population mean of the study variable using the linear combination of the Coefficient of. Variation and First quartile, Third quartile, Inter-quartile range, ...
International Journal of
Information and
Int e rn a t ion a l J o u rn al of Info r m a t io n a nd M an a gement Sci ences 24 (20 13 ), 2 13-224
Management Sciences
Estimation of Population Mean U sing Coefficient of Variation and Quartiles of an Auxiliary Variable J. Subramani and G. Kumarapandiyan
P ondicherry University Abstract
In t his paper we have prop osed a class of modified ratio est imat ors for est imat ion of po pul at ion mean of t he st udy variab le using t he linear com bination of the Coeffic ient of Var iation and First quartil e, Third quartile, In t er-quar til e range, Semi-q ua rt ile range, Semiquartile average of t he auxiliary va ria ble. T he bias an d the mean sq uared error of t he p roposed est imat ors are derived and are compared wit h t hat of t he Simple rand om sa m pling without rep lac eme nt (SRS WOR) sa mp le mean , t he classica l ratio estimator and t he exist ing mod ified ratio estimators . Further we have also derived t he conditions for which the proposed est imat or s perform better t han t he ex ist ing est imat ors. An empirica l st udy has been ca rr ied out for certain nat ur al populations to assess t he performances of the prop osed est ima t ors with t hat of t he exist ing est imat ors . From t he em pir ica l st udy it is observed t hat t he proposed mod ified rat io estimator s perfo rm bet t er t han t he existing estimators.
K eywords: Bias, mean sq uared error , modified rati o estimators , natural populat ion s, sim ple rando m sa mpling. 1. Introduct ion
TAO
The sim plest estimator of populat ion mean is t he sa m ple mean ob t ained by using sim ple random sa m pling wit ho ut replace me nt, wh en t here is no add it ional informati on on t he auxiliary variable availa ble. Sometimes in sam ple surveys, along with t he study variable Y , informati on on aux iliary variable X , cor related wit h Y , is also collected . This inform ati on on aux ilia ry variable X , may be utili zed to obtain a more efficient estimator of t he populati on mean. R ati o method of estimat ion is an attempt in t his directi on . T his metho d of estimat ion may b e used wh en (i) X re presents t he same character as Y, bu t measured at some previous dat e when a com plete count of t he po pulation was made and (ii) t he character X is cheaply, qui ckly and eas ily availa ble (see page 77 in Gupt a and K ab e [11]). Co nside r a finite p opulati on U = {Ul , U2 , .. . , UN} of N dist inct and ident ifiable units. Let Y is a study variab le with value Yi measured on Ui, i = 1, 2, 3, .. . , N givi ng a vect or Y = {Yl , Y2 , .. . , YN } and let X is an auxiliary variable which is readily available. T he prob lem is to estimate t he populati on mean
