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

INTERNATIONAL STATISTICAL REVIEW

Introduction to Probability

For any product with lifetime X, the probability of surviving of the product beyond the mission time t is defined as the mission time reliability function R(t) = P(X ≥ t). If the lifetime is expressed as the number of cycles of operation, then X will be a discrete random variable. In this article, the reliability function R(t), for two-parameter geometric distribution has been obtained. Maximum Likelihood Estimator (MLE) and an Unbiased Estimator (UE) of the reliability function have been derived. MLEandUEofthereliability function of k-out-of-m system have also been derived. In the stress-strength setup,R =P(X ≤ Y) originated in the context of the reliability of a component of strength Y subjected to a stress X. If a component fails at any time, then the applied stress for the component is greater than its strength (i.e. X &gt; Y) and there is no failure, when X ≤ Y. Thus, R is a measure of the reliability of the component. We estimated MLE and UE of R, when X and Y are assumed to follow twoparameter geometric distribution independently based on complete as well as censored samples. Finally, the performance of estimators was compared through simulation study.

World University root node

International Journal of Agricultural and Statistical Sciences

Inference on reliability for two-parameter geometric distribution

The kinematics of dwarf galaxies are strongly influenced by dark matter down to small galactocentric radii. So they are good candidates to investigate the nature of Dark Matter. In the present work we have carried out mass modeling of a number of recently observed dwarf galaxies Swaters et&nbsp;al. in Astron. Astrophys. 493:871, 2009. We have used a Navarro-Frenk-White (NFW) halo, Freeman disc along with a gaseous disc for modeling the observed rotation curves of those dwarf galaxies. For comparison we also used a Burkert halo, Freeman disc and gaseous disc. For both the scenario we have performed Kolmogorov–Smirnov (KS) test between the observed and predicted rotational velocity profiles. The tests are rejected for NFW halo almost in 50 per cent cases but they are accepted almost for all cases for Burkert halo, preferring a Burkert halo model generally for dwarf galaxies. The above results reveal a constant density core of dark matter (DM) in the halos of dwarf galaxies compared to a cuspy nature of NFW halo and a possible challenge to Λ$\Lambda$-CDM scenario for the nature of dark matter in most of the dwarf galaxies. © 2015, Springer Science+Business Media Dordrecht.

GENERAL

Applied Mathematics

Astrophysics and Space Science

Study of the nature of dark matter in halos of dwarf galaxies

People chronically exposed to environmental arsenic through their drinking water experience various arsenic induced clinical manifestations and there is modulation of methylation level in their genome. However the response varies widely among persons. The present manuscript deals with the evaluation of role of individual’s GST status in altering the degree of DNA methylation after chronic arsenic exposure in human. To study whether Glutathione-S-Transferase (GST) gene polymorphism plays any role in this variation, a total of 92 study subjects were recruited from the villages of southern region of West Bengal, India. Concentration of arsenic in their urine and water, extent of clinical manifestation, GST status and p53 and p16 gene promoter methylation status were determined. Results showed that genetic polymorphism of GSTM1 and T1 were significantly associated (p<0.05) with degree of methylation in p53 and p16 gene promoter region and urinary arsenic in higher exposure group. Persons having null genotype have significantly decreased urinary arsenic and increased DNA methylation level relative to persons with GSTM1 or GSTT1 nonnull genotype of same arsenic exposure group. In the present work we are therefore trying to show that individual’s GST polymorphic status may alter the degree of DNA methylation after arsenic exposure. © 2015 Informatics Publishing Limited and The Society of Toxicology. All rights reserved.

Toxicology International

Role of glutathione-s-transferase polymorphism on arsenic induced DNA hypermethylation

In the context of clinical trials for comparing two treatments, a new class of covariate adjusted response adaptive procedures is developed to achieve a balance between clinical optimality and inferential precision. Assuming normally distributed responses, several exact and asymptotic properties are studied and compared with a reasonable alternative under the presence of treatment covariate interaction. © 2015, Austrian Statistical Society. All rights reserved.

Fulltext

Austrian Journal of Statistics

On a class of optimal type covariate adjusted response adaptive allocations for normal treatment responses

The paper studies a periodic review inventory model with no shortages and different demand rates during pre- and post- deterioration periods. Deterioration of units start after a fixed time interval, and the deterioration rate is time dependent. The model determines the optimal reorder interval and the optimal order quantity so as to minimize the total cost per unit length of an inventory cycle. An extension of the model to include price discount has been further considered. Numerical examples are presented to illustrate the model and a sensitivity analysis is also reported.

Pakistan Journal of Statistics and Operation Research

Periodic review inventory policy for non-instantaneous deteriorating items with time dependent deterioration rate

Theoretical and indirect observational evidence suggests that the stellar initial mass function (IMF) increases with redshift. On the other hand, star formation rates (SFRs) may be as high as 100 M yr-1 in starburst galaxies. These may lead to the formation of massive clusters, hence massive stars, making the integrated galactic stellar initial mass function (IGIMF) top-heavy (i.e., the proportion of massive stars is higher than that of less massive stars). We investigate the joint effect of evolving the IMF and several measures of SFRs in dependence on the galaxywide IMF. The resulting IGIMFs have slopes α2,IGIMF in the high-mass regime, which is highly dependent on the minimum mass of the embedded cluster (Mecl,min), SFR, and mass-spectrum indices of embedded clusters (β). It is found that for z∼0-2, α2,IGIMF becomes steeper (i.e., bottom-heavy), for z∼2-4, α2,IGIMF becomes flatter (i.e., top-heavy ), and from z∼ 4 onward, α2,IGIMF again becomes steeper. The effects are faster for higher values of β. a2,IGIMF is also for higher values of Mecl,min. All of these effects may be attributable to the joint effect of increasing the temperature of the ambient medium as well as varying the SFR with increasing redshift.

Astrophysical Journal

COSMIC HISTORY of the INTEGRATED GALACTIC STELLAR INITIAL MASS FUNCTION: A SIMULATION STUDY

AstroStat is an easy-to-use tool for performing statistical analysis on data. It has been designed to be compatible with Virtual Observatory (VO) standards thus enabling it to become an integral part of the currently available collection of VO tools. A user can load data in a variety of formats into AstroStat and perform various statistical tests using a menu driven interface. Behind the scenes, all analyses are done using the public domain statistical software-R and the output returned is presented in a neatly formatted form to the user. The analyses performable include exploratory tests, visualizations, distribution fitting, correlation & causation, hypothesis testing, multivariate analysis and clustering. The tool is available in two versions with identical interface and features-as a web service that can be run using any standard browser and as an offline application. AstroStat will provide an easy-to-use interface which can allow for both fetching data and performing power statistical analysis on them. © 2015 Elsevier B.V.

Astronomy and Computing

AstroStat-A VO tool for statistical analysis

Indian Institute of Management Ahmedabad

A note on estimationg variance of finite population distribution function

In this chapter, we focus on finding optimum mixture designs for the estimation of natural parameters of models other than that of Scheffé viz., Becker’s models, Darroch–Waller [D–W] model and Log-contrast model. It is also equally fascinating to note that so much has been done in these other mixture models as well. We mainly review the results that are already available and some new findings are presented. © 2014, Springer India.