Papers by Aamir Sanaullah
In this paper, generalized exponential-type estimators have been proposed for estimating the fini... more In this paper, generalized exponential-type 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 (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.
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.
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].
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.
In this paper, generalized exponential-type estimator has been proposed
for estimating the popul... 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.
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 y 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.
introduced an exponential ratio-type and exponential product-type estimators for estimating popul... more introduced an exponential ratio-type and exponential product-type estimators for estimating population mean Y . suggested improved estimator using estimator. Most of them discussed these estimators along with their first order biases and mean square error's (MSE's). In this paper, we have tried to work out the second order biases and mean square errors of some estimators using information on auxiliary attributes based on simple random sampling. Finally, we have compared the performance of the estimators with help of some numerical illustration.
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.
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 (
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. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/authorsrights
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Papers by Aamir Sanaullah
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.
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].
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.
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.
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].
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.