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Narayanaswamy Balakrishnan

Bio: Narayanaswamy Balakrishnan is an academic researcher from McMaster University. The author has contributed to research in topics: Order statistic & Estimator. The author has an hindex of 82, co-authored 1348 publications receiving 42669 citations. Previous affiliations of Narayanaswamy Balakrishnan include Louisiana State University & National Oceanic and Atmospheric Administration.


Papers
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Book
01 Jan 1994
TL;DR: Continuous Distributions (General) Normal Distributions Lognormal Distributions Inverse Gaussian (Wald) Distributions Cauchy Distribution Gamma Distributions Chi-Square Distributions Including Chi and Rayleigh Exponential Distributions Pareto Distributions Weibull Distributions Abbreviations Indexes
Abstract: Continuous Distributions (General) Normal Distributions Lognormal Distributions Inverse Gaussian (Wald) Distributions Cauchy Distribution Gamma Distributions Chi-Square Distributions Including Chi and Rayleigh Exponential Distributions Pareto Distributions Weibull Distributions Abbreviations Indexes

7,270 citations

Book
01 Jul 1992
TL;DR: In this paper, the authors use order statistics in Statistical Inference Asymptotic Theory Record Values Bibliography Indexes to measure moment relations, bounds, and approximations.
Abstract: Basic Distribution Theory Discrete Order Statistics Order Statistics from Some Specific Distributions Moment Relations, Bounds, and Approximations Characterizations Using Order Statistics Order Statistics in Statistical Inference Asymptotic Theory Record Values Bibliography Indexes.

1,605 citations

OtherDOI
29 Sep 2014
TL;DR: In this article, the authors present a concise review of developments on various continuous multivariate distributions and present some basic definitions and notations, and present several important continuous multi-dimensional distributions and their significant properties and characteristics.
Abstract: In this article, we present a concise review of developments on various continuous multivariate distributions. We first present some basic definitions and notations. Then, we present several important continuous multivariate distributions and list their significant properties and characteristics. Keywords: generating function; moments; conditional distribution; truncated distribution; regression; bivariate normal; multivariate normal; multivariate exponential; multivariate gamma; dirichlet; inverted dirichlet; liouville; multivariate logistic; multivariate pareto; multivariate extreme value; multivariate t; wishart translated systems; multivariate exponential families

1,106 citations


Cited by
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Journal ArticleDOI
TL;DR: This work proposes a principled statistical framework for discerning and quantifying power-law behavior in empirical data by combining maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov (KS) statistic and likelihood ratios.
Abstract: Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events—and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov (KS) statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data, while in others the power law is ruled out.

8,753 citations

Journal ArticleDOI
Steven L. Heston1
TL;DR: In this paper, a closed-form solution for the price of a European call option on an asset with stochastic volatility is derived based on characteristi c functions and can be applied to other problems.
Abstract: I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strike-price biases in the BlackScholes (1973) model. The solution technique is based on characteristi c functions and can be applied to other problems.

7,867 citations

Book
01 Jan 2003
TL;DR: In this paper, the authors describe the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation, and compare simulation-assisted estimation procedures, including maximum simulated likelihood, method of simulated moments, and methods of simulated scores.
Abstract: This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum simulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. No other book incorporates all these fields, which have arisen in the past 20 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.

7,768 citations

Journal ArticleDOI
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.

7,412 citations

Journal ArticleDOI

6,278 citations