Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A Fortran 90 module GammaCHI for computing and inverting the gamma and chi-square cumulative distribution functions (central and noncentral) is presented. The main novelty of this package is the reliable and accurate inversion routines for the noncentral cumulative distribution functions. Additionally, the package also provides routines for computing the gamma function, the error function and other functions related to the gamma function. The module includes the routines cdfgamC, invcdfgamC, cdfgamNC, invcdfgamNC, errorfunction, inverfc, gamma, loggam, gamstar and quotgamm for the computation of the central gamma distribution function (and its complementary function), the inversion of the central gamma distribution function, the computation of the noncentral gamma distribution function (and its complementary function), the inversion of the noncentral gamma distribution function, the computation of the error function and its complementary function, the inversion of the complementary error function, the computation of: the gamma function, the logarithm of the gamma function, the regulated gamma function and the ratio of two gamma functions, respectively.#R##N#Program summary#R##N#Program title: Module GammaCHI#R##N##R##N#Catalogue identifier: AEVM_v1_0#R##N##R##N#Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEVM_v1_0.html#R##N##R##N#Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland#R##N##R##N#Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html#R##N##R##N#No. of lines in distributed program, including test data, etc.: 7653#R##N##R##N#No. of bytes in distributed program, including test data, etc.: 85283#R##N##R##N#Distribution format: tar.gz#R##N##R##N#Programming language: Fortran 90.#R##N##R##N#Computer: Any supporting a FORTRAN compiler.#R##N##R##N#Operating system: Any supporting a FORTRAN compiler.#R##N##R##N#RAM: a few MB#R##N##R##N#Classification: 4.7.#R##N##R##N#Nature of problem: The computation and inversion of gamma and chi-square cumulative distribution functions (central and noncentral) as ll as the computation of the error and gamma functions is needed in many problems of applied and mathematical physics.#R##N##R##N#Solution method: The algorithms use different methods of computation depending on the range of parameters: asymptotic expansions, quadrature methods, etc.#R##N##R##N#Restrictions:   In the inversion of the central gamma/chi-square distribution functions, very small input function values Pμ(x,y)Pμ(x,y), Qμ(x,y)Qμ(x,y) (lor than 10−15010−150) are not admissible.#R##N##R##N#The admissible input parameter ranges for computing the noncentral cumulative gamma distribution functions Pμ(x,y)Pμ(x,y), Qμ(x,y)Qμ(x,y) in standard IEEE double precision arithmetic are 0≤x≤10,0000≤x≤10,000, 0≤y≤0≤y≤10,000,0.5≤μ≤10,000,0.5≤μ≤ 10,000 and the related parameter ranges for the noncentral chi-square cumulative distribution function. In the inversion of the noncentral gamma/chi-square distribution functions, very small input function values Pμ(x,y)Pμ(x,y), Qμ(x,y)Qμ(x,y) (lor than 10−2510−25 and 10−3510−35, respectively) are not admissible.#R##N##R##N#Running time: It varies depending on the function and the parameter range. The test provided takes milliseconds.
['Amparo Gil', 'Javier Segura', 'Nico Temme']
I am writing a research paper on a idea GammaCHI: a package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral)
[{"from": "human", "value": "I am writing a research paper on a idea GammaCHI: a package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral)"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A Fortran 90 module GammaCHI for computing and inverting the gamma and chi-square cumulative distribution functions (central and noncentral) is presented. The main novelty of this package is the reliable and accurate inversion routines for the noncentral cumulative distribution functions. Additionally, the package also provides routines for computing the gamma function, the error function and other functions related to the gamma function. The module includes the routines cdfgamC, invcdfgamC, cdfgamNC, invcdfgamNC, errorfunction, inverfc, gamma, loggam, gamstar and quotgamm for the computation of the central gamma distribution function (and its complementary function), the inversion of the central gamma distribution function, the computation of the noncentral gamma distribution function (and its complementary function), the inversion of the noncentral gamma distribution function, the computation of the error function and its complementary function, the inversion of the complementary error function, the computation of: the gamma function, the logarithm of the gamma function, the regulated gamma function and the ratio of two gamma functions, respectively.#R##N#Program summary#R##N#Program title: Module GammaCHI#R##N##R##N#Catalogue identifier: AEVM_v1_0#R##N##R##N#Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEVM_v1_0.html#R##N##R##N#Program obtainable from: CPC Program Library, Queen\u2019s University, Belfast, N. Ireland#R##N##R##N#Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html#R##N##R##N#No. of lines in distributed program, including test data, etc.: 7653#R##N##R##N#No. of bytes in distributed program, including test data, etc.: 85283#R##N##R##N#Distribution format: tar.gz#R##N##R##N#Programming language: Fortran 90.#R##N##R##N#Computer: Any supporting a FORTRAN compiler.#R##N##R##N#Operating system: Any supporting a FORTRAN compiler.#R##N##R##N#RAM: a few MB#R##N##R##N#Classification: 4.7.#R##N##R##N#Nature of problem: The computation and inversion of gamma and chi-square cumulative distribution functions (central and noncentral) as ll as the computation of the error and gamma functions is needed in many problems of applied and mathematical physics.#R##N##R##N#Solution method: The algorithms use different methods of computation depending on the range of parameters: asymptotic expansions, quadrature methods, etc.#R##N##R##N#Restrictions: \u00a0 In the inversion of the central gamma/chi-square distribution functions, very small input function values P\u03bc(x,y)P\u03bc(x,y), Q\u03bc(x,y)Q\u03bc(x,y) (lor than 10\u221215010\u2212150) are not admissible.#R##N##R##N#The admissible input parameter ranges for computing the noncentral cumulative gamma distribution functions P\u03bc(x,y)P\u03bc(x,y), Q\u03bc(x,y)Q\u03bc(x,y) in standard IEEE double precision arithmetic are 0\u2264x\u226410,0000\u2264x\u226410,000, 0\u2264y\u22640\u2264y\u226410,000,0.5\u2264\u03bc\u226410,000,0.5\u2264\u03bc\u2264 10,000 and the related parameter ranges for the noncentral chi-square cumulative distribution function. In the inversion of the noncentral gamma/chi-square distribution functions, very small input function values P\u03bc(x,y)P\u03bc(x,y), Q\u03bc(x,y)Q\u03bc(x,y) (lor than 10\u22122510\u221225 and 10\u22123510\u221235, respectively) are not admissible.#R##N##R##N#Running time: It varies depending on the function and the parameter range. The test provided takes milliseconds."}]