Browsing by Author "Dr. Muhammad Ismail"

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GENERALIZED ESTIMATORS OF POPULATION MEAN IN TWO PHASE SAMPLING IN THE PRESENCE OF NON RESPONSE
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Muhammad Taimoor Safdar; FA14-MSSTAT-003; Dr. Muhammad Ismail; LHR TP 4484
In the mid of 1780’s, the famous mathematician Pierre Laplace thought to approximate the total French people by using the identified number of childbirths in a specified year and the estimated ratio of the population to annual births on the basis of population sample of 700 communes. However, his projected ratio was on no occasion recycled for its inventive purpose because it became problematic to obtain an appropriate total of childbirths for the entire French people due to many reasons including the military events against France during Napoleon’s early years.
Generalized Ratio Type Exponential Estimators for the Population Mean Using Ranked Set Sampling
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Amjad Ali; SP16-RST-002; LHR TP 4837; Dr. Muhammad Ismail
The dominance of using ranked set sampling, for estimating the mean of a population, as compare to simple random sampling is well reputable. This technique is useful when visual ordering of a small set of size “m” can be made simply and precisely, since exact measurement of a value is most of the times very hard to obtain. In this dissertation, exponential ratio type estimators are proposed for evaluating the population mean by using ranked set sampling. We found through numerical results that the results of proposed ratio type estimators which is estimated under ranked set sampling is more reliable and competent than the simple random sampling (SRS) and some other already existed estimators under SRS are suggested by Cochran (1977), Parsad 1989, Bahl and Tuteja (1991). The comparison is also made with estimators under ranked set sampling by Samawi and Muttalak (1996), Rabail (2014) and Gajendra , Zeeshan and Carlos (2017).
Ratio & Product estimators of mean using two-phase sampling in the presence of non-response
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2016) Muhammad Irfa; FA14-MSSTAT-001; Dr. Muhammad Ismail; LHR TP 4483
Many statisticians have been worked in the field of two-phase sampling when there is a non-response in the data using a single auxiliary variable and multi-auxiliary variables for different cases which begin since Hansen and Hurwitz’s (1946) work on non response. In this study, new estimators of mean in the form of ratio and product are proposed for different cases of two-phase sampling using a single auxiliary variable for non-response. The mean square errors expressions of the proposed estimators are also derived. An empirical study is also conducted to assess the performance of the proposed estimators with existing estimators
Variance Estimation in Two Phase Sampling in Presence of Non Response
(Library Information Services COMSATS University Islamabad Lahore Campus, 2021-01-30) Tanveer Akhlaq; FA13-PSTAT-004; Dr. Muhammad Ismail; LHR TP 7737
The variability in a process or estimate is of importance in almost all areas of life. The statistical measure to obtain variability in a process or estimate is the variance. The variance also appears as a parameter in well-known Gaussian distribution that is considered as a corner-stone in many statistical analyses. Variance provides an insight into average squared spread in the data from the mean. In the study of process control, a process with least spread is preferred as the process will provide products that have least variability from underlying specifications. In practice, the variance of a process is estimated by using the sample data and various methods are available to do the same. In this research we have proposed some efficient methods to estimate the spread of the data in single phase sampling by using single transformed auxiliary variable. The Mean Square Errors (MSE) of the proposed estimators have been obtained. The performance of the proposed estimator has been studied by using numerical as well as simulation studies. Some special cases of the new proposed estimator have been listed. An estimator of population variance using two transformed auxiliary variables has also been suggested. The Mean Square Error of the proposed estimator, up to first order of approximation, has been obtained. The numerical and simulation studies have been carried out to study the performance of the proposed estimator.
Variance Estimation in Two Phase Sampling in Presence of Non Response
(Library Information Services, CUI Lahore, 2021) Tanveer Akhlaq; FA13-PSTAT-004/; LHR TP 7737; Dr. Muhammad Ismail
The variability in a process or estimate is of importance in almost all areas of life. The statistical measure to obtain variability in a process or estimate is the variance. The variance also appears as a parameter in well-known Gaussian distribution that is considered as a corner-stone in many statistical analyses. Variance provides an insight into average squared spread in the data from the mean. In the study of process control, a process with least spread is preferred as the process will provide products that have least variability from underlying specifications. In practice, the variance of a process is estimated by using the sample data and various methods are available to do the same. In this research we have proposed some efficient methods to estimate the spread of the data in single phase sampling by using single transformed auxiliary variable. The Mean Square Errors (MSE) of the proposed estimators have been obtained. The performance of the proposed estimator has been studied by using numerical as well as simulation studies. Some special cases of the new proposed estimator have been listed. An estimator of population variance using two transformed auxiliary variables has also been suggested. The Mean Square Error of the proposed estimator, up to first order of approximation, has been obtained. The numerical and simulation studies have been carried out to study the performance of the proposed estimator. Estimators of the population variance have been derived under two situations of non- response in two phase sampling. The properties of the proposed methods were studied by conducting the numerical as well as simulation studies. The study has been conducted by using some special cases of the proposed estimator and some existing estimator. It has been found that our proposed estimators perform better as compared with the existing estimators as they have smaller mean square error in numerical as well as in simulation studies.