arXiv subjects

Indranil Ghosh

Publications and source records attributed to Indranil Ghosh.

32 records · Page 2Linked to original sources

arXiv2022

Numerical bifurcation analysis of improved denatured Morris-Lecar neuron model

It is well-known that the electrical activities of neurons are induced by a wide variety of external factors. This work considers the effect of electromagnetic induction on improved denatured Morris-Lecar neuron model. The dependence of dynamical behaviour of the original denatured Morris-Lecar model on parameters is addressed through numerical bifurcation analysis. This allows us to explore the changes in dynamics of the model qualitatively as parameters are varied. Then we investigate the effects of external periodic current and electromagnetic flux on the dynamical properties of the improved denatured Morris-Lecar neuron model. Different types of dynamical behaviour, ranging from regular periodic spiking to complex bursting, are found when the multiple parameters are varied simultaneously. The improved model could be applied to research where simple models are required for physiological and pathophysiological responses in neurons.

math.DS↗

arXiv2022

A physics-driven study of dominance space in soccer

In arXiv:2107.05714 the concept of the Voronoi diagram was investigated closely from a theoretical point of view. Then, a physics-driven kinematical method was introduced to produce an improved model for dominance space in soccer. Remaining faithful to the deterministic approach, we extend the original work by the introduction of (a) an asymmetric influence of the players in their surrounding area, (b) the frictional forces to the players' motion, and (c) the simultaneous combination of both effects. The asymmetric influence is fairly intuitive; players have more control in the direction they are running than any other direction. The sharper the turn they must make to reach a point on the pitch, the weaker their control of that point will be. From simple kinematical laws, this effect can be quantified explicitly. For the frictional force, a portion comes from air resistance, and so will be proportional to the square of the player's speed, as is well known from fluid dynamics. There are no other external frictional forces, but, at the suggestion of biokinematics, there is an internal frictional force, relating to the consumption of energy by the muscles, which is proportional to the player's speed. Although these additions are intuitively understood, mathematically they introduce many analytical complexities. We establish exact analytical solutions of the dominance areas of the pitch by introducing a few reasonable simplifying assumptions. Given these solutions the new Voronoi diagrams are drawn for the publicly available data by Metrica Sports. In general, it is not necessary anymore for the dominance regions to be convex, they might contain holes, and may be disconnected. The fastest player may dominate points far away from the rest of the players.

physics.soc-ph↗

arXiv2021

Robust Devaney chaos in the two-dimensional border-collision normal form

The collection of all non-degenerate, continuous, two-piece, piecewise-linear maps on $\mathbb{R}^2$ can be reduced to a four-parameter family known as the two-dimensional border-collision normal form. We prove that throughout an open region of parameter space this family has an attractor satisfying Devaney's definition of chaos. This strengthens existing results on the robustness of chaos in piecewise-linear maps. We further show that the stable manifold of a saddle fixed point, despite being a one-dimensional object, densely fills an open region containing the attractor. Finally we identify a heteroclinic bifurcation, not described previously, at which the attractor undergoes a crisis and may be destroyed.

math.DS↗

arXiv2021

Renormalisation of the two-dimensional border-collision normal form

We study the two-dimensional border-collision normal form (a four-parameter family of continuous, piecewise-linear maps on $\mathbb{R}^2$) in the robust chaos parameter region of [S. Banerjee, J.A. Yorke, C. Grebogi, Robust Chaos, Phys. Rev. Lett. 80(14):3049--3052, 1998]. We use renormalisation to partition this region by the number of connected components of a chaotic Milnor attractor. This reveals previously undescribed bifurcation structure in a succinct way.

nlin.CD↗

arXiv2020

On the discrete analog of gamma-Lomax distribution: properties and applications

This article represents how certain types of blockades in any industrial (heavy industries) production, in particular, industrial strikes can be modeled with the proposed discrete probabilistic distribution as a baseline distribution. We considered the number of outbreaks of strikes in the coal mining industry, the vehicle manufacturing industry, and the transpose industry in the UK obtained from Consul (1989). We fitted those data sets with the proposed discrete gamma-Lomax distribution and compared the fit with the discrete generalized Pareto distribution (Consul, 1989). For this purpose, we explore the basic properties of the discrete gamma-Lomax distribution including but not limited to: cumulative distribution, survival, probability mass, quantile and hazard functions, genesis and rth-order moments; consider maximum likelihood estimation under the normal set up as well as under the censored data set scenario. It is observed that the newly proposed model can be useful to describe strikes arising from various types of industries.

math.ST↗

arXiv2019

On compatibility/incompatibility of two discrete probability distributions in the presence of incomplete specification

Conditional specification of distributions is a developing area with many applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we propose an alternative approach to study the compatibility of two conditional probability distributions under the finite discrete set up. A technique based on rank-based criterion is shown to be particularly convenient for identifying compatible distributions corresponding to complete conditional specification, including the case with zeros. The proposed methods are finally illustrated with several examples.

math.ST↗

arXiv2018

A Class of Skewed Distributions with Applications in Environmental Data

In environmental studies, many data are typically skewed and it is desired to have a flexible statistical model for this kind of data. In this paper, we study a class of skewed distributions by invoking arguments as described by Ferreira and Steel (2006, Journal of the American Statistical Association, 101: 823--829). In particular, we consider using the logistic kernel to derive a class of univariate distribution called the truncated-logistic skew symmetric (TLSS) distribution. We provide some structural properties of the proposed distribution and develop the statistical inference for the TLSS distribution. A simulation study is conducted to investigate the efficacy of the maximum likelihood method. For illustrative purposes, two real data sets from environmental studies are used to exhibit the applicability of such a model.

stat.AP↗

arXiv2017

An alternative approach for compatibility of two discrete conditional distributions

Conditional specification of distributions is a developing area with increasing applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we propose an alternative approach to study the compatibility of two conditional probability distributions under the finite discrete setup. A technique based on rank-based criterion is shown to be particularly convenient for identifying compatible distributions corresponding to complete conditional specification including the case with zeros.The proposed methods are illustrated with several examples.

math.ST↗

arXiv2017

Statistical Inference of Kumaraswamy distribution under imprecise information

Traditional statistical approaches for estimating the parameters of the Kumaraswamy distribution have dealt with precise information. However, in real world situations, some information about an underlying experimental process might be imprecise and might be represented in the form of fuzzy information. In this paper, we consider the problem of estimating the parameters of a univariate Kumaraswamy distribution with two parameters when the available observations are described by means of fuzzy information. We derive the maximum likelihood estimate of the parameters by using Newton Raphson as well as EM algorithm method. The estimation procedures are discussed in details and compared via Markov Chain Monte Carlo simulations in terms of their average biases and mean squared errors.

stat.ME↗

arXiv2017

On the Ristic-Balakrishnan distribution: bivariate extension and characterizations

Over the last few decades, a significant development has been made towards the augmentation of some well-known lifetime distributions by various strategies. These newly developed models have enjoyed a considerable amount of success in modeling various real life phenomena. Motivated by this, Ristic & Balakrishnan (2012) developed a special class of univariate distributions (see Ristic- Balakrishnan (2012)). Henceforth we call this family of distribution as RB-G family of distributions. The RB-G family has the same parameters of the G distribution plus an additional positive shape parameter a. Several RB-G distribution can be obtained from a specified G distribution. For a = 1, the baseline G distribution is a basic exemplar of the RB-G family with a continuous crossover towards cases with various shapes. In this article we focus our attention on the characterization of this family and discuss some structural properties of the bivariate RB-G family of distributions which are not discussed in detail in Ristic and Balakrishnan (2012).

stat.ME↗

arXiv2017

On some further properties and application of Weibull-R family of distributions

In this paper, we provide some new results for the Weibull-R family of distributions (Alzaghal, Ghosh and Alzaatreh (2016)). We derive some new structural properties of the Weibull-R family of distributions. We provide various characterizations of the family via conditional moments, some functions of order statistics and via record values.

math.ST↗

arXiv2016

Artificial Neural Network and Time Series Modeling Based Approach to Forecasting the Exchange Rate in a Multivariate Framework

Any discussion on exchange rate movements and forecasting should include explanatory variables from both the current account and the capital account of the balance of payments. In this paper, we include such factors to forecast the value of the Indian rupee vis a vis the US Dollar. Further, factors reflecting political instability and lack of mechanism for enforcement of contracts that can affect both direct foreign investment and also portfolio investment, have been incorporated. The explanatory variables chosen are the 3 month Rupee Dollar futures exchange rate (FX4), NIFTY returns (NIFTYR), Dow Jones Industrial Average returns (DJIAR), Hang Seng returns (HSR), DAX returns (DR), crude oil price (COP), CBOE VIX (CV) and India VIX (IV). To forecast the exchange rate, we have used two different classes of frameworks namely, Artificial Neural Network (ANN) based models and Time Series Econometric models. Multilayer Feed Forward Neural Network (MLFFNN) and Nonlinear Autoregressive models with Exogenous Input (NARX) Neural Network are the approaches that we have used as ANN models. Generalized Autoregressive Conditional Heteroskedastic (GARCH) and Exponential Generalized Autoregressive Conditional Heteroskedastic (EGARCH) techniques are the ones that we have used as Time Series Econometric methods. Within our framework, our results indicate that, although the two different approaches are quite efficient in forecasting the exchange rate, MLFNN and NARX are the most efficient.

q-fin.ST↗

arXiv2016

Forecasting Volatility in Indian Stock Market using Artificial Neural Network with Multiple Inputs and Outputs

Volatility in stock markets has been extensively studied in the applied finance literature. In this paper, Artificial Neural Network models based on various back propagation algorithms have been constructed to predict volatility in the Indian stock market through volatility of NIFTY returns and volatility of gold returns. This model considers India VIX, CBOE VIX, volatility of crude oil returns (CRUDESDR), volatility of DJIA returns (DJIASDR), volatility of DAX returns (DAXSDR), volatility of Hang Seng returns (HANGSDR) and volatility of Nikkei returns (NIKKEISDR) as predictor variables. Three sets of experiments have been performed over three time periods to judge the effectiveness of the approach.

cs.NE↗

arXiv2016

Using Clustering Method to Understand Indian Stock Market Volatility

In this paper we use Clustering Method to understand whether stock market volatility can be predicted at all, and if so, when it can be predicted. The exercise has been performed for the Indian stock market on daily data for two years. For our analysis we map number of clusters against number of variables. We then test for efficiency of clustering. Our contention is that, given a fixed number of variables, one of them being historic volatility of NIFTY returns, if increase in the number of clusters improves clustering efficiency, then volatility cannot be predicted. Volatility then becomes random as, for a given time period, it gets classified in various clusters. On the other hand, if efficiency falls with increase in the number of clusters, then volatility can be predicted as there is some homogeneity in the data. If we fix the number of clusters and then increase the number of variables, this should have some impact on clustering efficiency. Indeed if we can hit upon, in a sense, an optimum number of variables, then if the number of clusters is reasonably small, we can use these variables to predict volatility. The variables that we consider for our study are volatility of NIFTY returns, volatility of gold returns, India VIX, CBOE VIX, volatility of crude oil returns, volatility of DJIA returns, volatility of DAX returns, volatility of Hang Seng returns and volatility of Nikkei returns. We use three clustering algorithms namely Kernel K-Means, Self Organizing Maps and Mixture of Gaussian models and two internal clustering validity measures, Silhouette Index and Dunn Index, to assess the quality of generated clusters.

cs.CE↗