Logical. Lower incomplete gamma function is
calculated if TRUE.
bit
Precision bit. A positive integer greater or equal 100.
Details
The lower incomplete gamma function is given by
γ(x, λ) = int_0^x e^{-t},t^{λ - 1}, dt.
Note
This function evaluates formulae in terms of complementary
error function for γ(x, λ) and its
upper counterpart when λ = pm(j + frac{1}{2}).
Currently, such formulae are only available when
λ = pmfrac{1}{2}.
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 (2011) Some Problems Concerning the
Generalized Hyperbolic and Related Distributions. Ph.D Thesis.
The University of Auckland, New Zealand.
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, besselK_inc_clo, pgig
Examples
## Accuracy tests
x <- 3
lambda <- 3/2
lower <- sapply(lambda, function(w.)
gamma_inc_err(x, lambda = w., 200, lower = TRUE))
upper <- sapply(lambda, function(w.)
gamma_inc_err(x, lambda = w., 200, lower = FALSE))
## sum of two parts
(lower + upper)
## equals the whole function
(gamma(lambda))