CalIncLapInt: Evaluation of Analytical Formulae for the Incomplete Laplace...

In frmqa: The Generalized Hyperbolic Distribution, Related Distributions and Their Applications in Finance

Description

Evaluates analytical formulae for the lower and upper incomplete Laplace integral in terms of the complementary error function.

Usage

   CalIncLapInt(lambda, a = 1, b = 1, x = 1, lower = TRUE, bit = 200)   

Arguments

lambda	Order λ = \pm(j + \frac{1}{2}) with j = 0, 1, 2, ….
a	Argument a > 0.
b	Argument b >= 0.
x	Limit of the incomplete Laplace integral.
lower	Logical. Lower incomplete Laplace integral is returned if TRUE.
bit	Precision bit. A positive integer greater or equal 100.

Details

The lower and upper extended Laplace integrals are given by

\widehat L_{λ}(x, a, b) = \int_0^{x} e^{-(a ξ^2 + b/ξ^2)}ξ^{-2λ - 1}\; dξ ,

and

\widetilde L_{λ}(x, a, b) = \int_x^{∞} e^{-(a ξ^2 + b/ξ^2)}ξ^{-2λ - 1}\; dξ

respectively. Calculation is performed using multiple precision floating-point reliably or MPFR-numbers instead of the default floating-point number in R, which ensure accuracy is at least 100 bit.

Author(s)

Thanh T. Tran [e-mail]

References

Hankin, R.K.S (2006) Additive integer partitions in R. Journal of Statistical Software, Code Snippets, 16.

Maechler, M Rmpfr: R MPFR - Multiple Precision Floating-Point Reliable. R package version 0.5-0, http://CRAN.R-project. org/package=Rmpfr.

Olver, F.W.J., Lozier, D.W., Boisver, R.F. and Clark, C.W (2010) Handbook of Mathematical Functions. New York: National Institute of Standards and Technology, and Cambridge University Press.

Tran, T. T., Yee, W.T. and Tee, J.G (2012) Formulae for the Extended Laplace Integral and Their Statistical Applications. Working Paper.

Watson, G.N (1931) A Treatise on the Theory of Bessel Functions and Their Applications to Physics. London: MacMillan and Co.

See Also

besselK_inc_err, gamma_inc_err, pgig

frmqa documentation built on May 2, 2019, 12:22 p.m.