The Experts below are selected from a list of 148116 Experts worldwide ranked by ideXlab platform
Giorgio Kaniadakis - One of the best experts on this subject based on the ideXlab platform.
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theoretical foundations and mathematical formalism of the power law tailed Statistical Distributions
Entropy, 2013Co-Authors: Giorgio KaniadakisAbstract:We present the main features of the mathematical theory generated by the κ-deformed exponential function exp k (x) = ( 1 + k 2 x 2 + kx) 1 k , with 0 ≤ κ < 1, developed in the last twelve years, which turns out to be a continuous one parameter deformation of the ordinary mathematics generated by the Euler exponential function. The κ-mathematics has its roots in special relativity and furnishes the theoretical foundations of the κ-Statistical mechanics predicting power law tailed Statistical Distributions, which have been observed experimentally in many physical, natural and artificial systems. After introducing the κ-algebra, we present the associated κ-differential and κ-integral calculus. Then, we obtain the corresponding κ-exponential and κ-logarithm functions and give the κ-version of the main functions of the ordinary mathematics.
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theoretical foundations and mathematical formalism of the power law tailed Statistical Distributions
Entropy, 2013Co-Authors: Giorgio KaniadakisAbstract:We present the main features of the mathematical theory generated by the κ-deformed exponential function exp k (x) = ( 1 + k 2 x 2 + kx) 1 k , with 0 ≤ κ < 1, developed in the last twelve years, which turns out to be a continuous one parameter deformation of the ordinary mathematics generated by the Euler exponential function. The κ-mathematics has its roots in special relativity and furnishes the theoretical foundations of the κ-Statistical mechanics predicting power law tailed Statistical Distributions, which have been observed experimentally in many physical, natural and artificial systems. After introducing the κ-algebra, we present the associated κ-differential and κ-integral calculus. Then, we obtain the corresponding κ-exponential and κ-logarithm functions and give the κ-version of the main functions of the ordinary mathematics.
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physical origin of the power law tailed Statistical Distributions
Modern Physics Letters B, 2012Co-Authors: Giorgio KaniadakisAbstract:Starting from the BBGKY hierarchy, describing the kinetics of nonlinear particle system, we obtain the relevant entropy and stationary distribution function. Subsequently, by employing the Lorentz transformations we propose the relativistic generalization of the exponential and logarithmic functions. The related particle distribution and entropy represents the relativistic extension of the classical Maxwell–Boltzmann distribution and of the Boltzmann entropy, respectively, and define the Statistical mechanics presented in [Phys. Rev. E66 (2002) 056125] and [Phys. Rev. E72 (2005) 036108]. The achievements of the present effort, support the idea that the experimentally observed power-law tailed Statistical Distributions in plasma physics, are enforced by the relativistic microscopic particle dynamics.
Jung-bin Su - One of the best experts on this subject based on the ideXlab platform.
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Alternative Statistical Distributions for estimating value-at-risk: theory and evidence
Review of Quantitative Finance and Accounting, 2012Co-Authors: Jung-bin SuAbstract:A number of applications presume that asset returns are normally distributed, even though they are widely known to be skewed leptokurtic and fat-tailed and excess kurtosis. This leads to the underestimation or overestimation of the true value-at-risk (VaR). This study utilizes a composite trapezoid rule, a numerical integral method, for estimating quantiles on the skewed generalized t distribution (SGT) which permits returns innovation to flexibly treat skewness, leptokurtosis and fat tails. Daily spot prices of the thirteen stock indices in North America, Europe and Asia provide data for examining the one-day-ahead VaR forecasting performance of the GARCH model with normal, student’s t and SGT Distributions. Empirical results indicate that the SGT provides a good fit to the empirical distribution of the log-returns followed by student’s t and normal Distributions. Moreover, for all confidence levels, all models tend to underestimate real market risk. Furthermore, the GARCH-based model, with SGT distributional setting, generates the most conservative VaR forecasts followed by student’s t and normal Distributions for a long position. Consequently, it appears reasonable to conclude that, from the viewpoint of accuracy, the influence of both skewness and fat-tails effects (SGT) is more important than only the effect of fat-tails (student’s t ) on VaR estimates in stock markets for a long position.
Cheng-few Lee - One of the best experts on this subject based on the ideXlab platform.
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Alternative Statistical Distributions for estimating value-at-risk: theory and evidence
Review of Quantitative Finance and Accounting, 2012Co-Authors: Cheng-few LeeAbstract:A number of applications presume that asset returns are normally distributed, even though they are widely known to be skewed leptokurtic and fat-tailed and excess kurtosis. This leads to the underestimation or overestimation of the true value-at-risk (VaR). This study utilizes a composite trapezoid rule, a numerical integral method, for estimating quantiles on the skewed generalized t distribution (SGT) which permits returns innovation to flexibly treat skewness, leptokurtosis and fat tails. Daily spot prices of the thirteen stock indices in North America, Europe and Asia provide data for examining the one-day-ahead VaR forecasting performance of the GARCH model with normal, student’s t and SGT Distributions. Empirical results indicate that the SGT provides a good fit to the empirical distribution of the log-returns followed by student’s t and normal Distributions. Moreover, for all confidence levels, all models tend to underestimate real market risk. Furthermore, the GARCH-based model, with SGT distributional setting, generates the most conservative VaR forecasts followed by student’s t and normal Distributions for a long position. Consequently, it appears reasonable to conclude that, from the viewpoint of accuracy, the influence of both skewness and fat-tails effects (SGT) is more important than only the effect of fat-tails (student’s t ) on VaR estimates in stock markets for a long position.
Su-shing Chen - One of the best experts on this subject based on the ideXlab platform.
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Statistical Distributions of optimal global alignment scores of random protein sequences.
BMC Bioinformatics, 2005Co-Authors: Hongxia Pang, Jiaowei Tang, Su-shing ChenAbstract:The inference of homology from Statistically significant sequence similarity is a central issue in sequence alignments. So far the Statistical distribution function underlying the optimal global alignments has not been completely determined. In this study, random and real but unrelated sequences prepared in six different ways were selected as reference datasets to obtain their respective Statistical Distributions of global alignment scores. All alignments were carried out with the Needleman-Wunsch algorithm and optimal scores were fitted to the Gumbel, normal and gamma Distributions respectively. The three-parameter gamma distribution performs the best as the theoretical distribution function of global alignment scores, as it agrees perfectly well with the distribution of alignment scores. The normal distribution also agrees well with the score distribution frequencies when the shape parameter of the gamma distribution is sufficiently large, for this is the scenario when the normal distribution can be viewed as an approximation of the gamma distribution. We have shown that the optimal global alignment scores of random protein sequences fit the three-parameter gamma distribution function. This would be useful for the inference of homology between sequences whose relationship is unknown, through the evaluation of gamma distribution significance between sequences.
C Ugalde - One of the best experts on this subject based on the ideXlab platform.
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charged particle thermonuclear reaction rates i monte carlo method and Statistical Distributions
Nuclear Physics, 2010Co-Authors: R Longland, Christian Iliadis, A E Champagne, Joe Newton, C UgaldeAbstract:Abstract A method based on Monte Carlo techniques is presented for evaluating thermonuclear reaction rates. We begin by reviewing commonly applied procedures and point out that reaction rates that have been reported up to now in the literature have no rigorous Statistical meaning. Subsequently, we associate each nuclear physics quantity entering in the calculation of reaction rates with a specific probability density function, including Gaussian, lognormal and chi-squared Distributions. Based on these probability density functions the total reaction rate is randomly sampled many times until the required Statistical precision is achieved. This procedure results in a median (Monte Carlo) rate which agrees under certain conditions with the commonly reported recommended “classical” rate. In addition, we present at each temperature a low rate and a high rate, corresponding to the 0.16 and 0.84 quantiles of the cumulative reaction rate distribution. These quantities are in general different from the Statistically meaningless “minimum” (or “lower limit”) and “maximum” (or “upper limit”) reaction rates which are commonly reported. Furthermore, we approximate the output reaction rate probability density function by a lognormal distribution and present, at each temperature, the lognormal parameters μ and σ . The values of these quantities will be crucial for future Monte Carlo nucleosynthesis studies. Our new reaction rates, appropriate for bare nuclei in the laboratory , are tabulated in the second paper of this issue (Paper II). The nuclear physics input used to derive our reaction rates is presented in the third paper of this issue (Paper III). In the fourth paper of this issue (Paper IV) we compare our new reaction rates to previous results.