Research & reviews journal of statistics (vol3, issue2) by STM Journals Publication

Research & Reviews Journal of Statistics (RRJHS)

(RRJoST) ISSN : 2348-7909

Volume 1, Issue 1-3 Compilation 2012

May - August 2014

STM JOURNALS Scientific

Technical

Medical

www.stmjournals.com

STM Publication(s) STM Publication, a strong initiative by Consortium E-Learning Network Private ltd.(Estd. 2006) was launched in the year 2010 under the support and guidance by our esteemed Editorial and Advisory board members from renowned institutes. Objectives of STM Publication(s): ? Scientific, Technical and Medical research promotions. ? Publication of genuine Research/Review, Short Articles and Case Studies through proper review

process. ? Publishing Special Issues on Conferences. ? Preparing online platform for other print Journals. ? Empowering the libraries with online and print Journals in Scientific, Technical and Medical

domains. ? Publishing and distribution of books on various subjects which mainly falls in the category of Nanotechnology, Scientific and technical writing & Environment, Health and Safety.

Salient Features: ? A bouquet of 100+ Journals that fall under Science, Technical & Medical domains. ? Employs Open Journals System (OJS) A Journal Management & Publishing System. ? The first and one of the fastest growing publication website in India as well as in abroad for its quality and coverage. ? Rapid online submission and publication of papers, soon after their formal acceptance/ finalization. ? Facilitates linking with the other authors or professionals. ? Worldwide circulation and visibility.

Research & Reviews : Journal of Statistics ISSN: 2278-2273 (Online), ISSN: 2348-7909 (Print) Focus and Scope Covers ? Theoretical and Computational Statistics

? Regression and Variance Analysis and Agricultural Statistics ? Foundations of Statistical Inference and Statistical Decision Theory ? Biostatistics, Testing Hypothesis and Parameter Estimation ? Nonparametric methods and Sequential procedures ? Time series, Statistical problems for Stochastic processes, Design of Experiments and Statistical

Data Analysis Research & Reviews : Journal of Statistics is published (frequency: three times a year) in India by STM Journals (division of Consortium e-Learning Network Private Ltd. Pvt.) The views expressed in the articles do not necessarily reflect of the Publisher. The publisher does not endorse the quality or value of the advertised/sponsored products described therein. Please consult full prescribing information before issuing a prescription for any products mentioned in this publication. No part of this publication may be reproduced, stored in retrieval system or transmitted in any from without written permission of the publisher. To cite any of the material contained in this Journal, in English or translation, please use the full English reference at the beginning of each article. To reuse any of the material, please contact STM Journals (info@stmjournals.com)

STM Journals (division of Consortium e-Learning Network Private Ltd. ) having its Marketing office located at Office No. 4, First Floor, CSC pocket E Market, Mayur Vihar Phase II, New Delhi-110091, India is the Publisher of Journal. Statements and opinions expressed in the Journal reflect the views of the author(s) and are not the opinion of STM Journals unless so stated. Subscription Information and Order: Cost of Journal: ? National Subscription: Rs. 3750/- per Journal (includes 3 print issues), Single Issue copy purchase Rs.1500/copy ? International Subscription: ? Online Only- $99, Print Only-$149 (includes 3 print issues) ? Online + Print-$199 (includes 3 print issues + online access of published back volumes )

To purchase print compilation of back issues please send your query at info@stmjournals.com Subscription must be prepaid. Rates outside the India includes speed delivery charges. Prices subject to change without notice. Mode of Payment: At par cheque, Demand draft, and RTGS (payment to be made in favor of Consortium E-Learning Network. Pvt. ltd., payable at Delhi/New Delhi. Online Access Policy A). For Authors: In order to provide maximum citation and wide publicity to the authors work, STM Journals also have Open Access Policy, authors who would like to get their work open access can opt for Optional Open Access publication at nominal cost as follows India, SARC and African Countries: INR 2500 or 100 USD including single hard copy of Author's Journal. Other Countries: USD 200 including single hard copy of Author's Journal. B). For Subscribers: ? Online access will be activated within 72 hours of receipt of the payment (working days), subject to receipt of

correct information on user details/Static IP address of the subscriber. ? The access will be blocked: ? If the user requests for the same and furnishes valid reasons for blocking. ? Due to technical issue. ? Misuse of the access rights as per the access policy.

Advertising and Commercial Reprint Inquiries: STM Journals with wide circulation and visibility offer an excellent media for showcasing/promotion of your products/services and the events-namely, Conferences, Symposia/Seminars etc. These journals have very high potential to deliver the message across the targeted audience regularly with each published issue. The advertisements on bulk subscriptions, gift subscriptions or reprint purchases for distribution etc. are also very welcome. Lost Issue Claims: Please note the following when applying for lost or missing issues: ? Claims for print copies lost will be honored only after 45 days of the dispatch date and before publication of the

next issue as per the frequency. ? Tracking id for the speed post will be provided to all our subscribers and the claims for the missing Journals will

be entertained only with the proofs which will be verified at both the ends. ? Claims filed due to insufficient (or no notice) of change of address will not be honored. ? Change of Address of Dispatch should be intimated to STM Journals at least 2 months prior to the dispatch

schedule as per the frequency by mentioning subscriber id and the subscription id. ? Refund requests will not be entertained.

Legal Disputes All the legal disputes are subjected to Delhi Jurisdiction only. If you have any questions, please contact the Publication Management Team: info@stmjournals.com; Tel : +91 0120-4781211.

Publication Management Team Chairman Mr. Puneet Mehrotra Managing Director STM Journals, Consortium eLearning Network Pvt. Ltd.(CELNET) Noida, India.

Group Managing Editor Dr. Archana Mehrotra Director CELNET, Delhi, India

Internal Members Puneet Pandeya Manager Associate Editors Gargi Asha Jha Nupur Anand

Monika Malhotra Assistant Manager Assistant Editors Priyanka Aswal Aditya Sanyal Anupama Garg Sona Chahal Himani Pandey

External Members

Dr. Bimlesh Lochab Industrial Tribology Machine Dynamics & Maintenance Engineering Centre (ITMMEC) Indian Institute of Technology Delhi, India

Dr. Rajiv Prakash School of Materials Science and Technology, Institute of Technology, Banaras Hindu University, Varanasi, India

Prof. S. Ramaprabhu Alternative Energy Technology Laboratory, Department of Physics, Indian Institute of Technology, Chennai, India

Dr. Rakesh Kumar Assistant Professor, Department of Applied Chemistry, BIT Mesra, Patna, India

STM Journal (s) Advisory Board

Dr. Baldev Raj Chairman, National Institute of Technology Puducherry, India. Former Director, Indira Gandhi Centre for Atomic Research, India.

Prof. Bankim Chandra Ray Professor and Head, Department of Metallurgical and Materials Engineering National Institute of Technology, Rourkela, India.

Dr. Hardev Singh Virk Professor Emeritus, Eternal University, Baru Sahib, India.

Dr. Baskar Kaliyamoorthy Associate Professor, Department of Civil Engineering National Institute of Technology Trichy, India.

Prof. D. N. Rao Professor, Department of Biochemistry, AIIMS, New Delhi, India.

Prof. Jugal Kishore Professor, Department of Community Medicine, Maulana Azad Medical College, New Delhi, India.

Dr. Ashish Runthala

Dr. Pankaj Poddar

Lecturer, Biological Sciences Group, Birla Institute of Technology & Science, Pilani Rajasthan, India.

Scientist, Physical & Materials Chemistry Division, National Chemical Laboratory, Pune, India.

Dr. Nandini Chatterjee Singh Associate Professor, National Brain Research Centre, Manesar, India.

STM Journal (s) Advisory Board

Dr. Priyavrat Thareja

Dr. Rakesh Kumar

Head, Materials and Metallurgical Engineering Department, PEC University of Technology, Chandigarh, India.

Assistant Professor, Department of Applied Chemistry, BIT Mesra, Patna, India.

Dr. Shankargouda Patil

Dr. Shrikant Balkisan Dhoot

Asst. Prof., Department of Oral Pathology, KLE Society's Institute of Dental Sciences, Bangalore, India.

Head Research & Development, Nurture Earth R&D Pvt Ltd MIT Campus, Beed bypass road, Aurangabad, India.

Prof. Subash Chandra Mishra

Prof. Sundara Ramaprabhu

Professor, Metallurgical & Materials Engineering Department, NIT, Rourkela, India.

Professor, Department of Physics Indian Institute of Technology Madras, India.

Prof. Yuwaraj Marotrao Ghugal Professor and Head Department, Govt. College of Engineering Station Road, Osmanpura, Aurangabad, India.

Editorial Board

Dr. Manjunatha Prasad Karantha Department of Statistics, Health Science Library Building, Manipal University, India.

R. Vijayaraghavan Department of Statistics, Bharathiar University, Coimbatore 641 046,Tamil Nadu, India.

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

Professor Somanath Bagh Professor of Statistics, School Of Mathematical Sciences, Sambalpur University, Jyotivihar-768019,Orissa, India.

Vijay Kumar Singh Department of Statistics, Banaras Hindu University, Varanasi â&#x20AC;&#x201C; 221005, India.

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

Prof. Harinder Singh Professor & Head Department of Mathematics, Jaypee University of Information Technology, Waknaghat , India.

Arijit Chaudhari Honorary Visiting Professor, Applied Statistics Unit, Indian Statistical Institute, India.

Rajyaguru Arti Department of Statistics Veer Narmad South Gujarat University, Udhna Magdalla Road.

Dr. Balkishan Sharma Associate Professor (Biostatistics), Department of Community Medicine, Sri Aurobindo Medical College and P. G. Institute, Indore (M. P.), India.

Director's Desk

STM JOURNALS

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 writeups/ 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

Research & Reviews : Journal of Statistics

Contents

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

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

3. Mann-Whitney Test for Imprecise Observations V. S. Vaidyanathan

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

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

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. Singh2, Rajesh Tailor2 1

Department of Community Medicine, Sri Aurobindo Medical College & P. G. Institute, Indore, M. P., India 2 School 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.â&#x20AC;&#x2122;s estimator. An empirical study is carried out to assess the comparative performance of the proposed estimator over other estimators.

Keywords: Study Double sampling

variate,

Auxiliary

variate,

Bias,

Mean

squared

error,

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

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 Majumder2 1

SASRD, Nagaland University, Medziphema, Nagaland-797106 Bidhan 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