Estimation of Average Paddy Production of Pira Nagar Village at Barabanki District in India

S. K. Yadav*, Shanya Baghel, Sugandha Saxena and Avinash Kumar Singh

Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow, India

E Mail:;;;

Corresponding Author


The idea of the present paper is the use of the known information on study variable for enhanced estimation of average paddy production of Pira Nagar village at Barabanki District in India under the Simple Random Sampling Scheme. This known information is utilzed in the form of median of primary variable as it is readily available and does not require every unit of the population to be inquired. The Bias and MSE of the suggested estimator are derived up to approximation of degree one.The minimum value of the MSE of suggested estimator is also obtained by optimizing the characterizing scalar. The MSE has also been compared with the considered competing estimators both theoretically and empirically. The theoretical efficiency conditions of the suggested estimator to be better than the considered estimators are verified using natural population on primary data collected from Pira Nagar Village at Barabanki District of Uttar Pradesh state in India.

Keywords: Study variable, median of study variable, simple random sampling, bias, MSE, PRE

1 Introduction

Cochran (1940) was the first who used the auxiliary information for enhancing the efficiency of the estimator of population mean. Since then a number of researchers have modified the usual ratio estimator, utilizing the auxiliary information in the form of its various parameters. Taking data on auxiliary variable requires extra cost. Sometimes it is not feasible to bear the extra cost and sometimes it becomes impossible to get information on auxiliary variable. In such situations we need to find an alternative to the auxiliary information. One of the solutions for such situations is to obtain some easily accessible chracteristics on study variable itself as supplementary information. For example Let the study variable is monthly salary of the workers working at a place. Most of the workers are unwilling to reveal their exact salary or in case of free lancers they don’t have a fixed salary. But they can tell whether their salary lies between 10000–15000, 15000–20000 and so on. Hence it is easier for them to tell the range within which their earning lies. In such kind of situations median can be obtained for the whole data and can be used for elevated estimation of average salary of the workers. In the present investigation, we make use of the known median of the main variable to obtain the estimate of average production of paddy crop at Pira Nagar Village of Barabanki District of Uttar Prdesh state in India.

Let U=U1,U2,,UN be population containing N units which are distinct and may be identified. The problem is to estimate the population mean Y¯=1Ni=1NYi of the main variable Y with higher efficiency. The most suitable estimator for Y¯ is the sample mean y¯. When it costs high to get auxiliary information, we may consider additional information on Y and may suggest a modified ratio type estimator for enhanced estimation of Y¯. If we go for biased estimator, we can obtain much lesser MSE than the variance of y¯ and MSE/Variance of other existing biased and unbiased estimators of Y¯.

1.1 Notation

N: Population Size
n: Sample Size
f: nN: Sampling Fraction
𝑪𝒏𝑵: All possible samples of size n
Y: Study variable
M: Median of the Y
X: Auxiliary variable
𝒀¯,𝑿¯: Population means
𝒚¯,𝒙¯: Sample means
𝝆: Correlation coefficient between X and Y
𝜷: Regression coefficient of Y on X
𝜷𝟏: Coefficient of Skewness of X
𝜷𝟐: Coefficient of Kurtosis of X
𝑴¯: Average of sample medians of Y
m: Sample median of Y
𝑸𝒓: Interquartile range
B(): Bias of the estimator
V(): Variance of the estimator
MSE(): Mean squared error of the estimator
𝑸𝟏,𝑸𝟐,𝑸𝟑: Quartiles of X
𝑪𝒚, Cx, 𝑪𝒎: Coefficient of variation of x, y and m respectively
𝑪𝒚𝒙, Cym: Relative Covariances
PRE(e,p): Percentage relative efficiency of the proposed
MSE(e)MSE(p)×100: estimator(p) with respect to the existing estimator (e)

1.2 Formulae

Variance of Study Variable:


Variance of Auxiliary variable:




Mean of medians of possible samples


Variance of Sample Median of Y


Covariance of 𝒚¯ and 𝒙¯




Covariance of 𝒚¯ and 𝒎


Coefficient of Variations

Cxx =V(x¯)X¯2=Cx2
Cyy =V(y¯)Y¯2=Cy2
Cmm =V(m)M2=Cm2
Cym =Cov(y¯,m)MY¯
Cyx =Cov(y¯,x¯)Y¯X¯

2 Literature Review of Existing Estimators

Under this section, various estimators of Y¯ along with their biases and MSEs are presented in Table 1. It is well known that in simple random sampling technique (y¯, x¯) are unbiased estimators for (Y¯, X¯) respectively.

Table 1 Various existing estimators of 𝒀¯ along with their biases & MSEs

S.No. Estimators Bias MSE/Variance
1 t0=y¯=1ni=1nyi Sample Mean 1-fnY¯2Cy2
2 Y¯^lr=y¯+β(X¯-x¯) Watson(1937) 1-fnY¯2Cy2(1-ρ2)
3 t1=y¯(X¯x¯) Cochron(1940) 1-fnY¯(Cx2-ρCyCx) 1-fnY¯2(Cy2+Cx2-2ρCyCx)
4 t2=X¯r¯ t2=X¯r¯+n(N-1)N(n-1)(y¯-r¯x¯) Goodman(1958) 1-fnY¯2(Cy2+Cx2-2ρCyCx)
5 t3=(1-α)y¯+αy¯X¯x¯ Chakrabarty (1979) 1-fnY¯(α2Cx2-αρCyCx) 1-fnY¯2(Cy2+α2Cx2-2αρCyCx)
6 t4=y¯{2-(x¯X¯)w} Sahai (1980) 1-fnY¯(-w(1-w)2Cx2-wρCyCx) 1-fnY¯2(Cy2+w2Cx2-2wρCyCx)
7 t5=y¯(X¯+Cxx¯+Cx) Sisodia (1981) 1-fnY¯(R52Cx2-R5ρCyCx) 1-fnY¯2(Cy2+R52Cx2-2R5ρCyCx)
8 t6=y¯exp(X¯-x¯X¯+x¯) Tuteja(1991) 1-f8nY¯(3Cx2-4ρCyCx) 1-fnY¯2(Cy2+Cx24-ρCyCx)
10 t8=y¯exp(X¯β2-Cxx¯β2+Cx) Upadhyaya(1999) 1-fnY¯(R82Cx2-R8ρCyCx) 1-fnY¯2(Cy2+R82Cx2-2R8ρCyCx)
11 t9=y¯(X¯2x¯2) Kadilar(2003) 1-fnY¯(3Cx2-2ρCyCx) 1-fnY¯2(Cy2+4Cx2-4ρCyCx)
12 t10=y¯(X¯β1+Sxx¯β1+Sx) Singh(2003) 1-fnY¯(R(10)2Cx2-R(10)ρCyCx) 1-fnY¯2(Cy2+R(10)2Cx2-2R(10)ρCyCx)
13 t11=y¯(X¯+ρx¯+ρ) Singh (2003) 1-fnY¯(R(11)2Cx2-R(11)ρCyCx) 1-fnY¯2(Cy2+R(10)2Cx2-2R(10)ρCyCx)
14 t12=y¯(X¯+β2x¯+β2) Singh et al. 1-fnY¯(R(11)2Cx2-R(11)ρCyCx) 1-fnY¯2(Cy2+R(12)2Cx2-2R(12)ρCyCx)
15 t13=y¯(X¯+β1x¯+β1) Yan and Tian (2010) 1-fnY¯(R(13)2Cx2-R(13)ρCyCx) 1-fnY¯2(Cy2+R(13)2Cx2-2R(13)ρCyCx)
16 t14=y¯(X¯β1+β2x¯β1+β2) Yan and Tian (2010) 1-fnY¯(R(14)2Cx2-R(14)ρCyCx) 1-fnY¯2(Cy2+R(14)2Cx2-2R(14)ρCyCx)
17 t15=y¯(X¯Cx+β1x¯Cx+β1) Yan and Tian (2010) 1-fnY¯(R(15)2Cx2-R(15)ρCyCx) 1-fnY¯2(Cy2+R(15)2Cx2-2R(15)ρCyCx)
18 t16=y¯(X¯β2+β1x¯β2+β1) Yan and Tian (2010) 1-fnY¯(R(16)2Cx2-R(16)ρCyCx) 1-fnY¯2(Cy2+R(16)2Cx2-2R(16)ρCyCx)
19 t17=y¯X¯x¯(1-kx¯s2nx¯3)-1 Pandey (2011) 1-fnY¯(kCx2-ρCyCx) 1-fnY¯2(Cy2+k2Cx2-2kρCyCx)
20 t18=y¯(X¯+Q3x¯+Q3) Al-Omari (2012) 1-fnY¯(R(18)2Cx2-R(18)ρCyCx) 1-fnY¯2(Cy2+R(18)2Cx2-2R(18)ρCyCx)
21 t19=y¯(X¯+Qrx¯+Qr) Al-Omari (2012) 1-fnY¯(R(19)2Cx2-R(19)ρCyCx) 1-fnY¯2(Cy2+R(19)2Cx2-2R(19)ρCyCx)
22 t20=y¯(X¯+Mdx¯+Md) Subramani and Kumarpandiyan (2012) 1-fnY¯(R(20)2Cx2-R(20)ρCyCx) 1-fnY¯2(Cy2+R(20)2Cx2-2R(20)ρCyCx)
23 t21=y¯(X¯Cx+Mdx¯Cx+Md) Subramani and Kumarpandiyan (2012) 1-fnY¯(R(21)2Cx2-R(21)ρCyCx) 1-fnY¯2(Cy2+R(21)2Cx2-2R(21)ρCyCx)
24 t22=y¯(X¯x¯)1/2 Swain (2014) 1-f8nY¯(3Cx2-4ρCyCx) 1-fnY¯2(Cy2+Cx24-ρCyCx)
25 t23=α+tRe+(1-α)tPe Yadav and Mishra (2015) Y¯[18(4α-1-7f+4f2)Cx2-(2α-1)2(1-f)ρCyCx] Y¯2(1-f)n(Cy2+α2Cx24-αρCyCx)
26 t24=y¯(X¯+nx¯+n) Jerjuddin and Kishun (2016) 1-fnY¯(R(24)2Cx2-R(24)ρCyCx) 1-fnY¯2(Cy2+R(24)2Cx2-2R(24)ρCyCx)
27 t25=y¯(X¯+Cxx¯+Cx)b1 Soponviwatkul and Lawson (2017) 1-fnY¯[b1(b1+1)2R52Cx2-b1R5ρCyCx] 1-fnY¯2Cy2(1-ρ2)
28 t26=y¯(X¯+ρx¯+ρ)b2 Soponviwatkul and Lawson (2017) 1-fnY¯[b2(b2+1)2R112Cx2-b2R11ρCyCx] 1-fnY¯2Cy2(1-ρ2)
29 t27=ω1y¯+(1-ω1)(y¯X¯x¯) Ijaz and Ali (2018) 1-fnY¯ρCy(Cx-ρ) 1-fnY¯2Cy2(1-ρ2)
30 t28=ω2y¯+(1-ω2)(y¯expX¯-x¯x¯-X¯) Ijaz and Ali (2018) 1-fnY¯ρCy(14Cx-ρCy) 1-fnY¯2Cy2(1-ρ2)
31 t29=y¯(abX¯+cdabx¯+cd) Yadav et al. (2019) 1-fnY¯2(Cy2-Cyx2Cx2)

Note: We will denote our measures in terms of Coefficient of Variation because it is a relative measure and most suitable to compare two series.


R5 =X¯X¯+Cx,R7=X¯CxX¯Cx+β2,R8=X¯β2X¯β2+Cx,R10=X¯β1X¯β1+Sx,
R11 =X¯X¯+ρ,R12=X¯X¯+β2,R13=X¯X¯+β1,R14=X¯β1X¯β1+β2,
R15 =X¯CxX¯Cx+β1,R16=X¯β2X¯β2+β1,k=ρCyCx,R18=X¯X¯+Q3,
R19 =X¯X¯+Qr,R20=X¯X¯+Md,R21=X¯CxX¯Cx+Md,α=ρ4CyCx,
ω1 =w/R5,ω2=w/R11,w=ρCyCx

a,b,c,d = Constants or Parametric Value

3 Proposed Estimator Based on Median

If the median M of Y is known so by utilizing it, we may suggest an elevated estimator of Y¯ as,

𝒕=𝒚¯+𝜶log𝒎𝑴 (1)

Where α is chosen such that MSE(t) is minimum. The bias and MSE of t up to approximation of order one is given by,

B(t) =αB(m)M-α2λCm2 (2)
𝑀𝑆𝐸(t) =λY¯2Cy2+λα2Cm2+2aY¯λCym (3)

where λ=1-fn


αmin =-Y¯CymCm2 (4)
andMSEmin(t) =λY¯2(Cy2-CYm2Cm2) (5)

3.1 Proposed Estimator Based on Median: Detailed Study


e0 =y¯-Y¯Y¯ande1=m-MM
theny¯ =Y¯(1+e0)andm=M(1+e1)


E(e0) =E(y¯-Y¯Y¯)=E(y¯)-Y¯Y¯=0orE(e0)=0 (6)
E(e1) =E(m-MM)=E(m)-MMor
E(e1) =M¯-MM=B(m)M (7)
E(e02) =E(y¯-Y¯Y¯)2=E(y¯-Y¯)2Y¯2=V(y¯)Y¯2=1-fnCy2
E(e02) =λCy2 (8)
E(e12) =E(m-MM)2=E(m-M)2M2=V(m)M2=1-fnCm2
E(e12) =λCm2 (9)
E(e0e1) =E[((y¯-Y¯)Y¯)(m-MM)]=Cov(y¯,m)Y¯M=λCym
E(e0e1) =Cym (10)

Hence the Estimator can be rewritten as,

t=Y¯+Y¯e0+α=(e1-e122) (11)

For Biasedness,

t =Y¯+Y¯e0+a(e1-e122)
(t-Y¯) =Y¯e0+ae1-ae122
E(t-Y¯) =Y¯E(e0)+aE(e1)-a2E(e12)
B(t) =0+aB(m)M-a2λCm2

(from Equation (6), (3.1) and (8))

Hence Biasedness is :

𝑩(𝒕)=𝜶𝑩(𝒎)𝑴-𝜶𝟐𝝀𝑪𝒎𝟐 (12)

For MSE,

𝑀𝑆𝐸(t) =E(t-Y¯)2
(second and higher order terms are ignored)


𝑴𝑺𝑬(𝒕)=𝝀𝒀¯𝟐𝑪𝒚𝟐+𝝀𝜶𝟐𝑪𝒎𝟐+𝟐𝜶𝒀¯𝝀𝑪𝒚𝒎 (13)

(from equation (8), (9) and (10))

Minimum Value of 𝒂

For Minimum value of α, we should have



𝑀𝑆𝐸(t)α =02αλCm2+2Y¯λCym=0
𝜶𝒎𝒊𝒏 =-𝒀¯𝑪𝒚𝒎𝑪𝒎𝟐 (14)

For Minima,


Hence a has a minimum value.

Minimum Value of MSE

Hence Minimum value of MSE(t) is obtained by putting the Value of α in Equation (3.3)

MSEmin(t) =λY¯2Cy2+λY¯2Cym2Cm2Cm4-2Y¯CymCm2Y¯λCym
𝑴𝑺𝑬𝒎𝒊𝒏(𝒕) =𝝀𝒀¯𝟐(𝑪𝒚𝟐-𝑪𝒚𝒎𝟐𝑪𝒎𝟐) (15)

4 Efficiency Comparison

In this section the suggested estimator is being compared with the competing estimators of Y¯ and the efficiency conditions are presented in Table 2.

Table 2 Efficiency comparison

S.No. 𝑀𝑆𝐸(t)<𝑀𝑆𝐸() Condition
1 𝑀𝑆𝐸(t)V(y¯) Cym2Cm20
2 𝑀𝑆𝐸(t)𝑀𝑆𝐸(t2) Cym2Cm2Cx(2ρCy-Cx)
3 𝑀𝑆𝐸(t)𝑀𝑆𝐸(tj),𝑀𝑆𝐸(y¯lr) CymCm2ρ2Cy2;j=3,4,25,,29
4 𝑀𝑆𝐸(t)𝑀𝑆𝐸(t5) Cym2Cm22R5Cx(2ρCy-R52Cx)
5 𝑀𝑆𝐸(t)𝑀𝑆𝐸(t6) Cym2Cm2Cx(ρCy-Cx4)
6 𝑀𝑆𝐸(t)𝑀𝑆𝐸(tj) Cym2Cm22RjCx(2ρCy-Rj2Cx);
7 𝑀𝑆𝐸(t)𝑀𝑆𝐸(t9) Cym2Cm24Cx(ρCy-Cx)
8 𝑀𝑆𝐸(t)𝑀𝑆𝐸(t17) CymCm2ρ2Cy2
9 𝑀𝑆𝐸(t)𝑀𝑆𝐸(t22) Cym2Cm2Cx(ρCy-Cx4)
10 𝑀𝑆𝐸(t)𝑀𝑆𝐸(t23) Cym2Cm2ρCyCx
11 𝑀𝑆𝐸(t)𝑀𝑆𝐸(t24) Cym2Cm22R24Cx(ρCy-R242Cx)

5 Numerical Study

Under this section the efficiency conditions of the suggested estimator over competing estimators are verified using real data sets.

5.1 Data Collection

To verify the results we have obtained for the Paddy Production data from the Pira Nagar Village of Barabanki Distrcit.The details of the obtained data is as follows:

Village Pira Nagar
District Barabanki
Time March 2018
Production Paddy Production
Type of Data Primary Data
Information Taken Name of Resident
Their Area of Cultivation (Unit in Hectares)
Yield obtained for each area ( Unit in Quintals):
one Quintal=100 Kilogram

For our Numerical Justification we have taken:

Study Variable Yield denoted as Y
Auxiliary Variable Area of Cultivation denoted as X
Population Size 52
Sample Size 3

5.2 Population Parameters

Parameter Value Units in
N 52
n 3
CnN 22100
Y¯ 14.721 Quintal
X¯ 0.46227 Hectare
M 10 Quintal
ρ 0.8046229
Sy2 190.8668 Quintal
Sx2 0.15675383 Hectare
Syx2 4.401155
Cy2 0.8807379
Cx2 0.7335474
Cyx 4.401155
β1 8.1028894
β2 14.146291
β 28.0769
Q1 0.4040 Hectare
Q3 0.5050 Hectare
Qr 0.2525 Hectare
M¯ 12.0119 Quintal
V(m) 37.7429 Quintal
Cym2 0.2536
Cm2 0.3774

5.3 Measurement on Population Parameters

On the basis of the data, The numerical values related to proposed estimators are obtained as follows:

t 14.022176
B(t) 1.5962096
amin 9.8921161
𝑀𝑆𝐸min(t) 14.211079

5.4 Numerical Comparison

We have constructed a table for numerical comparison of the suggested estimator with the estimators in competition. The following table gives:

• The values of the suggested and competing estimators on the Basis of the data obtained and sample taken.

• The Biases of competing and suggested Estimators.

• Mean Square Error (MSE) of competing and Proposed Estimators.

• The percentage relative efficiencies (PRE) of the suggested over competing estimators of Y¯.

Table 4 Biases, MSE’s and respective PRE’s

Estimator Bias MSE PRE
t0 0 V(t0)=59.951751 421.866
y¯lr 0 V(y¯lr)=21.137907 148.74245
t1 0.40139256 21.837168 153.66298
t2` 0 21.837168 153.66298
t3 -1.1203056 21.137907 148.74245
t4 -2.3629292 21.137907 148.74245
t5 -0.63149751 35.223464 247.8592
t6 -0.22328973 28.411333 199.92382
t7 -0.078904053 57.591622 405.25862
t8 0.0076015701 21.138228 148.74471
t9 4.1946732 83.587598 588.18614
t10 0.06976912 21.163736 148.9242
t11 -0.63958709 34.472784 242.5768
t12 -0.091234028 57.215612 402.6127
t13 -0.15151962 55.345217 389.4512
t14 -0.47740469 43.707413 307.5587
t15 -0.086059435 57.373669 403.7249
t16 -0.65903753 30.58859 215.2447
t17 0.27660967 21.493713 151.2462
t18 -0.65448695 29.277583 206.0194
t19 -0.51534035 23.893597 168.13359
t20 -0.62993932 27.185932 191.30097
t21 -0.64921611 28.605068 201.2871
t22 -0.22328973 28.411333 199.9238
t23 1.7460142 15.928206 112.0830
t24 -0.33881397 49.086159 345.4077
t25 -0.7940365 21.137907 148.74245
t26 -0.8804347 21.137907 148.74245
t27 0.1809299 21.137907 148.74245
t28 -1.888758 21.137907 148.74245
t29 - 21.137907 148.74245
(t) 1.5962096 14.211079

6 Results and Discussion

From the Table 4 it is observed from all the estimators that,

6.1 Biasednesses are ranging from -2.3629 to 4.1947.

6.2 Mean Square Errors are ranging from 14.2111 to 83.5875.

6.3 The PREs of the suggested estimator over estimators in competition are ranging from 112.0830 to 588.1861.

6.4 The sample mean (𝒕𝟎), Usual Regression Estimator (Watson,1937) 𝒚¯𝒍𝒓, Goodman and Hartely’s revised estimator (1958), 𝒕𝟐; are unbiased for 𝒀¯.

6.5 Among the existing estimators, the MSE of the estimator of Yadav and Mishra(2015), 𝒕𝟐𝟑 is minimum i.e. 15.9282 and MSE of the estimator of Kadilar and Kingi (2003), 𝒕𝟗 is maximum i.e. 83.5875.

6.6 The suggested estimator is 1.12% more efficient than 𝒕𝟐𝟑 and 5.88% more efficient than 𝒕𝟗.

6.7 Since Efficiency is stronger property than the unbiasedness. Hence here we prefer the biased estimator with minimum MSE instead of unbiased estimator with higher MSE.

6.8 It is observed from data that the given below inequalities hold good;

6.9 𝑴𝑺𝑬(𝒕)𝑴𝑺𝑬(𝒕𝟐𝟑)𝑽(𝒚¯𝒍𝒓)𝑴𝑺𝑬(𝒕𝟏)𝑽(𝒚¯)

6.10 The proposed estimator has minimum MSE and comes out to be more efficient than the other estimators which was our aim of study.

7 Conclusion

7.1 We have applied our proposed estimator successfully for the estimation of Average Paddy production. We can also use it for other agricultural areas and productions with larger sample size and population size.

7.2 In case the exact values are not known but we may know the ranges within which our values may be supposed to lie, this Median based estimator will give a precise result.

7.3 The use of this estimator can be extended to other fields also and can be used as an alternative of SRSWOR sample mean when exact values of characteristic under study are not known.

7.4 Whenever taking the auxiliary information involves very high cost we can use the proposed estimator as an alternative of Ratio and Regression type estimators.

7.5 It has been shown theoretically as well as numerically that the suggested estimator is better than the competing estimators for the estimating Y¯.

7.6 Mostly the minimum MSE of any ratio type estimator is equal to the variance of the regression estimator but the suggested ratio type estimator has its MSE less than the variance of the usual regression estimator.

7.7 Therefore, the suggested estimator is highly recommended for the practical applications.


The authors are very much thankful to the Editior-in-Chief of JRSS and the learned referees for critically examining the paper which improved the quality of the earlier draft.


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S. K. Yadav is a faculty in the Department of Statistics at Babasaheb Bhimrao Ambedkar University Lucknow, U.P., India. He earned his M.Sc. and Ph.D. degrees in Statistics from Lucknow University and qualified the National Eligibility Test. Dr. Yadav has published more than 40 research papers in national and international journals of repute indexed in Scopus/Web of science and two books from an international publisher. He is a referee for 20 reputed international journals. He has been awarded Young Scientist Award in 2016 for the contribution in the field survey sampling by Venus International Research Foundation, Chennai, India and best paper award in 2018 by MTMI, USA. He has presented papers in more than 20 national and international conferences and also delivered 18 invited talks in several conferences.


Shanya Baghel is pursuing her Ph.D in IIT(ISM) Dhanbad, Department of Mathematics and Computing as a JRF. She has completed her M.Phil. from Babasaheb Bhimrao Ambedkar University (BBAU), Lucknow, in 2020. She received her M.Sc. degree in Applied Statistics from BBAU, Lucknow in 2018. She attended University of Lucknow, India and received her B.Sc. in 2016. Her M.Phil work centers on Estimation of Population Mean using known Auxiliary Variable.


Sugandha Saxena is a postgraduate from Babasaheb Bhimrao Ambedkar University. She is an alumna of City Montessori School, Lucknow, India. She received a B.Sc. degree in Statistics and Mathematics from Mahila P.G. College, University of Lucknow. She completed her M.Sc. in Applied Statistics from Babasaheb Bhimrao Ambedkar University, Lucknow.


Avinash Kumar Singh received his M.Sc. degree in Applied Statistics form Babasaheb Bhimrao Ambedkar University, Lucknow, India. He attended the University of Lucknow, India and received his B.Sc. in Physics, Mathematics and Statistics.


1 Introduction

1.1 Notation

1.2 Formulae

2 Literature Review of Existing Estimators

3 Proposed Estimator Based on Median

3.1 Proposed Estimator Based on Median: Detailed Study

4 Efficiency Comparison

5 Numerical Study

5.1 Data Collection

5.2 Population Parameters

5.3 Measurement on Population Parameters

5.4 Numerical Comparison

6 Results and Discussion

7 Conclusion