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 revisit the problem of clustering 1318 new variable stars found in the Milky way. Our recent work distinguishes these stars based on their light curves which are univariate series of brightness from the stars observed at discrete time points. This work proposes a new approach to look at these discrete series as continuous curves over time by transforming them into functional data. Then, functional principal component analysis is performed using these functional light curves. Clustering based on the significant functional principal components reveals two distinct groups of eclipsing binaries with consistency and superiority compared to our previous results. This method is established as a new powerful light curve-based classifier, where implementation of a simple clustering algorithm is effective enough to uncover the true clusters based merely on the first few relevant functional principal components. Simultaneously we discard the noise from the data study involving the higher order functional principal components. Thus the suggested method is very useful for clustering big light curve data sets which is also verified by our simulation study. © 2022, The Author(s), under exclusive licence to Springer Nature B.V.

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Astrophysics and Space Science

Clustering of eclipsing binary light curves through functional principal component analysis

Compromising ethics and precision in the context of a multiarmed clinical trial, an optimal order adjusted response adaptive design is proposed for survival outcomes subject to independent random censoring. The operating characteristics of the proposed design and the follow-up inference are studied both theoretically as well as empirically and are compared with those of the competitors. Applicability of the developed design is further illustrated through redesigning a real clinical trial with survival responses. © 2021 Wiley-VCH GmbH.

Biometrical Journal

An optimal multiarmed response adaptive design for survival outcome with independent censoring

Mixture models were first introduced in canonical form of different degrees to represent the response function in a mixture experiment, and designs for the same were suggested. Later, several researchers derived optimum designs for the estimation of parameters and subset of parameters of the models. In this article, a study is carried out to find the D- and A-optimum designs for estimating the parameters of the quadratic mixture model, when the components of the mixture can be divided into two groups such that within a group there is synergism among the components, while the components between groups do not exhibit any synergism. © 2019 Taylor & Francis Group, LLC.

Communications in Statistics - Theory and Methods

Optimum designs for parameter estimation in mixture experiments with group synergism

Explicit expression of the Stress - Strength reliability function, (Formula presented.) is derived, when the stress (X) and strength (Y) distributions are different members of the Power series family of distributions. Minimum Variance Unbiased (MVU) estimator of R, variance of the MVU estimator together with its MVU estimator are derived for Power series family of distributions. Maximum Likelihood (ML) estimator of R along with related large sample results are also derived. Analytic expressions of the above mentioned quantities are provided for different members of the Power series family of distributions. Further, an application, in the context of real Soccer games, is enumerated. © 2019 Taylor & Francis Group, LLC.

On estimating reliability function for the family of power series distribution

The paper studies a mixture experiment with two responses–a primary response and a secondary response. The primary response function is assumed to be quadratic in the mixing proportions, while the secondary response is a linear function of the proportions. Optimum designs are investigated for estimating the optimum mixture combination that maximizes the mean primary response subject to the mean secondary response being above a certain specified value. © 2021 Taylor & Francis Group, LLC.

Communications in Statistics: Simulation and Computation

D-optimal design for estimation of optimum mixture in a three-component mixture experiment with two responses

Background: In this study we cluster the districts of India in terms of the spread of COVID-19 and related variables such as population density and the number of specialty hospitals. Simulation using a compartment model is used to provide insight into differences in response to public health interventions. Two case studies of interest from Nizamuddin and Dharavi provide contrasting pictures of the success in curbing spread. Methods: A cluster analysis of the worst affected districts in India provides insight about the similarities between them. The effects of public health interventions in flattening the curve in their respective states is studied using the individual contact SEIQHRF model, a stochastic individual compartment model which simulates disease prevalence in the susceptible, infected, recovered and fatal compartments. Results: The clustering of hotspot districts provide homogeneous groups that can be discriminated in terms of number of cases and related covariates. The cluster analysis reveal that the distribution of number of COVID-19 hospitals in the districts does not correlate with the distribution of confirmed COVID-19 cases. From the SEIQHRF model for Nizamuddin we observe in the second phase the number of infected individuals had seen a multitudinous increase in the states where Nizamuddin attendees returned, increasing the risk of the disease spread. However, the simulations reveal that implementing administrative interventions, flatten the curve. In Dharavi, through tracing, tracking, testing and treating, massive breakout of COVID-19 was brought under control. Conclusions: The cluster analysis performed on the districts reveal homogeneous groups of districts that can be ranked based on the burden placed on the healthcare system in terms of number of confirmed cases, population density and number of hospitals dedicated to COVID-19 treatment. The study rounds up with two important case studies on Nizamuddin basti and Dharavi to illustrate the growth curve of COVID-19 in two very densely populated regions in India. In the case of Nizamuddin, the study showed that there was a manifold increase in the risk of infection. In contrast it is seen that there was a rapid decline in the number of cases in Dharavi within a span of about one month. © 2021, The Author(s).

BMC Public Health

An analysis of COVID-19 clusters in India: Two case studies on Nizamuddin and Dharavi

The present work explores the origin of the formation of star clusters in our Galaxy and in the Small Magellanic Cloud (SMC) through simulated H-R diagrams and compare those with observed star clusters. The simulation study produces synthetic H-R diagrams through the Markov Chain Monte Carlo (MCMC) technique using the star formation history (SFH), luminosity function (LF), abundance of heavy metal (Z), and a big library of isochrones as basic inputs and compares them with observed H-R diagrams of various star clusters. The distance-based comparison between those two diagrams is carried out through two-dimensional matching of points in the color-magnitude diagram (CMD) after the optimal choice of bin size and appropriate distance function. It is found that in a poor medium of heavy elements (Z = 0.0004), the Gaia LF along with a mixture of multiple Gaussian distributions of the SFH may be the origin of formation of globular clusters (GCs). On the contrary, an enriched medium (Z = 0.019) is generally favored with the Gaia LF along with a double power law or Beta-type (i.e., unimodal) SFH, for the formation of globular clusters. For SMC clusters, the choice of an exponential LF and exponential SFH is the proper combination for a poor medium, whereas the Gaia LF with a Beta-type SFH is preferred for the formation of star clusters in an enriched medium. © 2021. The American Astronomical Society. All rights reserved.

Applied Mathematics

Astrophysical Journal

Exploration of the Origin of Galactic and Extragalactic Star Clusters through Simulated H-R Diagrams

Asymptotic tests for identical distribution of responses in two independent sets of Likert-type scale data using latent variable models are developed. The proposed tests are compared with regard to asymptotic relative efficiency with the commonly used two-sample t-test and Mann–Whitney U test. Robustness and unbiasedness of the tests are also established. © 2021 Taylor & Francis Group, LLC.

Large-sample tests for comparing Likert-type scale data

Journal of Applied Statistics

Bias-corrected estimators for proportion of true null hypotheses: application of adaptive FDR-controlling in segmented failure data

In clinical trials, fixed randomizations in a prefixed proportion (e.g. 1:1 or 2:1 for two treatment trials) may be adopted to allocate the entering patients among the competing treatments. However, such an allocation procedure ignores the knowledge obtained from the accrued information on the performance of the treatments until that point. However, while allocating, a fixed randomization may favor the most and the least effective treatments in a prefixed manner, and hence becomes instrumental to induce a conflict with the “individual ethics” requirement. Adaptive allocation designs are considered instead, for their ability to dynamically settle the issue of running randomization towards the treatment doing better–all using the available data but with a scope to compromise in statistical precision. Although most of the developments are pertinent to binary, continuous and survival responses, ordinal categorical responses are natural outcomes in many disciplines of clinical trials like Orthopedics and Ophthalmology. Therefore, to balance between ethics and precision in the context of a multi-treatment clinical trial producing ordinal categorical responses, an optimal response adaptive design is derived by minimizing a measure of “precision” subject to constrained number of “failures” ensuring higher number of assignments to the “best” treatment. Related design and inference-based characteristics are extensively studied–both theoretically and empirically. Further, the practical applicability of the developed design is envisaged through re-designing of a real clinical trial, where the responses are immediate and are measured in ordinal categorical scale. © 2021 Taylor & Francis Group, LLC.