Sum of One-Dimensional Functions

add(f, lower, upper, ..., abs.tol = .Machine$double.eps)

Arguments

f: an R function taking a numeric first argument and returning a numeric vector of the same length.
lower: the lower limit of sum. Can be infinite.
upper: the upper limit of sum. Can be infinite.
...: additional arguments to be passed to f.
abs.tol: absolute accuracy requested.

Value

This function returns the sum value.

Author

Freddy Hernandez, fhernanb@unal.edu.co

Examples

# 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
#>