Special Proceedings 22nd Annual Conference of SSCA held at Savitribai Phule Pune University, Pune Maharashtra 02-04 January 2020 UTILITY IN 74207281 2 -1 IS PRIME APPLICATIONS FOUNDED 1998 Society of Statistics, Computer and Applications https://ssca.org.in/ 2020 Society of Statistics, Computer and Applications Council and Office Bearers Founder President Late M.N. Das President Executive President V.K. Gupta Rajender Parsad Patrons A.C. Kulshreshtha A.K. Nigam Bikas Kumar Sinha D.K. Ghosh K.J.S. Satyasai P.P. Yadav Pankaj Mittal R.B. Barman R.C. Agrawal Rajpal Singh Vice Presidents A. Dhandapani Lal Mohan Bhar P. Venkatesan S.D. Sharma V.K. Bhatia Secretary Foreign Secretary D. Roy Choudhury Sudhir Gupta Treasurer Ashish Das Joint Secretaries Aloke Lahiri Hukum Chandra Shibani Roy Choudhury Council Members Alka Arora Anil Kumar Yadav Anshu Bhardwaj Manish Sharma Manish Trivedi Manisha Pal P. Rath Piyush Kant Rai Praggya Das R. Vishnu Vardhan Ranjit Kumar Paul Rao Saheb Latpate S.A. Mir Sanjeev Panwar V. Srinivasa Rao Ex-Officio Members (By Designation) Director General, Central Statistics Office, Government of India, New Delhi Director, ICAR-Indian Agricultural Statistics Research Institute, New Delhi Chair Editor, Statistics and Applications Executive Editor, Statistics and Applications Citation: Special Proceedings of 22nd Annual Conference of SSCA (2020). Society of Statistics, Computer and Applications, New Delhi. Special Proceedings 22nd Annual Conference of SSCA held at Savitribai Phule Pune University, Pune Maharashtra 02-04 January 2020 Editors V.K. Gupta Baidya Nath Mandal Rajender Parsad Hukum Chandra Ranjit Kumar Paul K.J.S. Satyasai D. Roy Choudhury Society of Statistics, Computer and Applications https://ssca.org.in/ 2020 CONTENTS Special Proceedings of 22nd Annual Conference of SSCA 2020 held at Savitribai Phule Pune University, PUNE during 02-04 January 2020 Preface 1. Correlated Inverse Gaussian Frailty Model 1-10 David D. Hanagal 2. Review of Temporal Point Process Models for Modeling Earthquake 11-24 Aftershocks Rupal Shah and K. Muralidharan 3. District-level Estimates of Extent of Food Insecurity for the State of Uttar 25-38 Pradesh in India by Combining Survey and Census Data Hukum Chandra 4. Linear Model Perspectives of fMRI Studies 39-51 Bikas Kumar Sinha 5. Statistical Inference for a One Unit System With Dependent Structure 53-58 V.S. Vaidyanathan 6. A Straight Forward Approach in Understanding the Improperness of ROC 59-71 Curve R. Vishnu Vardhan, S. Balaswamy and G. Sameera 7. Index Tracking for NIFTY50 73-84 Divyashish Choudhary and Rituparna Sen 8. Statistical Modelling and Calibration of a Dynamic Computer Simulator 85-101 Pritam Ranjan 9. Optimal Decisions Under Partial Refunds: A Reward-Earning Random Walk 103-116 on a Parity Dial Jyotirmoy Sarkar 10. NAFINDEX: Measure of Financial Inclusion based on NABARD All India 117-131 Rural Financial Inclusion Survey (NAFIS) Data K.J.S. Satyasai and Ashutosh Kumar 11. Large Scale Assessment Survey to Evaluate Learning Level of Students 133-144 Vishal D. Pajankar 12. Selection of Designs for Model Misspecification in Generalized Linear 145-152 Models: A Review Siuli Mukhopadhyay and Ishapathik Das 13. On Weighted Distributions and Applications 153-162 Saumyadipta Pyne 14. Digital Transactions Through Debit Cards – Costs and Prices for the Payment 163-174 Services Ashish Das 15. Role and Importance of Statistics in Business Management 175-180 Rashmy Moray 16. High Frequency Financial Data and Associated Financial Point Process: A 181-192 Nonparametric Bayesian Perspective Anuj Mishra and T. V. Ramanathan Preface The Society of Statistics, Computer and Applications (SSCA) was founded in 1998 with a goal to provide a platform for promotion and dissemination of research in Statistics, blended with information technology, among both theoretical and applied statisticians, who have keen interest in the applications of Statistics to varied fields like agriculture, biological sciences, medical sciences, financial statistics, and industrial statistics. Since then, the Society has been performing several activities and promoting development of theoretical and applied research work in Statistics and Informatics. One of the major activities of SSCA is to organise national/international conferences annually across the length and breadth of the country. SSCA also brings out a journal called Statistics and Applications. This is an open access journal and is available at the website of the Society (www.ssca.org.in). The full-length papers can be viewed and downloaded free of cost. Besides bringing out regular volumes of the journal, special volumes on emerging thematic areas of global/national importance are also brought out. The twenty-second Annual Conference of the SSCA was organised during 02-04 January 2020 at the Department of Statistics, Savitribai Phule Pune University, Pune, Maharashtra. The theme of the conference was Importance of Statistics in Emerging Global Scenario (ISEGS 2020). The conference was academically enriching with important and significant presentations made by scientists of international repute and eminence. Among the many technical sessions organised, were Professor C.R. Rao Birth Centenary Lecture Session, participated by renowned international and national statisticians and a session on Financial Statistics, in which renowned statisticians and leading practitioners from National Bank for Agriculture and Rural Development, Symbiosis Institute of Management Studies, Pune, Savitri Phule Pune University and Reserve Bank of India made presentations. The Executive Council of the SSCA decided to bring out “Special Proceedings” of the conference covering some important selected talks including those presented in the Financial Statistics session. The selection of authors was made based upon the contents as presented during the conference. The Executive Council of the Society nominated V.K. Gupta, Baidya Nath Mandal, Rajender Parsad, Hukum Chandra, Ranjit Kumar Paul, K.J.S. Satyasai and Dipak Roy Choudhury as Guest Editors for bringing out these special proceedings. The Guest Editors finalised the names of authors to be invited to submit their full paper, based upon their presentation during the conference, for the Special Proceedings. Distinguished speakers shortlisted for making contributions to the special proceedings were invited to submit their research papers for possible inclusion in the special proceedings. After the usual review process, 16 research papers were accepted for publication and are included in the special proceedings. We would like to express our sincere thanks to all the authors for responding to our request and submitting their research for publication in these special proceedings in time. The reviewers have also made a very big contribution by way of finishing the review process in a short span of time and it is a pleasure to thank each one of them individually. We would like to place on record our gratitude to all members and office bearers of the Executive Council of SSCA for their support. We would also like to express our sincerest thanks to Prof. T.V. Ramanathan, Dr. V.K. Gedam, and Dr. R.V. Latpate for organising the Conference. Guest Editors V.K. Gupta Baidya Nath Mandal Rajender Parsad Hukum Chandra Ranjit Kumar Paul K.J.S. Satyasai Dipak Roy Choudhury New Delhi September 2020 Special Proceedings of the 22nd Annual Conference of SSCA held at Savitribai Phule Pune University, Pune, during January 02-04, 2020; pp 1-10 Correlated Inverse Gaussian Frailty Model David D. Hanagal Symbiosis Statistical Institute, Symbiosis International University, Pune-411016, India and Department of Statistics, Savitribai Phule Pune University, Pune-411007, India. Received: 31 January 2020; Revised: 07 February 2020; Accepted: 09 February 2020 Abstract Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times, the shared frailty models were suggested. Shared frailty models are used despite their limitations. To overcome their disadvantages correlated frailty models may be used. In this paper, we introduce the inverse Gaussian correlated frailty models. Key words: Vivariate survival; Copula; Correlated inverse Gaussian frailty; Cross-ration function; Hazard rate. 1. Introduction The frailty model is a random effect model for time to event data which is an extension of the Cox’s proportional hazards model. Shared frailty models are the most commonly used frailty models in literature, where individuals in the same cluster share a common frailty. Frailty models (Vaupel et al. 1979) are used in the survival analysis to account for the unobserved heterogeneity in the individual risks to disease and death. The frailty model is usually modeled as an unobserved random variable acting multiplicatively on the baseline hazard function. Hanagal and Dabade (2013), Hanagal and Bhambure (2015, 2016) and Hanagal and Pandey (2014a, 2014b, 2015a, 2015b, 2016, 2017a) analyzed kidney infection data and Australian twin data using shared gamma and inverse Gaussian frailty models with different baseline distributions for the multiplicative model. Hanagal and Sharma (2013, 2015a, 2015b, 2015c) analyzed acute leukemia data, kidney infection data and diabetic retinopathy data using shared gamma and inverse Gaussian frailty models for the multiplicative model. Hanagal and Bhambure (2014) developed shared inverse Gaussian frailty