Sum of One-Dimensional Functions
add(f, lower, upper, ..., abs.tol = .Machine$double.eps)an R function taking a numeric first argument and returning a numeric vector of the same length.
the lower limit of sum. Can be infinite.
the upper limit of sum. Can be infinite.
additional arguments to be passed to f.
absolute accuracy requested.
This function returns the sum value.
# Poisson expected value
add(f=function(x, lambda) x*dpois(x, lambda), lower=0, upper=Inf,
lambda=7.5)
#> $value
#> [1] 7.5
#>
#> $abs.error
#> [1] 0
#>
# Binomial expected value
add(f=function(x, size, prob) x*dbinom(x, size, prob), lower=0, upper=20,
size=20, prob=0.5)
#> $value
#> [1] 10
#>
#> $abs.error
#> [1] 0
#>
# Examples with infinite series
add(f=function(x) 0.5^x, lower=0, upper=100) # Ans=2
#> $value
#> [1] 2
#>
#> $abs.error
#> [1] 0
#>
add(f=function(x) (1/3)^(x-1), lower=1, upper=Inf) # Ans=1.5
#> $value
#> [1] 1.5
#>
#> $abs.error
#> [1] 2.435019e-144
#>
add(f=function(x) 4/(x^2+3*x+2), lower=0, upper=Inf, abs.tol=0.001) # Ans=4.0
#> $value
#> [1] 3.986799
#>
#> $abs.error
#> [1] 4.371298e-05
#>
add(f=function(x) 1/(x*(log(x)^2)), lower=2, upper=Inf, abs.tol=0.000001) # Ans=2.02
#> $value
#> [1] 2.002743
#>
#> $abs.error
#> [1] 9.999232e-07
#>
add(f=function(x) 3*0.7^(x-1), lower=1, upper=Inf) # Ans=10
#> $value
#> [1] 10
#>
#> $abs.error
#> [1] 7.1061e-47
#>
add(f=function(x, a, b) a*b^(x-1), lower=1, upper=Inf, a=3, b=0.7) # Ans=10
#> $value
#> [1] 10
#>
#> $abs.error
#> [1] 7.1061e-47
#>
add(f=function(x, a=3, b=0.7) a*b^(x-1), lower=1, upper=Inf) # Ans=10
#> $value
#> [1] 10
#>
#> $abs.error
#> [1] 7.1061e-47
#>