pgig
(Package: frmqa) :
Accurate Evaluation of Tail Probabilities of the Generalized
Evaluates analytical formulae for distribution functions of the generalized inverse Gaussian distribution (GIG) by calling function besselK_inc_err .
● Data Source:
CranContrib
● Keywords:
● Alias: pgig
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gamma_inc_err
(Package: frmqa) :
Accurate Calculation of the Incomplete Gamma Functions
Evaluates explicit formulae for the lower and upper incomplete gamma functions in terms of complementary error function by calling CalIncLapInt .
● Data Source:
CranContrib
● Keywords:
● Alias: gamma_inc_err
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This package comprises of R and C++ functions which deal with issues relating to financial risk management and quantitative analysis by applying uni- and multi-variate generalized hyperbolic and related distributions. These issues are approached from both directions: analytical (i.e., deriving and programing analytic formulae) and numerical. Note that the latter appears to be the only approach currently used in practice because of the intractability of these families of distributions, which is caused by the presence of the modified Bessel function of the third kind BesselK K_{λ}(z), in their density functions. In this package, the naming of special functions and their related functions (e.g., BesselK and incomplete BesselK functions) follows the convention used in the R package gsl.
● Data Source:
CranContrib
● Keywords:
● Alias: frmqa, frmqa-package
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derivErfc
(Package: frmqa) :
Calculate High Order Derivatives of Composite Functions
Symbolically calculates high order derivative of composite functions involving complementary error function and exponential function.
● Data Source:
CranContrib
● Keywords:
● Alias: derivErfc
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CalIncLapInt
(Package: frmqa) :
Evaluation of Analytical Formulae for the
Evaluates analytical formulae for the lower and upper incomplete Laplace integral in terms of the complementary error function.
● Data Source:
CranContrib
● Keywords:
● Alias: CalIncLapInt
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besselK_inc_ite
(Package: frmqa) :
Approximation of the Incomplete BesselK Function Iteratively
Approximates incomplete modified Bessel function using the algorithm provided by Slevinsky and Safouhi (2010) and gives warnings when loss of accuracy or an exception occurs.
● Data Source:
CranContrib
● Keywords:
● Alias: besselK_inc_ite
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besselK_inc_err
(Package: frmqa) :
Calculation of the Incomplete BesselK Functions in Terms of the Complementary Error Functions
Calculates incomplete BesselK functions by evaluating explicit expressions for the lower and upper incomplete BesselK in terms of the complementary error function by calling CalIncLapInt .
● Data Source:
CranContrib
● Keywords:
● Alias: besselK_inc_err
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besselK_inc_clo
(Package: frmqa) :
Exact Calculation of the Incomplete BesselK Function
Calculates upper and lower incomplete functions of the modified Bessel function of the third kind K_{λ}(z), see details, using closed-form formulae.
● Data Source:
CranContrib
● Keywords:
● Alias: besselK_inc_clo
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Bell
(Package: frmqa) :
Bell Coefficients Calculation
This function calculates Bell coefficients as described on p.134–139 of Comtet (1974) for calculating high order derivative of composite function f(g(x)) wrt x, say.
● Data Source:
CranContrib
● Keywords:
● Alias: Bell
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