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STM JOURNALSScientific Technical Medical

www.stmjournals.com

May - August 2014

(RRJoST)ISSN : 2348-7909

Research & Reviews Journal of Statistics

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Industrial Tribology Machine Dynamics & Maintenance

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Indian Institute of Technology Delhi, India

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Alternative Energy Technology Laboratory,

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Indian Institute of Technology, Chennai, India

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STM Journal (s) Advisory Board

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Engineering Department, PEC University of Technology,

Chandigarh, India.

STM Journal (s) Advisory Board

Editorial Board

Dr. Manjunatha Prasad KaranthaDepartment of Statistics, Health Science Library Building, Manipal University,

India.

Kedar Nath Singh Yadava Deptt. of Statistics, BHU, Varanasi-5,

India.

Vijay Kumar SinghDepartment of Statistics, Banaras Hindu

University, Varanasi – 221005, India.

Prof. Satyanshu Kumar UpadhyayStatistics Professor, Department of Statistics, Banaras Hindu University, Varanasi-221005,

India.

Professor Somanath BaghProfessor of Statistics, School Of

Mathematical Sciences, Sambalpur University, Jyotivihar-768019,Orissa, India.

R. VijayaraghavanDepartment of Statistics, Bharathiar

University, Coimbatore 641 046,Tamil Nadu, India.

Prof. Harinder Singh Professor & Head Department of

Mathematics, Jaypee University of Information Technology, Waknaghat ,

India.

Rajyaguru Arti Department of Statistics

Veer Narmad South Gujarat University,Udhna Magdalla Road.

Arijit ChaudhariHonorary Visiting Professor,

Applied Statistics Unit, Indian Statistical Institute, India.

Dr. Balkishan Sharma Associate Professor (Biostatistics),

Department of Community Medicine, Sri Aurobindo Medical College and P. G.

Institute, Indore (M. P.), India.

I take the privilege to present the hard copy compilation for the [Volume 3 Issue (2)] of Research &

Reviews: Journal of Statistics. The intension of RRJoST is to create an atmosphere that stimulates

creativeness, research and growth in the area of Journal of Statistics.

The development and growth of the mankind is the consequence of brilliant Research done by

eminent Scientists and Engineers in every field. RRJoST provides an outlet for Research findings

and reviews in areas of Statistics found to be relevant for National and International recent

developments & research initiative.

The aim and scope of the Journal is to provide an academic medium and an important reference for

the advancement and dissemination of Research results that support high level learning, teaching and

research in the domain of Statistics.

Finally, I express my sincere gratitude and thanks to our Editorial/ Reviewer board and Authors for

their continued support and invaluable contributions and suggestions in the form of authoring write-

ups/ reviewing and providing constructive comments for the advancement of the journals. With

regards to their due continuous support and co-operation, we have been able to publish quality

Research/Reviews findings for our customers base.

I hope you will enjoy reading this issue and we welcome your feedback on any aspect of the Journal.

Dr. Archana Mehrotra

Director

STM Journals

Director's Desk

STM JOURNALS

1. Coefficient Estimation of Regression Model and Hypothesis Testing by Bootstrap Method Md. Siddikur Rahman 1

2. A Generalized Product Method of Estimation in Two Phase Sampling Balkishan Sharma, Housila P. Singh, Rajesh Tailor 8

3. Mann-Whitney Test for Imprecise ObservationsV. S. Vaidyanathan 16

4. Construction of Neighbour Balanced Nested Row Column Designs and µ-Resolvable All Order Neighbour Balance Design by using Mutually Orthogonal Latin SquaresAatish Kumar Sahu, Anurup Majumder 21

ContentsResearch & Reviews : Journal of Statistics

RRJoST (2014)© STM Journals 2014. All Rights Reserved

Research & Reviews: Journal of Statistics ISSN: 2278-2273 (online), ISSN: 2348-7909 (print)

Volume 3, Issue 2

www.stmjournals.com

Coefficient Estimation of Regression Model and

Hypothesis Testing by Bootstrap Method

Md. Siddikur Rahman

Department of Statistics, Begum Rokeya University, Rangpur, Bangladesh

Abstract The main concern of statistical inference is to achieve accurate result and to make proper

decision on the basis of sample observations. But in some practical cases, it is not

possible to reach the goal of statistics for the lack of desired number of sample. When the sample size is small and/or the empirical distribution is unknown, we have to use

bootstrapping method to increases the accuracy of the results. The bootstrap method of

regression analysis is discussed in this paper with practical example. In small sample case, there is a possibility of violating the normality assumption of the error. To avoid

this problem, the bootstrap method gives us better result. A key objective in classical testing of statistical hypothesis is achieving good power of the test. To compare the

existing simulation based test approach to bootstrap approach test, we calculated the

power of the test and then graphically shown in this paper. We have conducted a hypothesis testing of regression coefficient. We observe that power of the test with

bootstrap approach is much higher than the power of simulation approach. Actually, the power of the tests is compared and the better result of bootstrap method is found.

Keywords: Linear Regression model, Regression coefficient, Hypothesis testing,

Bootstrapping

RRJoST (2014)© STM Journals 2014. All Rights Reserved

Research & Reviews: Journal of Statistics ISSN: 2278-2273 (online), ISSN: 2348-7909 (print)

Volume 3, Issue 2

www.stmjournals.com

A Generalized Product Method of Estimation in

Two Phase Sampling

Balkishan Sharma1*, Housila P. Singh

2, Rajesh Tailor

2

1Department of Community Medicine, Sri Aurobindo Medical College & P. G. Institute,

Indore, M. P., India 2School of Studies in Statistics, Vikram University, Ujjain, M. P., India

Abstract This paper proposes a generalized product type estimator for population mean using two

phase sampling in the presence of available knowledge on second auxiliary variable z,

when the population mean of the main auxiliary variable x is not known. It is shown that the proposed estimator is more efficient than the usual unbiased estimator, the double

sampling product estimator and Sahoo et al.’s estimator. An empirical study is carried out to assess the comparative performance of the proposed estimator over other

estimators.

Keywords: Study variate, Auxiliary variate, Bias, Mean squared error,

Double sampling

RRJoST (2014)© STM Journals 2014. All Rights Reserved

Research & Reviews: Journal of Statistics ISSN: 2278-2273 (online), ISSN: 2348-7909 (print)

Volume 3, Issue 2

www.stmjournals.com

Mann-Whitney Test for Imprecise Observations

V. S. Vaidyanathan* Department of Statistics, Pondicherry University, Puducherry, India

Abstract Mann-Whitney test is a non-parametric test that is used to identify whether the

probability distributions corresponding to two populations are identical. This article extends the Mann-Whitney test by treating the underlying observations as imprecise

values. The test procedure is developed by using a novel approach to rank fuzzy values based on the concepts of “Credibility Theory” proposed by Liu (2007) for studying the

behavior of fuzzy phenomena. Numerical illustration is provided through simulation by

representing the observations as triangular fuzzy numbers.

Keywords: Credibility measure, Fuzzy number, Membership function, Ranking fuzzy

values, Mann-Whitney test statistic

RRJoST (2014)© STM Journals 2014. All Rights Reserved

Research & Reviews: Journal of Statistics ISSN: 2278-2273 (online), ISSN: 2348-7909 (print)

Volume 3, Issue 2

www.stmjournals.com

Construction of Neighbour Balanced Nested Row Column

Designs and µ-Resolvable All Order Neighbour Balance

Design by using Mutually Orthogonal Latin Squares

Aatish Kumar Sahu1*, Anurup Majumder

2

1SASRD, Nagaland University, Medziphema, Nagaland-797106

2Bidhan Chandra Krishi Viswavidyalaya, Mohanpur, Nadia, W. Bengal-741252

Abstract Latin Squares are known to possess very unique features and so is its utility. Construction

of Balance Incomplete Block with nested Row Column (BIBRC) designs having Neighbor

Balanced properties have been developed on the concept of Mutually Orthogonal Latin Squares (MOLS) of strength v, v being natural number and if it has at least four MOLS

available. The designs used minimal blocks and found to be exact neighbor balanced with respect to rows, columns as well as diagonally. In the second part of this paper, concept

of MOLS is used in construction of µ-Resolvable Balance Incomplete Block Designs

following Subramani [1]. The designs fulfill the criteria of one-dimensional All Order Neighbor Balanced (AONB), developed with v number of treatments, v being natural

number, if and only if, there is availability of minimum two Mutually Orthogonal Latin

Squares for v. These designs showed all order neighbor balanced with minimal number of blocks at v(v–1)/2.

Keywords: BIB designs, BIBRC designs, Neighbor Balanced designs, µ-resolvable

designs, AONBD, OLS and MOLS