed a family of ratio-type estimators for population mean using a... more Koyuncu and Kadilar (2009) proposed a family of ratio-type estimators for population mean using auxiliary information in simple random sampling. Srivastava and Garg (2009) proposed a general class of ratio estimator for estimating population mean using auxiliary variablein two-stage sampling. In this paper, motivated by Srivastava and Garg (2009) and Koyuncu and Kadilar (2009) we have proposed a general class of estimators for population mean for three different cases in two-stage sampling design. The mean square error (MSE) and bias expressions have been obtained in a general form up to the first order of approximation for the three cases. It has also been shown that for each of the three cases in two-stage sampling, minimum MSE of this class is asymptotical equal to the MSE of regression estimator. An empirical study has also been carried out, in order to demonstrate the performance of proposed general class of estimators for three cases in two-stage sampling design. KEYWORDS Auxi...
Journal of statistical theory and practice
In survey sampling, the improved estimators for the population mean of study variable have been o... more In survey sampling, the improved estimators for the population mean of study variable have been obtained using the transformations of auxiliary variables. In this context, Srivenkatramana [20] established a transformation using the mean of non-sampled observations. Mohanty and Sahoo [7] introduced linear transformation of auxiliary variable using the extreme value of auxiliary variable from the population. In this study, a linear transformation to the auxiliary variable has been introduced by combining the concepts of Srivenkatramana [20] and Mohanty and Sahoo [7]. The transformation is based on the assumption of prior knowledge of population extreme values of auxiliary variable and the mean of non-sampled observations of auxiliary variable. The usual ratio and product, exponential ratio and product estimators have developed using the proposed transformation. The mean square errors and biases have been obtained, up to first order of approximation. Theoretical comparison of proposed ...
This study presents the exponential type estimators under double sampling design using the inform... more This study presents the exponential type estimators under double sampling design using the information from two auxiliary variables. This paper deals with the nested samples and non-nested samples. The estimators in each case of double sampling are discussed for partial information and full information situation. The optimum properties and special cases of the estimators are discussed. An empirical study is conducted to examine the efficiency of the proposed estimators with respect to some estimators available in literature. 1. INTRODUCTION The precision of the estimators can be improved by using the auxiliary information. The ratio type and product type estimators are suggested for positive and negative correlation between study variable and auxiliary variable, respectively. The ratio or regression estimators are preferable when the linear relationship between study variable and auxiliary variable is strong enough, whereas, exponential estimators are suggested when the linear relat...
Revista Colombiana de Estadística, 2014
In this paper, generalized exponential-type estimator has been proposed for estimating the popula... more In this paper, generalized exponential-type estimator has been proposed for estimating the population variance using mean auxiliary variable in singlephase sampling. Some special cases of the proposed generalized estimator have also been discussed. The expressions for the mean square error and bias of the proposed generalized estimator have been derived. The proposed generalized estimator has been compared theoretically with the usual unbiased estimator, usual ratio and product, exponential-type ratio and product, and generalized exponential-type ratio estimators and the conditions under which the proposed estimators are better than some existing estimators have also been given. An empirical study has also been carried out to demonstrate the efficiencies of the proposed estimators.
Applied Mathematics and Computation, 2014
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.
International Journal of Applied and Computational Mathematics, 2015
In this study, two-phase sampling is considered for estimating the population variance of study v... more In this study, two-phase sampling is considered for estimating the population variance of study variable taking two auxiliary variables. The proposed generalized estimator and class of estimators are the exponential function of auxiliary variables. The mean square errors and biases equations have been obtained for the proposed estimators. The conditions for which proposed estimators are more efficient as compared to other estimators have been discussed. The empirical study showed that proposed estimators are more efficient as compared to the unbiased sample variance estimator, double sampling version of Isaki and Singh et al. (2011) generalized estimator.