Efficient families of ratio and product-type estimators

Ray, S. K.; Sahai, Ashok

doi:10.1093/biomet/67.1.211

Cited by 25 publications

(12 citation statements)

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“…ρ yz 2 : The correlation coefficient between the variables y on z 2 . Ray and Sahai (1980) have proposed a two parameter family of estimators under SRSWOR scheme using auxiliary variate for estimating the population meanȲ . The objective of this paper is to develop a two parameter family of estimators that estimate the population mean on the current occasion in successive sampling using auxiliary variables on the both occasions and it is known.…”

Section: Xmentioning

confidence: 99%

“…This family of estimators have been studied by Ray and Sahai (1980) under simple random sampling using one auxiliary variable for estimation of the population mean. Using these estimators in successive sampling, the expression for bias and mean squared error of the proposed estimators are obtained up to the first order of approximation.…”

Section: Introductionmentioning

confidence: 99%

“…In many situations, information on an auxiliary variate may be readily available on the first as well as the second occasions; for example, tonnage (or seat capacity) of each vehicle or ship is known in survey sampling of transportation and the number of beds in hospital surveys. Ray and Sahai (1980) have proposed two parameter family of estimators under SRSWOR scheme using auxiliary variate for estimating the population meanȲ and assuming population meanX of auxiliary variate to be known. The objective of this paper is to develop a two parameter family of estimators that estimate the population mean on the current occasion in successive sampling using auxiliary variables on both occasions.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Family of Ratio-Type Estimators for Mean Estimation in Successive Sampling on two Occasions Using Auxiliary Information

Beevi

Chandran²

2017

Statistics in Transition New Series

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In this paper, we proposed an efficient family of ratio-type estimators using one auxiliary variable for the estimation of the current population mean under successive sampling scheme. This family of estimators have been studied by Ray and Sahai (1980) under simple random sampling using one auxiliary variable for estimation of the population mean. Using these estimators in successive sampling, the expression for bias and mean squared error of the proposed estimators are obtained up to the first order of approximation. Usual ratio estimator is identified as a particular case of the suggested estimators. Optimum replacement strategy is also discussed. The proposed family of estimators at optimum condition is compared with the simple mean per unit estimator, Cochran (1977) estimator and existing other members of the family. Expressions of optimization are derived and results have been justified through numerical study interpretation.

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Section: Xmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient Family of Ratio-Type Estimators for Mean Estimation in Successive Sampling on two Occasions Using Auxiliary Information

Beevi

Chandran²

2017

Statistics in Transition New Series

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“…More detailed discussion about the ratio estimator and its modification can be found in Abdia and Shahbaz (2006), Ahmad et al (2009), Al-Jararha and AlHaj Ebrahem (2012), Bhushan (2012, Cochran (1977), Dalabehera and Sahoo (1994), David and Sukhatme (1974), Goodman and Hartley (1958), Gupta and Shabbir (2008), Jhajj et al (2006), Cingi (2003, 2004), Khoshnevisan et al (2007), Koyuncu and Kadilar (2009), Kulkarni (1978), Murthy (1967), Naik andGupta (1991), Olkin (1958), Pathak (1964), Perri (2007), Ray and Sahai (1980), Reddy (1973), Robinson (1987), Sen (1993), Shabbir and Yaab (2003), Sharma and Tailor (2010), Singh and Chaudhary (1986), Singh (2003), Singh and Espejo (2003), Singh and Agnihotri (2008), Singh and Solanki (2012), Singh andTailor (2003, 2005), Singh et al (2004, Sisodia and Dwivedi (1981) , Solanki et al (2012), Srivenkataramana (1980, Sharma (2009), Tin (1965), Upadhyaya and Singh (1999) and Yan and Tian (2010).…”

Section: Y Y Ith Existing (Jth Proposed) Modified Ratio Estimator Of Ymentioning

confidence: 99%

Generalized Modified Ratio Estimator for Estimation of Finite Population Mean

Subramani

2013

J. Mod. App. Stat. Meth.

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A generalized modified ratio estimator is proposed for estimating the population mean using the known population parameters. It is shown that the simple random sampling without replacement sample mean, the usual ratio estimator, the linear regression estimator and all the existing modified ratio estimators are the particular cases of the proposed estimator. The bias and the mean squared error of the proposed estimator are derived and are compared with that of existing estimators. The conditions for which the proposed estimator performs better than the existing estimators are also derived. The performance of the proposed estimator is assessed with that of the existing estimators for certain natural populations

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“…More detailed discussion about the ratio estimator and its modification can be found in Abdia and Shahbaz (2006), Ahmad et al (2009), Al-Jararha and AlHaj Ebrahem (2012), Bhushan (2012), Cochran (1977), Dalabehera and Sahoo (1994), David and Sukhatme (1974), Goodman and Hartley (1958), Gupta and Shabbir (2008), Jhajj et al (2006), Cingi (2003, 2004), Khoshnevisan et al (2007), Koyuncu and Kadilar (2009), Kulkarni (1978), Murthy (1967), Naik and Gupta (1991), Olkin (1958), Pathak (1964), Perri (2007), Ray and Sahai (1980), Reddy (1973), Robinson (1987), Sen (1993), Shabbir and Yaab (2003), Sharma and Tailor (2010), Singh and Chaudhary (1986), , Singh and Espejo (2003), Singh and Agnihotri (2008), Singh and Solanki (2012), Tailor (2003, 2005), Singh et al (2004Singh et al ( , 2008, Sisodia and Dwivedi (1981) , Solanki et al (2012), Srivenkataramana (1980), Tailor andSharma (2009), Tin (1965), Upadhyaya and Singh (1999) and Yan and Tian (2010).…”

Section: Y Y Ith Existing (Jth Proposed) Modified Ratio Estimator Of Ymentioning

confidence: 99%

Vol. 12, No. 2 (Full Issue)

2013

J. Mod. App. Stat. Meth.

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EDITORIAL ASSISTANCEJMASM (ISSN 1538−9472, http://digitalcommons.wayne.edu/jmasm) is an independent, open access electronic journal, published biannually in May and November by JMASM Inc. (PO Box 48023, Oak Park, MI, 48237) in collaboration with the Wayne State University Library System. JMASM seeks to publish (1) new statistical tests or procedures, or the comparison of existing statistical tests or procedures, using computer-intensive Monte Carlo, bootstrap, jackknife, or resampling methods, (2) the study of nonparametric, robust, permutation, exact, and approximate randomization methods, and (3) applications of computer programming, preferably in Fortran (all other programming environments are welcome), related to statistical algorithms, pseudo-random number generators, simulation techniques, and self-contained executable code to carry out new or interesting statistical methods.Journal correspondence (other than manuscript submissions) and requests for advertising may be forwarded to ea@jmasm.com. See back matter for instructions for authors. Normality is a distributional requirement of classical test statistics. In order for the test statistic to provide valid results leading to sound and reliable conclusions this requirement must be satisfied. In the not too distant past, it was claimed that violations of normality would not likely jeopardize scientific findings (See Hsu & Feldt, 1969; Lunney, 1970). Recent revelations suggest otherwise (See e.g., Micceri, 1989; Keselman, Huberty, Lix et al., 1998;Erceg-Hurn, Wilcox, & Keselman, 2013; Wilcox and Keselman, 2003; Wilcox, 2012a, b). Unfortunately the data obtained in psychological investigations rarely, if ever, meet the requirement of normally distributed data (Micceri, 1989; Wilcox, 2012a, b). Consequently, it could be the case that the results from many of the investigations conducted in psychology provide invalid results. Accordingly, authors recommend that researchers attempt to assess the validity of assuming data are normal in form prior to conducting a test of significance (Erceg-Hurn, et al., 2013; Keselman, et al., 1998). Present evidence suggests that a popular fit-statistic, the Kolmogorov-Smirnov test does a poor job of evaluating whether data are normal. Our investigation based on this statistic and other fit-statistics provides a more favorable picture of preliminary testing for normality. Keywords:Assessing normality, fit statistics, g-and-h non-normal skewed and kurtotic data, contaminated mixed-normal distributions; outlying value(s), Likert scales IntroductionPsychological researchers are often reminded that the validity of their statistical tests and the conclusions derived from these tests depends to a great extent on whether the derivational assumptions of the test procedures have been satisfied (e.g., See Keselman, Huberty, Lix et al., 1998; Wilcox, 2012a, b; Wilcox & KESELMAN ET AL 3 Keselman, 2003). Consequently, though not a common practice, researchers are still reminded about assessing derivational assumptions (See Erce...

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Efficient families of ratio and product-type estimators

Cited by 25 publications

References 1 publication

Efficient Family of Ratio-Type Estimators for Mean Estimation in Successive Sampling on two Occasions Using Auxiliary Information

Efficient Family of Ratio-Type Estimators for Mean Estimation in Successive Sampling on two Occasions Using Auxiliary Information

Generalized Modified Ratio Estimator for Estimation of Finite Population Mean

Vol. 12, No. 2 (Full Issue)

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