We consider the Branching Random Walk on $d$-ary tree of height $n$ under the presence of a hard ... more We consider the Branching Random Walk on $d$-ary tree of height $n$ under the presence of a hard wall which restricts each value to be positive. The question of behavior of Gaussian process with long range interactions under the presence of a hard wall has been addressed, and a relation with the expected maxima of the processes has been established. We find the probability of event corresponding to the hard wall and show that the conditional expectation of the gaussian variable at a typical vertex, under positivity, is at least less than the expected maxima by order of $\log n$.
The celebrated lack of memory property is a unique property of the exponential distribution in th... more The celebrated lack of memory property is a unique property of the exponential distribution in the continuous domain. It is expressed in terms of equality of residual survival function with the survival function of the original distribution. We propose to extend this lack of memory property in terms of probability density function and examine therefrom its characterization and stability properties. In this process the density version of the lack of memory property can be interlinked with reciprocal coordinate subtangent of the density curve and a few other derived measures.
We consider a sequence of variables having multinomial distribution with the number of trials cor... more We consider a sequence of variables having multinomial distribution with the number of trials corresponding to these variables being large and possibly different. The multinomial probabilities of the categories are assumed to vary randomly depending on batches. The proposed framework is interesting from the perspective of various applications in practice such as predicting the winner of an election, forecasting the market share of different brands etc. In this work, first we derive sufficient conditions of asymptotic normality of the estimates of the multinomial cell probabilities, and corresponding suitable transformations. Then, we consider a Bayesian setting to implement our model. We consider hierarchical priors using multivariate normal and inverse Wishart distributions, and establish the posterior consistency. Based on this result and following appropriate Gibbs sampling algorithms, we can infer about aggregate data. The methodology is illustrated in detail with two real life ...
We will study the extreme values for log-correlated discrete Gaussian fields on boxes of any fixe... more We will study the extreme values for log-correlated discrete Gaussian fields on boxes of any fixed dimension. I will first discuss two-dimensional discrete Gaussian free fields, reviewing recent works on the tightness of the re-centered maximum and the convergence in law. Then I will present an ongoing work which aims to extend these results to general log-correlated Gaussian fields, of which the Gaussian membrane model at the critical dimension is a particular example.
Tests for equality of mean directions in independent circular populations is an important practic... more Tests for equality of mean directions in independent circular populations is an important practical problem in many areas of applied research, for which results are yet to be obtained. Dispersion model approach with analysis of deviance is an appealing approach for testing equality of parameters under non-normal setups. In view of its wide applicability, the present endeavour is to examine whether standard circular models for describing directional data can be viewed as special cases of dispersion model. The answer is affirmative and this leads us to explore whether analysis of deviance can be employed for circular observations. Special emphasis is given on circular normal and wrapped Cauchy distributions for carrying out deviance analysis. Interestingly, we demonstrate that the Watson-Williams ad-hoc test (1956) proposed for independent von Mises distributions is equivalent to the analysis of deviance test. We thereby also exhibit the rare property possessed by von Mises distributi...
Communications in Statistics - Theory and Methods, 2014
The lack of memory property is a characterizing property of the exponential distribution in the c... more The lack of memory property is a characterizing property of the exponential distribution in the continuous domain. In the bivariate setup different generalizations of the same are available in terms of survival function. We extend this lack of memory property in terms of bivariate probability density function and examine its characterization properties. In this process the density version of the lack of memory property can be interlinked with conditionally specified exponential distribution, bivariate reciprocal coordinate subtangent of the density curve and a few other derived measures.
Communications in Statistics - Theory and Methods, 2009
The subtangent is the projection of the tangent upon the axis of abscissa. The usefulness of the ... more The subtangent is the projection of the tangent upon the axis of abscissa. The usefulness of the reciprocal subtangent as a measure of the survival and density curves has earlier been reported in the literature for univariate distributions. This measure was generalized for bivariate and multivariate setups and related characterization problems were examined. The conditionally specified bivariate exponential distribution has been uniquely determined from the local constancy of the bivariate reciprocal subtangents. The case of global constancy and other related results have been studied. Conditionally specified bivariate Lomax distribution and normal distribution were also studied. Further, the conditionally specified multivariate exponential distribution was uniquely determined from the local constancy of the multivariate reciprocal subtangents.
Communications in Statistics - Simulation and Computation, 2013
Network analysis is an important technique for project management. However, the current literatur... more Network analysis is an important technique for project management. However, the current literature is biased toward beta distribution for modeling activity times. In this article, we have critically examined the role of beta distribution. It has been shown that beta distribution plays no specific role. Further, the method for calculating the chance of project completion must be revised. We have accordingly suggested an alternative modeling in terms of gamma distribution and proposed how to calculate the chance of project completion by taking into consideration both critical and noncritical paths. For demonstration purposes, we have considered a small project.
We consider the Branching Random Walk on $d$-ary tree of height $n$ under the presence of a hard ... more We consider the Branching Random Walk on $d$-ary tree of height $n$ under the presence of a hard wall which restricts each value to be positive. The question of behavior of Gaussian process with long range interactions under the presence of a hard wall has been addressed, and a relation with the expected maxima of the processes has been established. We find the probability of event corresponding to the hard wall and show that the conditional expectation of the gaussian variable at a typical vertex, under positivity, is at least less than the expected maxima by order of $\log n$.
The celebrated lack of memory property is a unique property of the exponential distribution in th... more The celebrated lack of memory property is a unique property of the exponential distribution in the continuous domain. It is expressed in terms of equality of residual survival function with the survival function of the original distribution. We propose to extend this lack of memory property in terms of probability density function and examine therefrom its characterization and stability properties. In this process the density version of the lack of memory property can be interlinked with reciprocal coordinate subtangent of the density curve and a few other derived measures.
We consider a sequence of variables having multinomial distribution with the number of trials cor... more We consider a sequence of variables having multinomial distribution with the number of trials corresponding to these variables being large and possibly different. The multinomial probabilities of the categories are assumed to vary randomly depending on batches. The proposed framework is interesting from the perspective of various applications in practice such as predicting the winner of an election, forecasting the market share of different brands etc. In this work, first we derive sufficient conditions of asymptotic normality of the estimates of the multinomial cell probabilities, and corresponding suitable transformations. Then, we consider a Bayesian setting to implement our model. We consider hierarchical priors using multivariate normal and inverse Wishart distributions, and establish the posterior consistency. Based on this result and following appropriate Gibbs sampling algorithms, we can infer about aggregate data. The methodology is illustrated in detail with two real life ...
We will study the extreme values for log-correlated discrete Gaussian fields on boxes of any fixe... more We will study the extreme values for log-correlated discrete Gaussian fields on boxes of any fixed dimension. I will first discuss two-dimensional discrete Gaussian free fields, reviewing recent works on the tightness of the re-centered maximum and the convergence in law. Then I will present an ongoing work which aims to extend these results to general log-correlated Gaussian fields, of which the Gaussian membrane model at the critical dimension is a particular example.
Tests for equality of mean directions in independent circular populations is an important practic... more Tests for equality of mean directions in independent circular populations is an important practical problem in many areas of applied research, for which results are yet to be obtained. Dispersion model approach with analysis of deviance is an appealing approach for testing equality of parameters under non-normal setups. In view of its wide applicability, the present endeavour is to examine whether standard circular models for describing directional data can be viewed as special cases of dispersion model. The answer is affirmative and this leads us to explore whether analysis of deviance can be employed for circular observations. Special emphasis is given on circular normal and wrapped Cauchy distributions for carrying out deviance analysis. Interestingly, we demonstrate that the Watson-Williams ad-hoc test (1956) proposed for independent von Mises distributions is equivalent to the analysis of deviance test. We thereby also exhibit the rare property possessed by von Mises distributi...
Communications in Statistics - Theory and Methods, 2014
The lack of memory property is a characterizing property of the exponential distribution in the c... more The lack of memory property is a characterizing property of the exponential distribution in the continuous domain. In the bivariate setup different generalizations of the same are available in terms of survival function. We extend this lack of memory property in terms of bivariate probability density function and examine its characterization properties. In this process the density version of the lack of memory property can be interlinked with conditionally specified exponential distribution, bivariate reciprocal coordinate subtangent of the density curve and a few other derived measures.
Communications in Statistics - Theory and Methods, 2009
The subtangent is the projection of the tangent upon the axis of abscissa. The usefulness of the ... more The subtangent is the projection of the tangent upon the axis of abscissa. The usefulness of the reciprocal subtangent as a measure of the survival and density curves has earlier been reported in the literature for univariate distributions. This measure was generalized for bivariate and multivariate setups and related characterization problems were examined. The conditionally specified bivariate exponential distribution has been uniquely determined from the local constancy of the bivariate reciprocal subtangents. The case of global constancy and other related results have been studied. Conditionally specified bivariate Lomax distribution and normal distribution were also studied. Further, the conditionally specified multivariate exponential distribution was uniquely determined from the local constancy of the multivariate reciprocal subtangents.
Communications in Statistics - Simulation and Computation, 2013
Network analysis is an important technique for project management. However, the current literatur... more Network analysis is an important technique for project management. However, the current literature is biased toward beta distribution for modeling activity times. In this article, we have critically examined the role of beta distribution. It has been shown that beta distribution plays no specific role. Further, the method for calculating the chance of project completion must be revised. We have accordingly suggested an alternative modeling in terms of gamma distribution and proposed how to calculate the chance of project completion by taking into consideration both critical and noncritical paths. For demonstration purposes, we have considered a small project.
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Papers by Rishideep Roy