Volume-7 , Issue-3 , Jun 2020, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Auxiliary Information and Its Implication in Indirect Method of Domain Estimation

  Shreya Agarwal, Sarla Pareek, Piyush Kant Rai

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.3 , pp.89-92, Jun-2020

  Abstract

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  Abstract
  The governmental studies regularly provide precise measurements to large domain. The issue begins when we talk about the exact insights for the sub population called ?domains ". The quantity of perceptions that happen to fall in the domain is customarily arbitrary and in some cases small. These are the highlights that give domain estimation its specific flavor. To expand the effectiveness of assessments for small domains in which the example estimate is small, assistant factors from authoritative records are domain estimation in factual writing are for the most part plan and model based and assistant variable have extraordinary effect in the advancement of aberrant strategy for domain estimation under above said condition. The present paper portrays the utilization of two auxiliary variables in different proposed estimators for domains which are plan and model based. Likewise, a recreated work is done to think about the proficiency of various proposed estimators under two assistant factors as far as absolute relative bias ( (ARB) and Simulated Relative Standard Error (SRSE) for various domains.

  Key-Words / Index Term
  Auxiliary variables, Domain estimation, Indirect method of domain estimation

  References
  [1] Rai, P.K. and Pandey, K.K.(2013). Synthetic estimators using Auxiliary information in small domains. Statistics in Transition-new series, spring 2013. Vol. 14, No. 1, pp. 31 - 44.
  [2] Pandey, K.K. and Tikkiwal, G.c.(2010). Generalized class of synthetic estimators for small domains under synthetiv sampling scheme.Statistics in Transition-new series, july 2010. Vol. 11, No. 1, pp. 75 ? 89
  [3] Tikkiwal,G.C.and pandey, K.K.(2007). On synthetic and composite stimators for small domain estimation under lahiri-midzuno sampling scheme.Statistics in Transition-new series, april 2007. Vol. 8, No. 1, pp. 111 ? 123
  [4] Tikkiwal,G.C.and Ghiya, A.(2000). A generalized class of synthetic estimators with application to crop acreage estimation for small domains.Biometrical Journal. Vol. 7, pp. 865 - 876.
  [5] Noel J. Purcell and Leslie Kish(1979)Estimation for small domains.Biometrics,Jun., 1979, Vol. 35, No. 2 , pp. 365-384.
  [6] Gonzalez, M. E. and Waksberg, J. (1973).Estimation of the error of synthetic estimates.paper presented at first meeting of the International association of survey statisticians,august 1973, Vienna, Austria, pp.18-25.
  [7] Cochran, W.G. (1977).Sampling Techniques,Wiley & Sons. Singh, D. and Chaudhary, F.S.(1986). Theory and Analysis of Sample Survey Design.Wiley Eastern Limited..
  [8] Lessler, J. T., and Kalsbeek, W. D. (1992) Nonsampling Error in Surveys, Wiley, New York.
  [9] Small, R. J. (1986) Survey Nonresponse Adjustments for Estimates of Means, International Statistical Review, 54, 139-157.
  [10] Madow, W. G., Nisselson, H., and Olkin, I. (Editors) (1983) Incomplete data in sample surveys, Volume 2 Theory and Bibliographies, Academic Press, New York.
  [11] Montaquila, J. M., Brick, J. M., Hagedorn, M. C., Kennedy, C., and Keeter, S. (2008) Aspects of Nonresponse Bias in RDD Telephone Surveys, Chapter 25, In: J. M. Lepkowski.
  [12] H. L., and Scheuren, F. J. (1983) Weighting Adjustment for Unit Nonresponse, Chapter 13, In: W. G. Madow, H. Nisselson, and I. Olkin (eds.): ?Incomplete data in sample surveys, Volume 2 Theory and Bibliographies?, Academic Press, New York, 143-184.
  [13] Rizzo, L., Kalton, G., and Brick, J. M. (1996) A Comparison of Some Weighting Adjustment Methods for Panel Nonresponse, Survey Methodology, 22 (1), 43-53.

  Citation
  Shreya Agarwal, Sarla Pareek, Piyush Kant Rai , "Auxiliary Information and Its Implication in Indirect Method of Domain Estimation," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.3, pp.89-92, 2020

• Open Access   Article

  Asymptotic Behaviours of the Generalized Hypergeometric Polynomials Set Sn(x, y) for Large Value of n

  B.K. Singh

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.7 , Issue.3 , pp.93-102, Jun-2020

  Abstract

  Full-Text HTML

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  Citation

  Abstract
  In this paper, we study the asymptotic behaviours of generalized hypergeometric polynomial Set Sn(x,y) for large value of n, the order of the polynomial sets. Generating function is generally used for the determination of the asymptotic behaviours of the polynomial set as the order of the polynomial set tends to infinity. Hence if the radius of convergence is finite, then the generating function has one or several singularities on the circle of convergence and the location and nature of these singularities determine the behaviours of the polynomial set when the order tends to infinity, But here we have obtained the asymptotic behaviours not from the generating function but by another method directly from the polynomial set. These behaviours for large n have been given in the form of Theorem. A number of well known results for orthogonal and non-orthogonal polynomials have been deduced as particular cases of these theorems.

  Key-Words / Index Term
  Appell function, Hypergeometric polynomial, Orthogonal polynomial, Generating function, Asymptotic Behaviours

  References
  [1] Sanjay Kr. Suman and Brijendra Kr. Singh ?An Effort towards the generalized hypergeometric Polynomials of two variables? Research Guru online Journal Vol. 13, Issue 4, pp.1-11, March 2020 (ISSN: 2349-266X)
  [2] P. Appell, and Kampe de Feriet, J. ?Fonctions Hypergeometriques et Hyperspheriques, polynomies d? Hemite, Gauthier-Villars? Paris,1926.
  [3] J.L. Burchnall and T.W. Chaundy ?Expansions of Appell`s double Hypergeometric function (II)? Quart. J. Math. Oxford ser, 12, pp.112-128, 1941.
  [4] E.D. Rainville Special functions. Mac Millan Co. New York,1960.

  Citation
  B.K. Singh, "Asymptotic Behaviours of the Generalized Hypergeometric Polynomials Set Sn(x, y) for Large Value of n," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.3, pp.93-102, 2020