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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.37 no.1 Bogotá Jan./June 2014

https://doi.org/10.15446/rce.v37n1.44366 

http://dx.doi.org/10.15446/rce.v37n1.44366

A New Difference-Cum-Exponential Type Estimator of Finite Population Mean in Simple Random Sampling

Un nuevo estimador tipo diferencia-cum-exponencial de la media de una población finita en muestras aleatorias simple

JAVID SHABBIR1, ABDUL HAQ2, SAT GUPTA3

1Quaid-I-Azam University, Department of Statistics, Islamabad, Pakistan. Professor. Email: javidshabbir@gmail.com
2Quaid-I-Azam University, Department of Statistics, Islamabad, Pakistan. Lecturer. Email: aaabdulhaq@gmail.com
3The University of North Carolina at Greensboro, Department of Mathematics and Statistics, Greensboro, USA. Professor. Email: sngupta@uncg.edu


Abstract

Auxiliary information is frequently used to improve the accuracy of the estimators when estimating the unknown population parameters. In this paper, we propose a new difference-cum-exponential type estimator for the finite population mean using auxiliary information in simple random sampling. The expressions for the bias and mean squared error of the proposed estimator are obtained under first order of approximation. It is shown theoretically, that the proposed estimator is always more efficient than the sample mean, ratio, product, regression and several other existing estimators considered here. An empirical study using 10 data sets is also conducted to validate the theoretical findings.

Key words: Ratio estimator, Auxiliary Variable, Exponential type estimator, Bias, MSE, Efficiency.


Resumen

Información auxiliar se utiliza con frecuencia para mejorar la precisión de los estimadores al estimar los parámetros poblacionales desconocidos. En este trabajo, se propone un nuevo tipo de diferencia-cum-exponencial estimador de la población finita implicar el uso de información auxiliar en muestreo aleatorio simple. Las expresiones para el sesgo y el error cuadrático medio del estimador propuesto se obtienen en primer orden de aproximación. Se muestra teóricamente, que el estimador propuesto es siempre más eficiente que la media de la muestra, la relación de, producto, regresión y varios otros estimadores existentes considerados aquí. Un estudio empírico utilizando 10 conjuntos de datos también se lleva a cabo para validar los resultados teóricos.

Palabras clave: estimador de razón, variables auxiliares, estimador tipo exponencial, sesgo, error cuadrático medio.


Texto completo disponible en PDF


References

1. A.K. Das, (1988), Contribution to the Theory of Sampling Strategies Based on Auxiliary Information, Ph.D. thesis, Bidhan Chandra Krishi Viswavidyalay, Nadia West Bengal, India.         [ Links ]

2. Abdul Haq, & Javid Shabbir, (2013), 'Improved family of ratio estimators in simple and stratified random sampling', Communications in Statistics-Theory and Methods 42(5), 782-799.         [ Links ]

3. B.V. Sukhatme, & L. Chand, (1977), Multivariate Ratio-type Estimators, 'Proceedings of the Social Statistics Section', American Statistical Association, Michigan, p. 927-931.         [ Links ]

4. C Kalidar, & H Cingi, (2007), 'Improvement in Variance Estimation in Simple Random Sampling', Communication in Statistics-Theory and Methods 36, 2075-2081.         [ Links ]

5. C. Kalidar, & H. Cingi, (2005), 'A new Estimator using two Auxiliary Variables', Applied Mathematics and Computation 162(2), 901-908.         [ Links ]

6. Donald T Searls, (1964), 'The utilization of a known coefficient of variation in the estimation procedure', Journal of the American Statistical Association 59(308), 1225-1226.         [ Links ]

7. G. S. Maddala, (1977), Econometrics, Economics handbook series, McGraw Hills Publication Company, New York.         [ Links ]

8. Housila P. Singh,, Balkishan Sharma, & Rajesh Tailor, (2014), 'Hartley-Ross Type Estimators for Population Mean Using Known Parameters of Auxiliary Variate', Communications in Statistics-Theory and Methods 43(3), 547-565.         [ Links ]

9. Lovleen Kumar Grover, & Parmdeep Kaur, (2011), 'An Improved Estimator of the Finite Population Mean in Simple Random Sampling', Model Assisted Statistics and Applications 6(1), 47-55.         [ Links ]

10. Lovleen Kumar Grover, & Parmdeep Kaur, (2014), 'A Generalized Class of Ratio Type Exponential Estimators of Population Mean Under Linear Transformation of Auxiliary Variable', Communications in Statistics-Simulation and Computation 43(7), 1552-1574.         [ Links ]

11. M. N. Murthy, (1977), Sampling: Theory and Methods, Statistical Pub. Society.         [ Links ]

12. M.N. Murthy, (1964), 'Product method of estimation', Sankhya A 26(1), 69-74.         [ Links ]

13. R Singh,, P Chauhan,, N Sawan, & F Smarandache, (2009), 'Improvement in estimating the population mean using exponential estimator in simple random sampling', Bulletin of Statistics and Economics 3(13), 13-18.         [ Links ]

14. R Singh,, P. Chauhan, & N. Sawan, (2008), 'On linear combination of ratio and product type exponential estimator for estimating the finite population mean', Statistics in Transition 9(1), 105-115.         [ Links ]

15. R.G.D Steel,, J.H. Torrie, & D.A. Dickey, (1960), Principles and Procedures of Statistics, McGraw-Hill Companies, Michigan.         [ Links ]

16. Rani S Srivnstava,, SP Srivastava, & BB Khare, (1989), 'Chain ratio type estimator for ratio of two population means using auxiliary characters', Communications in Statistics-Theory and Methods 18(10), 3917-3926.         [ Links ]

17. Shashi Bahl, & RK Tuteja, (1991), 'Ratio and product type exponential estimators', Journal of Information and Optimization Sciences 12(1), 159-164.         [ Links ]

18. Subhash Kumar Yadav, & Cem Kadilar, (2013), 'Improved Exponential Type Ratio Estimator of Population Variance', Revista Colombiana de Estadística 36(1), 145-152.         [ Links ]

19. TJ Rao, (1991), 'On certain methods of improving ratio and regression estimators', Communications in Statistics-Theory and Methods 20(10), 3325-3340.         [ Links ]

20. W. G. Cochran, (1940), 'The estimation of the yields of cereal experiments by sampling for the ratio of grain to total produce', The Journal of Agricultural Science 30(02), 262-275.         [ Links ]

21. W. G. Cochran, (1977), Sampling Techniques, 3 edn, John Wiley and Sons, New York.         [ Links ]


[Recibido en octubre de 2013. Aceptado en marzo de 2014]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv37n1a13,
    AUTHOR  = {Shabbir, Javid and Haq, Abdul and Gupta, Sat},
    TITLE   = {{A New Difference-Cum-Exponential Type Estimator of Finite Population Mean in Simple Random Sampling}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2014},
    volume  = {37},
    number  = {1},
    pages   = {199-211}
}