wedge: Computes wedge probabilities
In rcqls/wedge: Computing wedge probabilities using R and Rcpp

Description Usage Arguments Details Value Author(s) References Examples

Computes the probability for a standard Brownian motion to stay in a wedge of the plane limited by two straight lines, given by their slopes and intercepts.

1	wedge(a1, b1, a2, b2, N = 3, lower.tail = TRUE, type = c("R","Rcpp","RcppParallel"), nb.threads)

`a1`	vector of numeric: slopes of lower boundaries
`b1`	vector of numeric: intercepts of lower boundaries
`a2`	vector of numeric: slopes of upper boundaries
`b2`	vector of numeric: intercepts of upper boundaries
`N`	integer: number of terms to be computed in each series
`lower.tail`	logical: if `TRUE` the probabilities to stay inside the wedges are returned; if `FALSE` the exit probabilities are returned.
`type`	character: type of function to wrap
`nb.threads`	integer: number of threads

Wedge probabilities are invariant through symmetry: wedge(a1,b1,a2,b2) returns the same as wedge(b1,a1,b2,a2) and wedge(a2,b2,a1,b1). Depending on N a threshold is computed. If (a1+a2)*(b1+b2)/4 is above the threshold, N terms of Doob's formula are computed. If it is below the threshold, N terms of the theta-function transform are computed.

a vector of wedge probabilities.

R\'emy Drouilhet and Bernard Ycart

B. Ycart and R. Drouilhet (2016) Computing wedge probabilities. arXiv:1612.05764

# random wedges
a1 <- 10*runif(10^6)^2
b1 <- 10*runif(10^6)^2
a2 <- 10*runif(10^6)^2
b2 <- 10*runif(10^6)^2
# wedge probabilities, 3 term approximation
pw3 <- wedge(a1,b1,a2,b2)
summary(pw3)
# wedge probabilities, 4 term approximation
pw4 <- wedge(a1,b1,a2,b2,N=4)
summary(abs(pw3-pw4))
#  exit probabilities, 3 term approximation
length(which(pw3==1))
pw3m <- wedge(a1,b1,a2,b2,lower.tail=FALSE)
summary(pw3+pw3m)