Precision bit. A positive integer greater or equal 100.
Details
The GIG is given by
GIG(w|λ, χ, ψ) =
frac{(ψ/χ)^{λ/2}}{2 K_{λ}
(√{χψ})},e^{-≤ft(χ w^{-1} ,+,
ψ w
ight)/2}, w^{λ - 1} qquad w >0.
This distribution has been used in hydrology, reliability
analysis, extreme events modelling in
financial risk management, and as the mixing
distribution to form the family of generalized hyperbolic
distributions in statistics.
Note
This function allows for accurate evaluation of distribution
functions (c.d.f and c.c.d.f) of the family of GIG distributions
with λ = pm(j + frac{1}{2}). Currently,
only c.d.f of inverse Gaussian
distribution, λ = -frac{1}{2}, is available.
Barndorff-Nielsen, O. E (1977) Exponentially decreasing
distributions for the logarithm of particle size.
Proceedings of the Royal Society of London.
Series A, 353, 401–419.
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
CalIncLapInt, gamma_inc_err
Examples
## Accuracy tests
q <- 1
chi <- 3
psi <- 15
lambda <- 5/2
lowerTail <- sapply(lambda, function(w.)
pgig(q, chi, psi, lambda = w., lower.tail = TRUE, 200))
upperTail <- sapply(lambda, function(w.)
pgig(q, chi, psi, lambda = w., lower.tail = FALSE, 200))
## sum of two parts equals 1
(lowerTail + upperTail)