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Rizvi, S. E. H.
- A New Approach of Ratio Estimation in Sample Surveys
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Authors
Affiliations
1 Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu, Jammu (J&K), IN
1 Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu, Jammu (J&K), IN
Source
International Research Journal of Agricultural Economics and Statistics, Vol 8, No 1 (2017), Pagination: 100-103Abstract
This article deals with the estimation of population mean under simple random sampling using a new form of ratio estimator. The expression for mean square error and bias has been obtained. An efficiency comparison is considered for proposed estimator with the classical ratio, product and exponential ratio estimator. Finally an empirical study is also carried out to judge the performance of proposed estimator.Keywords
Simple Random Sampling, Ratio Estimator, Mean Square Error, Efficiency, AMS Classification: 62D05.
References
- Bahl, S. and Tuteja, R.K. (1991). Ratio and product exponential estimator. Information & Optimazimation Sci., 12 (1) : 159-163
- Cochran, W.G. (1997). Sampling Techniques, 3rd Ed., John Wiley & Sons, Inc., New York, U.S.A.
- Jeelani, M.I. and Maqbool, S. (2013). Modified ratio estimators of population mean using linear combination of coefficient of skewness and quartile deviation. South Pacific J. Nat. & Appl. Sci., 31 (1) : 39-44.
- Murthy, M.N. (1967). Sampling theory and methods, Statistical Publishing Society, Calcutta (W.B.) India
- Prasad, B. (1989). Some improved ratio type estimators of population mean and ratio infinite population sample surveys, Communications in Statistics: Theory & Methods, 18 : 379–392.
- Sen, A.R. (1993). Some early developments in ratio estimation, Biometric J., 35 (1) : 3-13
- Singh, D. and Chaudhary, F.S. (1986). Theory and analysis of sample survey designs, New Age International Publisher.
- Singh, H.P. and Tailor, R. (2003). Use of known correlation Coefficient in estimating the finite population means, Statistics Transition, 6(4) : 555-560
- Singh, H.P., Singh, P., Tailor, R. and Kakran, M.S. (2004). An Improved Estimator of population mean using Power transformation. J. Indian Soc. Agric. Stat., 58(2) : 223-230.
- Singh, H.P. and Tailor, R. (2005). Estimation of finite population mean with known co-efficient of variation of an auxiliary, STATISTICA, anno 65 (3) : 301-313
- Upadhyaya, L.N. and Singh, H.P. (1999). Use of transformed auxiliary variable in estimating the finite population mean. Biometrical J., 41(5) : 627-636
- Yan, Z. and Tian, B. (2010).Ratio method to the mean estimation using co-efficient of skewness of auxiliary variable, ICICA2010, PartII,CCIS106(2010):103–110.
- On Optimum Stratification Using Mathematical Programming Approach
Abstract Views :143 |
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Authors
Affiliations
1 Division of Statistics and Computer Science, SKUAST-J, Main Campus, Chatha, Jammu (J&K), IN
2 Division of Statistics and Computer Science, SKUAST-J, Chatha (J&K), IN
1 Division of Statistics and Computer Science, SKUAST-J, Main Campus, Chatha, Jammu (J&K), IN
2 Division of Statistics and Computer Science, SKUAST-J, Chatha (J&K), IN
Source
International Research Journal of Agricultural Economics and Statistics, Vol 8, No 2 (2017), Pagination: 435-439Abstract
Optimum stratification is a technique which results in minimum possible variance of the estimator for the population characteristic under study. The main objective of stratification is to give a better cross-section of the population so as to gain a higher degree of relative precision. The problem of determining optimum strata boundaries (OSB) was pioneered by Dalenius (1950). The problem of obtaining OSB was recently studied by Khan et al. (2009) who formulated the problem as a mathematical programming problem (MPP) by minimizing variance of the estimated population parameter subject to the condition that the sum of the widths of all the strata would be equal to the range of the given distribution under given allocation procedure. In the present investigation the problem of finding OSB has been taken into consideration as the problem of optimum strata width (OSW), using MPP by dynamic programming technique, when the study variable is uniformly distributed. Empirical study has also been taken where it is revealed that with the increase in the number of strata to a fixed number the precision of the method goes on increasing. Also the proposed method proves better than other stratification method (Singh, 1967).Keywords
Mathematical Programming Problem, Optimum Stratification, Optimum Strata Boundaries, Optimum Strata Width.References
- Aoyama, H. (1954). A study of stratified random sampling. Annl. Instit. Statist. Mathemat., 6 : 1-36.
- Cochran, W.G. (1977). Sampling techniques. 3rd Ed. John Wiley and Sons, Inc., NEW YORK, U.S.A.
- Dalenius, T. (1950). The problem of optimum stratification. Skandinavisk Aktuarietidskrift, 33 : 203-213.
- Dalenius, T. and Gurney, M. (1951). The problem of optimum stratification II. Skandinavisk Aktuarietidskrift, 34 : 133-148.
- Dalenius, T. and Hodges, J.L. Jr. (1959). Minimum variance stratification. J. American Statist. Assoc., 54 : 88-101.
- Ekman, G. (1959). Approximation expression for the conditional mean and variance over small intervals of a continuous distribution. Annl. Mathemat. Statist., 30 : 1131-1134.
- Gupta, R. K., Singh, R. and Mahajan, P. K. (2005).Approximate optimum strata boundaries for ratio and regression estimators. Aligarh J. Statist., 25 : 49-55.
- Hidiroglou, M.A. and Srinath, K.P. (1993). Problems associated to sub annual business surveys. J. Business & Econ. Statist., 11 : 397-405.
- Isii, K. and Taga, Y. (1969). On optimal stratification for multivariate distributions. Skand. Akt., 52 : 24-38.
- Khan, E. A. Khan, M. G. M. and Ahsan, M. J. (2002).Optimum stratification:A mathematical programming approach. Calcutta Statist. Assoc. Bull., 52 : 323-333.
- Khan, M.G.M., Ahmad, N. and Khan, S. (2009). Determination the optimum stratum boundaries using mathematical programming. J. Mathemat. Modelling & Algorithms, 8 : 409-423.
- Kozak, M. and Verma, M.R. (2006). Geometric versus optimization stratification: A comparison of efficiency. Survey Methodology, 32(2) : 157-163.
- Lavallee, P. and Hidiriglou, M. (1988). On the stratification of skewed populations. Survey Methodology, 14 : 33-43.
- Mahalanobis, P.C. (1952). Some aspect of design of sample surveys. Sankhya, 12 : 1-17.
- Rivest, R.J. (2002). A generalization of Lavallee and Hidiroglou algorithm for stratification in survey. Survey Methodology, 28 : 191-198.
- Rizvi, S.E.H., Gupta, J.P and Bargava, M. (2002). Optimum stratification based on auxiliary variable for compromise allocation.Metron, 28 (1) : 201-215.
- Serfling, R.J. (1968). Approximately optimum stratification. J. American Statist. Assoc., 63 : 1298-1309.
- Singh, R. (1967). Some contributions to the theory of construction of Strata. Ph.D. Thesis, Indian Agriculture Research Institute, NEW DELHI, INDIA.
- Singh, R. (1971). Approximately optimum stratification on auxiliary variable. J. American Statist. Assoc., 66 : 829-833.
- Sweet, E.M. and Sigman, R.S. (1995).Evaluation of model-assisted procedures for stratifying skewed populations using auxiliary data. Proceedings of the Survey Research Methods Section, American Statistical Association, Alexandria, 491–496.
- Unnithan, V.K.G. (1978). The minimum variance boundary points of stratification. Sankhya, 40 (C) : 60-72.
- A Generalized Class of Synthetic Estimator with Application to Estimation of Milk Production for Small Domains
Abstract Views :297 |
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Authors
Affiliations
1 Division of Statistics and Computer Science, SKUAST- J, Chatha (J&K), IN
2 Division of Statistics and Computer Science,SKUAST-J, Chatha (J&K), IN
1 Division of Statistics and Computer Science, SKUAST- J, Chatha (J&K), IN
2 Division of Statistics and Computer Science,SKUAST-J, Chatha (J&K), IN
Source
International Research Journal of Agricultural Economics and Statistics, Vol 10, No 1 (2019), Pagination: 115-121Abstract
The demand for small area statistics is growing day-by-day not only in public but also in private sectors, and small area estimation technique (SAE) is becoming very important in survey sampling due to the thrust of planning process has shifted from macro to micro level. Small area estimation is one of the several techniques which involves the estimation of parameters for small subpopulation generally used when the sub-population of interest is included in a larger survey. In this article the proposed class of synthetic estimators gives consistent estimators if the synthetic assumption holds. Further it demonstrates the use of the generalized synthetic and ratio synthetic estimators for estimating the milk production for small domains, empirically through a real data set.Keywords
Synthetic Estimator, Small Area Estimation, Small Area.References
- Brackstone, G.J. (1987). Small area data: Policy issues and technical challenges, In : R. Platek, J.N.K. Rao, C.E. Sarndal and M.P. Singh (Edition), Small area statistics, John Wiley and Sons, New York, U.S.A., pp.3-20.
- Ghosh, M. and Rao, J.N.K. (1994). Small area estimation: an appraisal (with discussion). Statistical Sci., 9: 65-93.
- Gonzales, M.E. (1973). Use and evaluation of synthetic estimators, Proceedings of the Social Statistics Section of the American Statistical Association, 33-36pp.
- Pandey, Krishan K. (2011). Generalized class of synthetic estimators for small area under systematic sampling design. Statistics in Transition- New Series, Poland, 11 (1) 75-89.
- Tikkiwal, G. C. and Ghiya, A. (2000). A generalized class of synthetic estimators with application to crop acreage estimation for small domains. Biometrical J., 42 (7) : 865876.