Author

# Debasis Kundu

Other affiliations: University of Texas at Dallas, Indian Institutes of Technology, Pennsylvania State University

Bio: Debasis Kundu is an academic researcher from Indian Institute of Technology Kanpur. The author has contributed to research in topics: Estimator & Asymptotic distribution. The author has an hindex of 53, co-authored 335 publications receiving 10805 citations. Previous affiliations of Debasis Kundu include University of Texas at Dallas & Indian Institutes of Technology.

##### Papers published on a yearly basis

##### Papers

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TL;DR: In this article, a three-parameter generalized exponential distribution (GED) was used for analysis of lifetime data, which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar et al.

Abstract: Summary The three-parameter gamma and three-parameter Weibull distributions are commonly used for analysing any lifetime data or skewed data. Both distributions have several desirable properties, and nice physical interpretations. Because of the scale and shape parameters, both have quite a bit of flexibility for analysing different types of lifetime data. They have increasing as well as decreasing hazard rate depending on the shape parameter. Unfortunately both distributions also have certain drawbacks. This paper considers a three-parameter distribution which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar, Srivastava & Freimer (1995) when the location parameter is not present. The study examines different properties of this model and observes that this family has some interesting features which are quite similar to those of the gamma family and the Weibull family, and certain distinct properties also. It appears this model can be used as an alternative to the gamma model or the Weibull model in many situations. One dataset is provided where the three-parameter generalized exponential distribution fits better than the three-parameter Weibull distribution or the three-parameter gamma distribution.

1,084 citations

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TL;DR: In this paper, the authors studied the properties of a new family of distributions known as the Exponentiated Exponential (exponential) distribution, discussed in Gupta, Gupta, and Gupta (1998).

Abstract: Summary In this article we study some properties of a new family of distributions, namely Exponentiated Exponentialdistribution, discussed in Gupta, Gupta, and Gupta (1998). The Exponentiated Exponential family has two parameters (scale and shape) similar to a Weibull or a gamma family. It is observed that many properties of this new family are quite similar to those of a Weibull or a gamma family, therefore this distribution can be used as a possible alternative to a Weibull or a gamma distribution. We present two reall ife data sets, where it is observed that in one data set exponentiated exponential distribution has a better fit compared to Weibull or gamma distribution and in the other data set Weibull has a better fit than exponentiated exponential or gamma distribution. Some numerical experiments are performed to see how the maximum likelihood estimators and their asymptotic results work for finite sample sizes.

684 citations

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TL;DR: In this article, the authors considered the maximum likelihood estimation of the different parameters of a generalized exponential distribution and discussed some of the testing of hypothesis problems, and compared their performances through numerical simulations.

Abstract: Recently a new distribution, named as generalized exponential distribution has been introduced and studied quite extensively by the authors. Generalized exponential distribution can be used as an alternative to gamma or Weibull distribution in many situations. In a companion paper, the authors considered the maximum likelihood estimation of the different parameters of a generalized exponential distribution and discussed some of the testing of hypothesis problems. In this paper we mainly consider five other estimation procedures and compare their performances through numerical simulations.

320 citations

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TL;DR: Different estimation procedures have been used to estimate the unknown parameter(s) and their performances are compared using Monte Carlo simulations, and it is observed that this particular skewed distribution can be used quite effectively in analyzing lifetime data.

Abstract: Recently, Surles and Padgett (Lifetime Data Anal., 187-200, 7, 2001) introduced two-parameter Burr Type X distribution, which can also be described as generalized Rayleigh distribution. It is observed that this particular skewed distribution can be used quite effectively in analyzing lifetime data. Different estimation procedures have been used to estimate the unknown parameter(s) and their performances are compared using Monte Carlo simulations.

302 citations

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TL;DR: In this paper, the authors proposed a generalized exponential distribution for analyzing bathtub failure data, which has a right skewed unimodal density function and monotone hazard function similar to the density functions and hazard functions of the gamma and Weibull distributions.

Abstract: Mudholkar and Srivastava [1993. Exponentiated Weibull family for analyzing bathtub failure data. IEEE Trans. Reliability 42, 299–302] introduced three-parameter exponentiated Weibull distribution. Two-parameter exponentiated exponential or generalized exponential distribution is a particular member of the exponentiated Weibull distribution. Generalized exponential distribution has a right skewed unimodal density function and monotone hazard function similar to the density functions and hazard functions of the gamma and Weibull distributions. It is observed that it can be used quite effectively to analyze lifetime data in place of gamma, Weibull and log-normal distributions. The genesis of this model, several properties, different estimation procedures and their properties, estimation of the stress-strength parameter, closeness of this distribution to some of the well-known distribution functions are discussed in this article.

284 citations

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TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.
Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

01 Jan 2016

TL;DR: The table of integrals series and products is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.

Abstract: Thank you very much for downloading table of integrals series and products. Maybe you have knowledge that, people have look hundreds times for their chosen books like this table of integrals series and products, but end up in harmful downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they cope with some harmful virus inside their laptop. table of integrals series and products is available in our book collection an online access to it is set as public so you can get it instantly. Our book servers saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the table of integrals series and products is universally compatible with any devices to read.

4,085 citations

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2,345 citations

01 Jan 2011

TL;DR: In this paper, a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions is presented.

Abstract: This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol’s method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent. Mathematical modeling of complex systems often requires sensitivity analysis to determine how an output variable of interest is influenced by individual or subsets of input variables. A traditional local sensitivity analysis entails gradients or derivatives, often invoked in design optimization, describing changes in the model response due to the local variation of input. Depending on the model output, obtaining gradients or derivatives, if they exist, can be simple or difficult. In contrast, a global sensitivity analysis (GSA), increasingly becoming mainstream, characterizes how the global variation of input, due to its uncertainty, impacts the overall uncertain behavior of the model. In other words, GSA constitutes the study of how the output uncertainty from a mathematical model is divvied up, qualitatively or quantitatively, to distinct sources of input variation in the model [1].

1,296 citations

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TL;DR: In this article, a three-parameter generalized exponential distribution (GED) was used for analysis of lifetime data, which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar et al.

Abstract: Summary The three-parameter gamma and three-parameter Weibull distributions are commonly used for analysing any lifetime data or skewed data. Both distributions have several desirable properties, and nice physical interpretations. Because of the scale and shape parameters, both have quite a bit of flexibility for analysing different types of lifetime data. They have increasing as well as decreasing hazard rate depending on the shape parameter. Unfortunately both distributions also have certain drawbacks. This paper considers a three-parameter distribution which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar, Srivastava & Freimer (1995) when the location parameter is not present. The study examines different properties of this model and observes that this family has some interesting features which are quite similar to those of the gamma family and the Weibull family, and certain distinct properties also. It appears this model can be used as an alternative to the gamma model or the Weibull model in many situations. One dataset is provided where the three-parameter generalized exponential distribution fits better than the three-parameter Weibull distribution or the three-parameter gamma distribution.

1,084 citations