The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
Ibrahim A. Ahmad - One of the best experts on this subject based on the ideXlab platform.
-
Recent developments in Systematic Sampling: A review
Journal of Statistical Theory and Practice, 2017Co-Authors: Sayed A. Mostafa, Ibrahim A. AhmadAbstract:Systematic Sampling is one of the most prevalent Sampling techniques. The popularity of the Systematic design is mainly due to its practicality. Compared with simple random Sampling, it is easier t...
-
Remainder linear Systematic Sampling with multiple random starts
Journal of Statistical Theory and Practice, 2016Co-Authors: Sayed A. Mostafa, Ibrahim A. AhmadAbstract:ABSTRACTDue to its simplicity and operational convenience, Systematic Sampling is one of the most prevalent Sampling techniques. However, this Sampling design has two main statistical drawbacks. First, the actual sample size is unfixed when the population size, N, is not an integral multiple of the desired sample size, n. Second, the Sampling variance cannot be unbiasedly estimated on the basis of a single Systematic sample. In this article we introduce a new generalized Systematic Sampling design that handles these two issues simultaneously. The proposed design combines the remainder linear Systematic Sampling design, which handles only the first problem, along with the idea of multistart Systematic Sampling that provides an unbiased estimator for the Sampling variance. Unbiased estimators for both the finite population mean and the Sampling variance are derived under the proposed design. The performance of the new design is evaluated relative to another six Sampling schemes under several superpopulation...
Sat Gupta - One of the best experts on this subject based on the ideXlab platform.
-
An optimal Systematic Sampling scheme
Journal of Statistical Computation and Simulation, 2020Co-Authors: Zaheen Khan, Sat Gupta, Javid Shabbir, Amjad ShamimAbstract:This paper aims to increase the efficiency of estimator through the optimal pairing of units in Systematic Sampling. The proposed Optimal Systematic Sampling Scheme is very simple, yet more general...
-
Circular versions of Systematic Sampling in the presence of linear trend
Communications in Statistics - Simulation and Computation, 2017Co-Authors: Zaheen Khan, Javid Shabbir, Sat GuptaAbstract:AbstractRecently, Khan and Shabbir (2016) proposed some modifications in the selection procedures of circular and diagonal circular Systematic Sampling schemes. In this paper, the properties of modified version of these schemes has been studied using an alternative approach introduced by Khan and Shabbir (2015). This approach enabled us to derive the explicit expressions of sample mean and its variance for circular and diagonal circular Systematic schemes which are not yet available in literature. Moreover, corrected estimator of population mean and average variance under super-population model has also been derived. It has also been observed that circular Systematic Sampling almost perform better than diagonal circular Systematic Sampling in both linear and auto-correlated super-population models.
-
Generalized modified linear Systematic Sampling scheme for finite populations
Hacettepe Journal of Mathematics and Statistics, 2014Co-Authors: Jambulingam Subramani, Sat GuptaAbstract:The present paper deals with a further modification on the selection of linear Systematic sample, which leads to the introduction of a more generalized form of modified linear Systematic Sampling namely generalized modified linear Systematic Sampling (GMLSS) scheme, which is applicable for any sample size, irrespective of the population size whether it is a multiple of sample size or not. The performances of the proposed modified linear Systematic Sampling scheme are assessed with that of simple random Sampling, circular Systematic Sampling for certain hypothetical populations as well as for some natural populations. As a result, it is observed that the proposed modified linear Systematic sample means perform better than the simple random sample mean and circular Systematic sample mean for estimating the population mean in the presence of linear trend among the population values. Further improvements on GMLSS are achieved by introducing Yates type end corrections.
-
A Note on Diagonal Circular Systematic Sampling
Journal of Statistical Theory and Practice, 2014Co-Authors: Zaheen Khan, Sat Gupta, Javid ShabbirAbstract:Sampath and Varalakshmi (2008) proposed an equal probability scheme called diagonal circular Systematic Sampling (DCSS) under the conditions stated by Sudhakar (1978). However, it is observed that DCSS does not fulfill the conditions stated by Sudhakar (1978). In this article, we suggest some conditions for DCSS to be applicable using a modification in the theorem proposed by Sengupta and Chattophadyay (1987). Under these conditions one can easily decide when and where DCSS is applicable.
-
Generalized Systematic Sampling
Communications in Statistics - Simulation and Computation, 2014Co-Authors: Zaheen Khan, Javid Shabbir, Sat GuptaAbstract:In this paper, we introduce a new Systematic Sampling design, called a Generalized Systematic Sampling (GSS), for estimation of finite population mean. The proposed design is found to be better than Simple Random Sampling (SRS) and the generalization of the several existing Systematic Sampling schemes such as, Linear Systematic Sampling (LSS), Diagonal Systematic Sampling (DSS), and Generalized Diagonal Systematic Sampling (GDSS). All of these designs become special cases of the proposed design.
Zaheen Khan - One of the best experts on this subject based on the ideXlab platform.
-
An optimal Systematic Sampling scheme
Journal of Statistical Computation and Simulation, 2020Co-Authors: Zaheen Khan, Sat Gupta, Javid Shabbir, Amjad ShamimAbstract:This paper aims to increase the efficiency of estimator through the optimal pairing of units in Systematic Sampling. The proposed Optimal Systematic Sampling Scheme is very simple, yet more general...
-
Circular versions of Systematic Sampling in the presence of linear trend
Communications in Statistics - Simulation and Computation, 2017Co-Authors: Zaheen Khan, Javid Shabbir, Sat GuptaAbstract:AbstractRecently, Khan and Shabbir (2016) proposed some modifications in the selection procedures of circular and diagonal circular Systematic Sampling schemes. In this paper, the properties of modified version of these schemes has been studied using an alternative approach introduced by Khan and Shabbir (2015). This approach enabled us to derive the explicit expressions of sample mean and its variance for circular and diagonal circular Systematic schemes which are not yet available in literature. Moreover, corrected estimator of population mean and average variance under super-population model has also been derived. It has also been observed that circular Systematic Sampling almost perform better than diagonal circular Systematic Sampling in both linear and auto-correlated super-population models.
-
Generalized Designing of Systematic Sampling Schemes
2015Co-Authors: Zaheen KhanAbstract:After a detailed review of existing Sampling schemes, a new class of Systematic Sampling design, called a Generalized Linear Systematic Sampling (GLSS) for estimation of ?nite population mean is introduced. The proposed design is found to be better than Simple Random Sampling (SRS) and is the generalization of the several existing Systematic Sampling schemes such as Linear Systematic Sampling (LSS), Diagonal Systematic Sampling (DSS) and Generalized Diagonal Systematic Sampling (GDSS). All of these designs become special cases of the proposed design. In this design an optimum choice of Sampling interval under linear trend is also be discussed. Sampath and Varalakshmi (2008) proposed an equal probability scheme called Diagonal Circular Systematic Sampling (DCSS) under the conditions stated by Sudhakar (1978). However, it is observed that DCSS does not ful?ll these conditions. Therefore, a necessary and su?cient condition has been suggested for DCSS after a slight modi?cation in the theorem proposed by Sengupta and Chattophadyay (1987). Under this condition, one can easily decide when and where DCSS is applicable. Some de?ciencies in traditional selection procedure of circular version of Systematic Sampling schemes are also investigated and alternative methods are proposed. Some rules of thumb for coincidence of units in the sample are also introduced. The end corrections proposed by Bellhouse and Rao (1975) and Sampath and Varalakshmi (2008) for circular Systematic Sampling (CSS) and DCSS respectively are also modi?ed. Theoretical selection procedure has also been established for several cyclic CSS regarding the suggestion of Sudhakar (1978). Mean and variance expressions of CSS for perfect linear trend are not available in the literature. Therefore, a new approach is introduced to study the characteristic of circular version of Systematic Sampling. By using it, mean and variance expressions of CSS for perfect linear trend has been derived. Mean and variance of DCSS can be deduced from these expressions. Average variance expressions of corrected sample means for modi?ed CSS and DCSS are derived under the super population model. Based on the average variances, numerical e?ciency comparison of CSS and DCSS has also been carried out. In the current study a new Sampling design called Modi?ed Systematic Sampling (MSS) is proposed. In this design each unit has an equal probability of selection. Moreover, it works for both situations: N = nk or N 6= nk. Modi?ed Systematic Sampling reduces to LSS, if N = nk and becomes CSS, if N and n are co-prime. The proposed MSS performs better than CSS in every aspect of Systematic Sampling, speci?cally, simplicity, e?ciency and even coverage of sample unit over the entire population. E?ciency comparison of MSS with CSS is also carried out for natural populations. Furthermore, MSS is also studied for populations having a linear trend. Expressions for mean and variance of sample mean are obtained for the population having perfect linear trend among population values. Average variance of corrected sample mean under super population linear model and average variance of sample mean under super population auto-correlated model are also obtained. Further,numerical e?ciency comparisons using these average variances are also obtained for di?erent sample sizes. One of the major and long-standing problem of unbiased estimation of population variance is also discussed in the current study. In this case, the concept of multiple random start is extended from linear version (where N = nk) to the general case (where N 6= nk). As a result, a new Sampling design called "Universal Systematic Sampling (USS)" is introduced. Linear Systematic Sampling and Simple Random Sampling (SRS) are the two extreme cases of this design. Mean and variance of mean for LSS and SRS can be extracted from the derived expressions of mean and variance of mean of USS. An explicit expressions of unbiased estimator of population variance and its variance are also derived. Finally, an e?ciency comparison with SRS is also carried out for natural populations, simulated populations and population having linear trend.
-
Modified Systematic Sampling in the presence of linear trend
Hacettepe Journal of Mathematics and Statistics, 2014Co-Authors: Javid Shabbir, Zaheen KhanAbstract:A new Systematic Sampling design called “Modified Systematic Sampling (MSS)”, proposed by [2] is more general than Linear Systematic Sampling (LSS) and Circular Systematic Sampling (CSS). In the present paper, this scheme is further extended for populations having a linear trend. Expressions for mean and variance of sample mean are obtained for the population having perfect linear trend among population values. Expression for the average variance is also obtained for super population model. Further, eciency of MSS with respect to CSS is obtained for dierent sample size. 2000 AMS Classification: 62DO5.
-
A Note on Diagonal Circular Systematic Sampling
Journal of Statistical Theory and Practice, 2014Co-Authors: Zaheen Khan, Sat Gupta, Javid ShabbirAbstract:Sampath and Varalakshmi (2008) proposed an equal probability scheme called diagonal circular Systematic Sampling (DCSS) under the conditions stated by Sudhakar (1978). However, it is observed that DCSS does not fulfill the conditions stated by Sudhakar (1978). In this article, we suggest some conditions for DCSS to be applicable using a modification in the theorem proposed by Sengupta and Chattophadyay (1987). Under these conditions one can easily decide when and where DCSS is applicable.
Sayed A. Mostafa - One of the best experts on this subject based on the ideXlab platform.
-
Recent developments in Systematic Sampling: A review
Journal of Statistical Theory and Practice, 2017Co-Authors: Sayed A. Mostafa, Ibrahim A. AhmadAbstract:Systematic Sampling is one of the most prevalent Sampling techniques. The popularity of the Systematic design is mainly due to its practicality. Compared with simple random Sampling, it is easier t...
-
Remainder linear Systematic Sampling with multiple random starts
Journal of Statistical Theory and Practice, 2016Co-Authors: Sayed A. Mostafa, Ibrahim A. AhmadAbstract:ABSTRACTDue to its simplicity and operational convenience, Systematic Sampling is one of the most prevalent Sampling techniques. However, this Sampling design has two main statistical drawbacks. First, the actual sample size is unfixed when the population size, N, is not an integral multiple of the desired sample size, n. Second, the Sampling variance cannot be unbiasedly estimated on the basis of a single Systematic sample. In this article we introduce a new generalized Systematic Sampling design that handles these two issues simultaneously. The proposed design combines the remainder linear Systematic Sampling design, which handles only the first problem, along with the idea of multistart Systematic Sampling that provides an unbiased estimator for the Sampling variance. Unbiased estimators for both the finite population mean and the Sampling variance are derived under the proposed design. The performance of the new design is evaluated relative to another six Sampling schemes under several superpopulation...
Jambulingam Subramani - One of the best experts on this subject based on the ideXlab platform.
-
Linear Systematic Sampling with Unequal Sampling Intervals in the Presence of Linear Trend
Electronic Journal of Applied Statistical Analysis, 2019Co-Authors: Jambulingam SubramaniAbstract:The present paper deals with the linear Systematic Sampling with unequal Sampling intervals in the presence of linear trend among the population values. As a result, explicit expressions for the linear Systematic sample means with different random starts in a labelled population with linear trend for a pre-assigned fixed sample size and the population size together its variance are obtained. The efficiencies of the proposed linear Systematic Sampling with that of simple random Sampling without replacement, linear Systematic Sampling and diagonal Systematic Sampling schemes are assessed algebraically and also for certain natural populations. It is observed that the proposed linear Systematic Sampling performs better than the Sampling schemes mentioned above.
-
Generalized modified linear Systematic Sampling scheme for finite populations
Hacettepe Journal of Mathematics and Statistics, 2014Co-Authors: Jambulingam Subramani, Sat GuptaAbstract:The present paper deals with a further modification on the selection of linear Systematic sample, which leads to the introduction of a more generalized form of modified linear Systematic Sampling namely generalized modified linear Systematic Sampling (GMLSS) scheme, which is applicable for any sample size, irrespective of the population size whether it is a multiple of sample size or not. The performances of the proposed modified linear Systematic Sampling scheme are assessed with that of simple random Sampling, circular Systematic Sampling for certain hypothetical populations as well as for some natural populations. As a result, it is observed that the proposed modified linear Systematic sample means perform better than the simple random sample mean and circular Systematic sample mean for estimating the population mean in the presence of linear trend among the population values. Further improvements on GMLSS are achieved by introducing Yates type end corrections.
-
Circular Systematic Sampling in the Presence of Linear Trend
American Journal of Mathematical and Management Sciences, 2014Co-Authors: Jambulingam Subramani, Sat Gupta, G. PrabavathyAbstract:SYNOPTIC ABSTRACTThe present article deals with circular Systematic Sampling for estimation of a finite population mean in the presence of a linear trend among the population values. As a result, the optimum choice for the Sampling interval kis obtained for a preassigned fixed sample size n and the population size N. Further, the explicit expression for the variance of a circular Systematic sample mean is also obtained. The relative performance of the proposed circular Systematic Sampling with that of simple random Sampling without replacement is assessed for a hypothetical population and also for some natural populations.
-
A modification on linear Systematic Sampling
Model Assisted Statistics and Applications, 2013Co-Authors: Jambulingam SubramaniAbstract:The present paper deals with a modification on the selection of linear Systematic sample, consequently the proposed method is called modified linear Systematic Sampling. The performances of the modified linear Systematic Sampling are assessed with that of simple random Sampling and the linear Systematic Sampling for certain hypothetical populations as well as for certain natural populations. As a result, it is observed that the modified linear Systematic sample mean performs better than the simple random sample mean and the usual Systematic sample mean for estimating the population mean in the presence of linear trend among the population values. Further improvements are achieved by introducing Yates type end corrections. The applications of the proposed Sampling scheme in constructing mating designs are also discussed with an example.
-
A Further Modification on Linear Systematic Sampling for Finite Populations
Journal of Statistical Theory and Practice, 2013Co-Authors: Jambulingam SubramaniAbstract:This article deals with a further modification on the selection of linear Systematic sample. Consequently, the proposed method is an optimal modified linear Systematic Sampling. The performances of the modified linear Systematic Sampling are assessed with that of simple random Sampling and linear Systematic Sampling for certain hypothetical populations, as well as for certain natural populations. As a result, it is observed that the proposed modified linear Systematic sample mean performs better than the simple random sample mean and the usual Systematic sample mean for estimating the population mean in the presence of linear trend among the population values. Further improvements are achieved by introducing Yates-type end corrections.
