A general procedure for estimating population variance in successive sampling using fuzzy tools
Yıl 2017,
Cilt: 46 Sayı: 4, 695 - 712, 01.08.2017
A. Chatterjee
,
G.n. Singh
,
A. Bandyopadhyay
,
P. Mukhopadhyay
Öz
This paper defines a general class of estimators for estimating population variance on current occasion in two occasion successive sampling.
Detail behaviors of the proposed class of estimators have been studied and its optimum replacement strategy has also been discussed. The proposed class of estimators has been compared with the sample variance estimator and the results obtained are demonstrated through empirical studies. Categorization of the dominance ranges of the proposed estimation strategies are deployed through defuzzication tools which are followed by suitable recommendations.
Kaynakça
- Chand, L. Some ratio type estimators based on two or more auxiliary variables, Unpublished
Ph. D. thesis, Iowa State University, Ames, Iowa (USA),1975.
- Chaturvedi, D. K. and Tripathi, T. P. Estimation of population ratio on two occasion us-
ing multivariate auxiliary information,Journal of Indian Statistical Association (21),113-
120,1983.
- Das, A. K. Estimation of population ratio on two occasions,Journal of Indian Society Agri-
cultures Statistics (34),1-9,1982.
- Gupta, P. C. Sampling on two successive occasions, Journal of Statistical Research (13),
7-16,1979.
- Gupta, S. and Shabbir, J. On improvement in estimating the population mean in simple
random sampling, Journal of Applied Statistics 35(5), 559-566, 2008.
- Jessen, R. J. Statistical investigation of a sample survey for obtaining farm facts, Agricul-
tural Experiment Station Research (Bulletin No.304) Ames, Iowa, USA, 1-104, 1942.
- Mamdani, E. H. and Assilian, S. An experiment in linguistic synthesis with a fuzzy logic
controller,International Journal of Man-Machine Studies 7(1), 1-13, 1975.
- Murthy, M. N. Sampling theory and methods, Statistical Publishing Society, Calcutta,India
1967.
- Patterson, H. D. Sampling on successive occasions with partial replacement of units, Journal
of the Royal Statistical Society (12), 241-255, 1950.
- Rao, J. N. K. and Graham, J. E. Rotation design for sampling on repeated occasions, Journal
of American Statistical Association (59), 492-509, 1964.
- Reddy, V. N. A study on the use of prior knowledge on certain population parameters in
estimation, Sankhya Series C (40), 29-37, 1978.
- Sahoo, J. and Sahoo, L. N. A class of estimators in two-phase sampling using two auxiliary
variables, Journal of Indian statistical Association (37),107-114, 1993.
- Singh, G. N., Singh, V. K., Priyanka, K., Prasad, S. and Karna, J. P. Rotation patterns
under imputation of missing data over two-occasion, Communications in Statistics-Theory
and Methods 41(4), 619-137, 2012a.
- Singh, G. N., Priyanka, k., Prasad, S., Singh, S. and Kim, J. M. A class of estimators
for population variance in two occasion rotation patterns, Communications for Statistical
Applications and Methods, 20(4), 247-257, 2013.
- Singh, H. P., Chandra, P., Joarder, A. H. and Singh, S. Family of estimators of mean, ratio
and product of a nite population using random nonresponse, Test(16), 565-597, 2007.
- Singh, H. P. and Vishwakarma, G. K. A general class of estimators in successive sampling,
Metron LXV(2), 201-227, 2007a.
- Singh, H. P., Mathur, N. and Chandra, P. A chain-type estimator for population variance
using two auxiliary variables in two-phase sampling, Statistics in Transition new series
10(1), 75-84, 2009.
- Singh, S. and Deo, B. Imputation by power transformation, Statistical Papers (44), 555-579,
2003.
- Singh, S., Joarder , A. H. and Tracy, D. S. Median estimation using double sampling,
Australian and New Zealand Journal of Statistics, 43(1), 2001.
- Singh, V. K. and Shukla, D. One parameter family of factor-type ratio estimators, Metron,
45, 1-2, 30, 273-283, 1987.
- Srivastava, S. K. Generalized estimator for the mean of a finite population using multi
auxiliary information, Journal of the American Statistical Association (66), 404-407, 1971.
- Srivastava, S. K. and Jhaji, H. S. A class of estimators using auxiliary information for
estimating nite population variance, Sankhya series C (42), 87-96, 1980.
- Sukhatme, P. V. and Sukhatme, B. V. Sampling theory of surveys with applications, Asia
Publishing House, India, 1970.
- Sukhatme, P. V., Sukhatme, B.V., Sukhatme, S. and Asok, C. Sampling theory of surveys
with applications, Iowa State University Press, Iowa (USA) and Indian Society of Agricul-
tural Statistics, New Delhi (India), 1984.
- Tracy, D. S., Singh, H. P. and Singh, R. An alternative to the ratio-cum-product estimator
in sample surveys, Journal of Statistical Planning and Inference (53), 375-387, 1996.
- Upadhyaya, L. N. and Singh, H. P. Use of transformed auxiliary variable in estimating the
nite population mean, Biometrical Journal 41(5), 627-636, 1999.
- Upadhyaya, L. N. and Singh, H. P. Almost unbiased ratio and product type estimators nite
population variance in sample surveys, Statistics in Transition 7(5), 1087-1096, 2006.
- Zadeh, L.A. Outline of a new approach to the analysis of complex systems and decision
processes, IEEE Transaction on systems, man and cybernetics 3(1), 28-44, 1973.
Yıl 2017,
Cilt: 46 Sayı: 4, 695 - 712, 01.08.2017
A. Chatterjee
,
G.n. Singh
,
A. Bandyopadhyay
,
P. Mukhopadhyay
Kaynakça
- Chand, L. Some ratio type estimators based on two or more auxiliary variables, Unpublished
Ph. D. thesis, Iowa State University, Ames, Iowa (USA),1975.
- Chaturvedi, D. K. and Tripathi, T. P. Estimation of population ratio on two occasion us-
ing multivariate auxiliary information,Journal of Indian Statistical Association (21),113-
120,1983.
- Das, A. K. Estimation of population ratio on two occasions,Journal of Indian Society Agri-
cultures Statistics (34),1-9,1982.
- Gupta, P. C. Sampling on two successive occasions, Journal of Statistical Research (13),
7-16,1979.
- Gupta, S. and Shabbir, J. On improvement in estimating the population mean in simple
random sampling, Journal of Applied Statistics 35(5), 559-566, 2008.
- Jessen, R. J. Statistical investigation of a sample survey for obtaining farm facts, Agricul-
tural Experiment Station Research (Bulletin No.304) Ames, Iowa, USA, 1-104, 1942.
- Mamdani, E. H. and Assilian, S. An experiment in linguistic synthesis with a fuzzy logic
controller,International Journal of Man-Machine Studies 7(1), 1-13, 1975.
- Murthy, M. N. Sampling theory and methods, Statistical Publishing Society, Calcutta,India
1967.
- Patterson, H. D. Sampling on successive occasions with partial replacement of units, Journal
of the Royal Statistical Society (12), 241-255, 1950.
- Rao, J. N. K. and Graham, J. E. Rotation design for sampling on repeated occasions, Journal
of American Statistical Association (59), 492-509, 1964.
- Reddy, V. N. A study on the use of prior knowledge on certain population parameters in
estimation, Sankhya Series C (40), 29-37, 1978.
- Sahoo, J. and Sahoo, L. N. A class of estimators in two-phase sampling using two auxiliary
variables, Journal of Indian statistical Association (37),107-114, 1993.
- Singh, G. N., Singh, V. K., Priyanka, K., Prasad, S. and Karna, J. P. Rotation patterns
under imputation of missing data over two-occasion, Communications in Statistics-Theory
and Methods 41(4), 619-137, 2012a.
- Singh, G. N., Priyanka, k., Prasad, S., Singh, S. and Kim, J. M. A class of estimators
for population variance in two occasion rotation patterns, Communications for Statistical
Applications and Methods, 20(4), 247-257, 2013.
- Singh, H. P., Chandra, P., Joarder, A. H. and Singh, S. Family of estimators of mean, ratio
and product of a nite population using random nonresponse, Test(16), 565-597, 2007.
- Singh, H. P. and Vishwakarma, G. K. A general class of estimators in successive sampling,
Metron LXV(2), 201-227, 2007a.
- Singh, H. P., Mathur, N. and Chandra, P. A chain-type estimator for population variance
using two auxiliary variables in two-phase sampling, Statistics in Transition new series
10(1), 75-84, 2009.
- Singh, S. and Deo, B. Imputation by power transformation, Statistical Papers (44), 555-579,
2003.
- Singh, S., Joarder , A. H. and Tracy, D. S. Median estimation using double sampling,
Australian and New Zealand Journal of Statistics, 43(1), 2001.
- Singh, V. K. and Shukla, D. One parameter family of factor-type ratio estimators, Metron,
45, 1-2, 30, 273-283, 1987.
- Srivastava, S. K. Generalized estimator for the mean of a finite population using multi
auxiliary information, Journal of the American Statistical Association (66), 404-407, 1971.
- Srivastava, S. K. and Jhaji, H. S. A class of estimators using auxiliary information for
estimating nite population variance, Sankhya series C (42), 87-96, 1980.
- Sukhatme, P. V. and Sukhatme, B. V. Sampling theory of surveys with applications, Asia
Publishing House, India, 1970.
- Sukhatme, P. V., Sukhatme, B.V., Sukhatme, S. and Asok, C. Sampling theory of surveys
with applications, Iowa State University Press, Iowa (USA) and Indian Society of Agricul-
tural Statistics, New Delhi (India), 1984.
- Tracy, D. S., Singh, H. P. and Singh, R. An alternative to the ratio-cum-product estimator
in sample surveys, Journal of Statistical Planning and Inference (53), 375-387, 1996.
- Upadhyaya, L. N. and Singh, H. P. Use of transformed auxiliary variable in estimating the
nite population mean, Biometrical Journal 41(5), 627-636, 1999.
- Upadhyaya, L. N. and Singh, H. P. Almost unbiased ratio and product type estimators nite
population variance in sample surveys, Statistics in Transition 7(5), 1087-1096, 2006.
- Zadeh, L.A. Outline of a new approach to the analysis of complex systems and decision
processes, IEEE Transaction on systems, man and cybernetics 3(1), 28-44, 1973.