Statistics

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

In this paper, we investigate a mixture problem with two responses, which are functions of the mixing proportions, and are correlated with known dispersion matrix. We obtain D- and A-optimal designs for estimating the parameters of the response functions, when none or some of the regression coefficients of the two functions are the same. It is shown that when no prior knowledge about the regression coefficients is available, the D-optimal design is independent of the dispersion matrix, while the A-optimal design depends on it, provided the response functions are of different degree. On the other hand, when some of the regression coefficients are known to be the same for both the functions, the D-optimal design depends on the dispersion matrix when the two response functions are not of the same degree. © 2017 Taylor & Francis Group, LLC.

GENERAL

Communications in Statistics: Simulation and Computation

Optimum designs for parameter estimation in a mixture experiment with two correlated responses

Area of study is the formation mechanism of the present-day population of elliptical galaxies, in the context of hierarchical cosmological models accompanied by accretion and minor mergers. The present work investigates the formation and evolution of several components of the nearby massive early-type galaxies (ETGs) through cross-correlation function (CCF), using the spatial parameters right ascension (RA) and declination (DEC), and the intrinsic parameters mass (M∗) and size. According to the astrophysical terminology, here these variables, namely mass, size, RA and DEC are termed as parameters, whereas the unknown constants involved in the kernel function are called hyperparameters. Throughout this paper, the parameter size is used to represent the effective radius (Re). Following Huang et&nbsp;al. (2013a), each nearby ETG is divided into three parts on the basis of its Re value. We study the CCF between each of these three components of nearby massive ETGs and the ETGs in the high redshift range, 0.5 &lt; z≤ 2.7. It is found that the innermost components of nearby ETGs are highly correlated with ETGs in the redshift range, 2 &lt; z≤ 2.7 , known as ‘red nuggets’. The intermediate and the outermost parts have moderate correlations with ETGs in the redshift range, 0.5 &lt; z≤ 0.75. The quantitative measures are highly consistent with the two phase formation scenario of nearby massive ETGs, as suggested by various authors, and resolve the conflict raised in a previous work (De et&nbsp;al. 2014) suggesting other possibilities for the formation of the outermost part. A&nbsp;probable cause of this improvement is the inclusion of the spatial effects in addition to the other parameters in the study. © 2017, Springer Science+Business Media B.V.

Applied Mathematics

Fulltext

Astrophysics and Space Science

Two phase formation of massive elliptical galaxies: study through cross-correlation including spatial effect

The present article discusses the use of properly designed experiments to improve reliability. It also points out the importance of specifying the manner in which the results of an experiment should be recorded when the aim is to improve the reliability of a product. A numerical example is cited to illustrate the use of an appropriate design in achieving desired reliability. © ISOSS Publications 2017.

Physiology

Journal of Applied Probability and Statistics

Reliability improvement through designed experiments

World University root node

arXiv preprint arXiv:1611.

{Two phase formation of massive elliptical galaxies: study through cross-correlation including spatial effect Soumita Modak1, Tanuka Chattopadhyay2, Asis Kumar Chattopadhyay3 {\ldots}}

A class of optimal covariate-adjusted response adaptive procedures is developed for phase III clinical trials when the treatment response is a survival time and there is random censoring. The basic aim is to develop an allocation design by combining the ethical aspects with statistical precision in a reasonable way under the presence of covariate information. Considering minimisation of total hazards as the ethical requirement, the proposed procedure is assessed in terms of the assignment to the better treatment and the efficiency (i.e. power) to detect a small departure in treatment effectiveness. The applicability of the proposed methodology is also illustrated using a real data set. © SAGE Publications.

Statistical Methods in Medical Research

On a class of optimal covariate-adjusted response adaptive designs for survival outcomes

International Journal of Statistics in Medical Research

Study on Temporal Effects of Urban Malaria Incidences

A variety of response-adaptive randomization procedures have been proposed in literature assuming binary outcomes. However, the list is not so long for continuous outcomes though many real clinical trials deal with continuous treatment responses. In this paper, we attempt to explore the available procedures together with a comparison of their performances. Some real-life adaptive trial is also reviewed. © SAGE Publications 2012.

Response-adaptive designs for continuous treatment responses in phase III clinical trials: A review

A stochastic model has been developed to study the hierarchical fragmentation process of young massive clusters in external galaxies considering close binary components along with individual ones. Stellar masses for individual ones have been generated from truncated Pareto distribution and stellar masses for close binary components have been generated from a truncated Bi-variate Gumbel Exponential distribution. The above distribution is identified by fitting the observed bi-variate distribution of masses of eclipsing binary stars computed from the light curves catalogued in the package Binary Maker 3.0. The resulting mass spectra computed at different projected distances, show signature of mass segregation. Degree of mass segregation becomes reduced due to the inclusion of binary fraction. This might be due to the reduction of massive stars and inclusion of less massive stars rather than inclusion of single massive stars and the effect of line of sight length projected to an observer. © 2016, Springer Science+Business Media Dordrecht.

Influence of binary fraction on the fragmentation of young massive clustersâ€”a Monte Carlo simulation

Response-adaptive designs are important in clinical trials for their ability to skew the allocation towards the better performing treatment. Most of the designs are derived under specific assumptions (e.g., normality, existence of first few moments, etc.) on the response model. However, responses may be nonnormal and consequently the existence of moments is not guaranteed. Moreover, in most of the cases, a treatment yielding a higher expected response is regarded as better, ignoring the possible effect of variability. In this article, we consider location and variability aspects simultaneously and redefine the criterion of the best treatment and develop a reasonable covariate adjusted allocation procedure for two treatment trials. A detailed study is also conducted to explore the performance. © 2016 Grace Scientific Publishing, LLC.