Simple Monte-Carlo integration

Compute an approximation of the integral of the function f(x) with respect to dx in the range [a, b] by Monte-Carlo integration using uniform sampling.

mc_int(x_range, fun, B, seed = 1291)

Arguments

x_range	A vector of dimension 2 used to denote the integration region of interest, i.e. [a, b].
fun	A string containing the function to integrated. It is assumed that x is used as the variable of interest.
B	A numeric (integer) used to denote the number of simulation.
seed	A numeric used to control the seed of the random number generated by this function.

Value

A list containing the following attributes:

I

Estimated value of the integral

var

Estimated variance of the estimator

Examples

mc_int(x_range = c(0,1), fun = "x^2", B = 10^5)
#> $I
#> [1] 0.3322249
#> 
#> $var
#> [1] 8.882763e-07
#> 
#> $fun
#> [1] "x^2"
#> 
#> $x_range
#> [1] 0 1
#> 
#> $B
#> [1] 1e+05
#> 
#> attr(,"class")
#> [1] "MCI"
mc_int(x_range = c(0,1), fun = "x^2*sin(x^2/pi)", B = 10^5)
#> $I
#> [1] 0.06281515
#> 
#> $var
#> [1] 7.002655e-08
#> 
#> $fun
#> [1] "x^2*sin(x^2/pi)"
#> 
#> $x_range
#> [1] 0 1
#> 
#> $B
#> [1] 1e+05
#> 
#> attr(,"class")
#> [1] "MCI"