Linear Systematic Sampling with Unequal Sampling Intervals in the Presence of Linear Trend
Abstract
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.
References
BELLHOUSE D R . On the choice of sampling interval in circular systematic sampling, Shankya, B, 247-248, 1984
BELLHOUSE D R . Systematic sampling, Handbook of Statistics, Edited by P R Krishnaiah and C R Rao, Vol 6, 125-145, 1988
BELLHOUSE D R & RAO J N K . Systematic sampling in the presence of linear trends. Biometrika,62, 694-697, 1975
CHANG, H. J AND HUANG, K. C. Remainder linear systematic sampling, Sankhya B 62, 249-256, 2000
COCHRAN WG . Sampling Techniques, 3rd Edition, John Wiley and Sons, New York, 1977
FOUNTAIN R L & PATHAK P L. Systematic and Non-random Sampling in the Presence of Linear Trends. Communications in statistics- Theory and Methods 18, 2511-2526, 1989
GUPTA A K & KABE D G. Theory of Sample Surveys, World Scientific Publishing Company, 2011
KHAN Z, SHABBIR J, GUPTA S . A New Sampling Design for Systematic Sampling, Communications in Statistics-Theory and Methods,42, 2659-2670 DOI:10.1080/03610926.2011.628771, 2013
KHAN Z, GUPTA S, SHABBIR J. A Note on Diagonal Circular Systematic Sampling, Journal of Statistical Theory and Practice, 8, 439-443, 2013
KHAN Z, GUPTA S, SHABBIR J. Generalized Systematic Sampling, Communications in Statistics-Simulation and Computation, 44, 2240-2250, 2015
MADOW W G. On the theory of systematic sampling III. Comparison of centered and random start systematic sampling. Ann.Math.Statist, 24, 101-106, 1953
MUKERJEE R & SENGUPTA S. Optimal Estimation of a Finite Population Means in the Presence of Linear Trend. Biometrika 77, 625-630, 1990
MURTHY M.N. Sampling Theory and Methods, Statistical Publishing House, Calcutta, India, 1967
MURTHY M N and RAO T J. Systematic sampling with illustrative examples, Handbook of Statistics, Edited by P R Krishnaiah and C R Rao, Vol 6, 147-185, 1988
SARJINDER SINGH. Advanced Sampling Theory with Applications, Springer, 2003
SETHI V K. On optimum pairing of units, Sankhya, B27, 315-320, 1965
SINGH D, JINDAL K K & GARG J N. On modified systematic sampling, Biometrika, 55, 541-546, 1968
SUDAKAR K. A note on circular systematic sampling, Sankhya C, 40, 72-73, 1978
SUBRAMANI, J. Diagonal Systematic Sampling Scheme for Finite Populations, Journal of the Indian Society of Agricultural Statistics, 53(2), 187-195, 2000
SUBRAMANI, J. Further results on diagonal systematic sampling for finite populations, Journal of the Indian Society of Agricultural Statistics, 63(3) 277-282, 2009
SUBRAMANI, J. Generalization of Diagonal Systematic Sampling Scheme for Finite Populations, Model Assisted Statistics and Applications, 5, 117-128, 2010
SUBRAMANI, J. A modification on linear systematic sampling for odd sample size, Bonfring International Journal of Data Mining 2 (2), 32-36, 2012
SUBRAMANI J. A Modification on Systematic Sampling, Model Assisted Statistics and Applications, 8(3), 215-227, 2013
SUBRAMANI J. A Further Modification on Systematic Sampling for Finite Populations, Journal of Statistical Theory and Practice, 7, 471–479, 2013
SUBRAMANI J. Star Type Systematic Sampling Schemes for Finite Populations, Communications in Statistics- Theory and Methods, 43(1), 175-190, 2014
SUBRAMANI J and GUPTA S N. Generalized modified linear systematic sampling scheme for finite populations, Hacettepe Journal of Mathematics and Statistics, 43(3), 529-542, 2014
SUBRAMANI J, GUPTA S N and PRABAVATHY G. Circular systematic sampling in the presence of linear trend, American Journal of Mathematical and Management Sciences, 33(1), 1-19, 2014
SUBRAMANI J and SARJINDER SINGH. Estimation of Population Mean in the Presence of Linear Trend, Communications in Statistics- Theory and Methods, 43(15), 3095-3116, 2013
SUBRAMANI, J and TRACY D. S. Determinant Sampling Scheme for Finite Populations, Internl. J. Math. .& Statist. Sci. 8, (1), 27-41, 1999
SUKHATME, P. V, SUKHATME, B.V, SUKHATME, S & ASOK, C. Sampling Theory of Surveys with Applications, Iowa State Univ. Press, Ames, Iowa, USA, 1984
YATES F. Systematic Sampling, Phil. Trans. Royal. Soc., A, 241, 345-377, 1948
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