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A set of new three-parameter entropies in terms of a generalized incomplete gamma function

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2013年第9期392卷 1972-1976页

作者： Asgarani, Somayeh Payame Noor Univ Dept Phys Tehran Iran

In this paper, by considering the first three Khinchin axioms (K1-K3) and neglecting the fourth (K4), a set of new three-parameter entropies will be introduced which are expressed in terms of a generalized incomplete gamma function as S-d,S-c1,S-c2[p] proportional to Sigma(i) gamma(d + 1, 1 - c(1) ln p(i), 1 - c(2) ln p(i)). Also, its asymptotic behavior will be found and it will be shown that, for some special values of parameters, some known entropies like Tsallis, Kaniadakis and Abe entropies are recovered. (c) 2012 Elsevier B.V. All rights reserved.

关键词： generalized entropy generalized incomplete gamma function Nonextensive statistical mechanics

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Evaluation of modified Hantush's function: A tool for parametric study with the finite line-source model

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GEOTHERMICS 2023年第1期113卷

作者： Bandos, Tatyana, V Martin-Escudero, Koldobika Sala-Lizarraga, Jose M. Univ Basque Country Dept Ingn Energet Grp Invest ENEDI Alda Urquijo S-N Bilbao 48013 Spain

A solution to the three-dimensional finite line-source (FLS) model for borehole heat exchangers (BHEs) is identical to Hantush's M function, commonly used in groundwater pumping modeling. A modified Hantush function E appears in the steady-state solution to the moving finite line-source (MFLS) model for borehole heat exchangers (BHEs) with groundwater flow that takes into account heat conduction and advection by Peclet number. An exact series representation is obtained for this two-parametric function E, and from it two-types of approximate expressions for the E are derived. One is suitable for small values of a parameter Pe and the other for its large values. High accuracy of the approximate formulae is verified by comparison with the exact values provided by modified Hantush's function E in those validity *** analytical expressions can be used for designing complex borehole configurations and may be useful in steady-state analysis of partially penetrated wells (PPWs) in a leaky aquifer.

关键词： Hantush's well function Leaky well function generalized incomplete gamma function Moving finite line-source Partially penetrating wells Borehole heat exchangers Groundwater

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Analytic expressions for the moving infinite line source model

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GEOTHERMICS 2022年 103卷 1页

作者： Pasquier, Philippe Lamarche, Louis Polytech Montreal Dept Civil Geol & Min Engn POB 6079 Ctr Ville Montreal PQ H3C 3A7 Canada ETS Dept Mech Engn 1100 Notre Dame W Montreal PQ H3C 1K3 Canada

Groundwater flow can have a significant impact on the thermal response of ground heat exchangers. The moving infinite line source model is thus widely used in practice as it considers both conductive and advective heat transfert processes. Solution of this model involves a relatively heavy numerical quadrature. Contrarily to the infinite line source model, there is currently no known first-order approximation that could be useful for many practical applications. In this paper, known analytical expressions of the Hantush well function and generalized incomplete gamma function are first revisited. A clear link between these functions and the moving infinite line source model is then established. Then, two new exact and integral-free analytical expressions are proposed, along with two new first-order approximations. The new analytical expressions proposed take the form of convergent power series involving no recursive evaluations. It is shown that relative errors less than 1% can be obtained with only a few summands. The convergence properties of the series, their accuracy and the validity domain of the first-order approximations are also presented and discussed.

关键词： Moving infinite line source Ground heat exchanger Hantush well function generalized incomplete gamma function

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Bivariate Matern covariances with cross-dimple for modeling coregionalized variables

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SPATIAL STATISTICS 2021年 41卷

作者： Alegria, A. Emery, X. Porcu, E. Univ Tecn Federico Santa Maria Dept Matemat Valparaiso Chile Univ Chile Dept Min Engn Santiago Chile Univ Chile Adv Min Technol Ctr Santiago Chile Khalifa Univ Dept Math Abu Dhabi U Arab Emirates

Modeling the spatial correlation structure of coregionalized data is a frequent task in numerous fields of the natural sciences. Even in the isotropic case, experimental covariances may exhibit complex features, such as a maximum cross-correlation attained at non-collocated locations (dimple or hole effect). Current construction principles for multivariate covariance models on Euclidean spaces do not allow accounting for such a property. We propose a spectral approach to modify cross-covariance functions of the isotropic bivariate Matern model in order to obtain a cross-dimple. Our model admits analytic expressions in terms of special functions. Our findings are illustrated through applications to data sets from the fields of mining and geochemistry. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Coregionalization modeling Bivariate covariance functions Dimple Inverse gamma distribution generalized incomplete gamma function Spectral density

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The generalized incomplete gamma function as sum over Modified Bessel functions of the First Kind

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2011年第14期235卷 4107-4116页

作者： Veling, E. J. M. Delft Univ Technol Fac Civil Engn & Geosci Dept Watermanagement NL-2600 GA Delft Netherlands

We represent the generalized incomplete gamma function gamma(alpha, x;b) = integral(infinity)(x) t(alpha-1) exp (-t - b/t) dt, alpha is an element of R, x >= 0, b >= 0, but not both x = b = 0. if a <= 0, as a sum of Modified Bessel functions valid for non-integer a. For integer values of a we derive the corresponding limit case. Moreover, we discuss numerical techniques to evaluate this function. (C) 2011 Elsevier B.V. All rights reserved.

关键词： generalized incomplete gamma function Hantush Well function Modified Bessel function Closed-form representation

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On New Formulas for the Cumulative Distribution function of the Noncentral Chi-Square Distribution

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MEDITERRANEAN JOURNAL OF MATHEMATICS 2017年第2期14卷 1-13页

作者： Masirevic, Dragana Jankov Univ Osijek Dept Math Trg Lj Gaja 6 Osijek Croatia

The main aim of this article is to derive three new formulas for the cumulative distribution function of the noncentral chi-square distribution. The main advantage of such formulas is that they are given in terms of modified Bessel functions, leaky aquifer function and generalized incomplete gamma function which have a wide range of applications. In addition, the computational efficiency of the newly derived formulas versus already known formulas is established.

关键词： Noncentral chi-square distribution Modified Bessel functions Neumann series generalized incomplete gamma function leaky aquifer function

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incomplete Kratzel function Model of Leaky Aquifer and Alike functions 10

Incomplete Kratzel Function Model of Leaky Aquifer and Alike...

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10th Jubilee IEEE International Symposium on Applied Computational Intelligence and Informatics

作者： Pogany, Tibor K. Baricz, Arpad Rudas, Imre Univ Rijeka Fac Maritime Studies Rijeka 51000 Croatia Obuda Univ Inst Appl Math H-1034 Budapest Hungary Univ Babes Bolyai Dept Econ Cluj Napoca 400591 Romania

In this note our aim is to derive certain important properties of a general mathematical model given in the form of an incomplete Kratzel function which contains as sub-models the generalized leaky aquifer function, t... 详细信息

ISBN: (纸本)9781479999118

关键词： Leaky aquifer function Kratzel function incomplete Kratzel function Laguerre-type inequality temperature integral thermonuclear integral Turan-type inequality upper incomplete gamma function generalized incomplete gamma function log-convexity bilateral bounding inequalities

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Hantush Well function revisited

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JOURNAL OF HYDROLOGY 2010年第3-4期393卷 381-388页

作者： Veling, E. J. M. Maas, C. Delft Univ Technol Fac Civil Engn & Geosci Dept Watermanagement NL-2600 GA Delft Netherlands KWR NL-3430 BB Nieuwegein Netherlands

In this paper, we comment on some recent numerical and analytical work to evaluate the Hantush Well function. We correct an expression found in a Comment by Nadarajah [Nadarajah, S., 2007. A comment on numerical evaluation of Theis and Hantush-Jacob well functions. Journal of Hydrology 338, 152-153] to a paper by Prodanoff et al. [Prodanoff, J.A., Mansur, W.J., Mascarenhas, F.C.B., 2006. Numerical evaluation of Theis and Hantush-Jacob well functions. Journal of Hydrology 318, 173-183]. We subsequently derived another analytic representation based on a generalized hypergeometric function in two variables and from the hydrological literature we cite an analytic representation by Hunt [Hunt, B., 1977. Calculation of the leaky aquifer function. Journal of Hydrology 33, 179-183]. We have implemented both representations and compared the results. Using a convergence accelerator Hunt's representation of Hantush Well function is efficient and accurate. While checking our implementations we found that Bear's table of the Hantush Well function [Bear, J., 1979. Hydraulics of Groundwater. McGraw-Hill, New York, Tables 8-6] contains a number of typographical errors that are not present in the original table published by Hantush [Hantush, M.S., 1956. Analysis of data from pumping tests in leaky aquifers. Transactions, American Geophysical Union 37, 702-714]. Finally, we offer a very fast approximation with a maximum relative error of 0.0033 for the parameter range in the table given by Bear. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Hantush Well function generalized incomplete gamma function Pumping test Leaky aquifer Closed-form representation Time series analysis

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On the approximation of a generalized incomplete gamma function arising in heat conduction problems

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2000年第2期248卷 509-519页

作者： Boudjelkha, MT Chaudhry, MA King Fahd Univ Petr & Minerals Dept Math Sci Dhahran 31261 Saudi Arabia

Several asymptotic expansions are given for the generalized incomplete gamma function gamma(alpha, x;b) = integral(x)(infinity)t(alpha-1)e(-t-b/t)dt, x > 0, Re b greater than or equal to 0, b not equal 0, as x tends to infinity, where the real paramete alpha is allowed to take negative values. In the case b = -i omega, omega > 0, we obtain the expansions of the decomposition functions C-gamma(alpha, x;omega) and S-gamma(alpha,x;omega). Closed form expressions are also given for alpha = -3/2, -5/2, ... (C) Academic Press.

关键词： generalized incomplete gamma function decomposition functions asymptotic expansion error function KdF function

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generalized gamma type distribution and its hazard rate function

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2001年第2期30卷 309-318页

作者： Agarwal, SK Al-Saleh, JA Kuwait Univ Fac Sci Dept Stat & OR Safat Kuwait

A new generalized gamma distribution is defined involving a parameter delta = lambda - 1;lambda greater than or equal to 0 in the Kobayashi's (1991) function gamma (lambda)(m, n). The parameter delta will relax the restriction on the parameter lambda > 0 in all probability distributions using Kobayashi's (1991) type functions. The hazard rate function of this distribution has the property of monotonicity and that of bathtub. The trend of density function and statistical properties are studied for generalized gamma distribution. With the help of a real life data set the fitting of the distribution is shown. A new Weibull type distribution is also considered and the hazard rate function of this distribution also has both the properties namely bathtub and monotonicity.

关键词： generalized gamma distribution generalized gamma function generalized incomplete gamma function hazard rate function mean residual life Weibull distribution

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