helperTrapezoidRule: Helper function to compute the integrals in each interval.

In RVCompare: Compare Real Valued Random Variables

Helper function to compute the integrals in each interval.

Description

Computes a vector in which each index i is the integral in the interval (0, p[[i]]) of the function described by the densityVec Uses the trapezoidal rule # https://en.wikipedia.org/wiki/Trapezoidal_rule to integrate the values in the interval [0,1]. The x corexponding to the values (the f(x)) are assumed to be equidistantly distributed in the interval, where the x corresponding to densitiesVec[[1]] is located in 0.0 andthe x corresponding to densitiesVec[[length(densitiesVec)]] is located in 1.0

Usage

helperTrapezoidRule(densitiesVec)

Arguments

densitiesVec

the vector of values to be integrated

Value

a vector in which each index i is the integral in the interval (0, p[[i]]). Consequently, the first element in the vector returned will be 0, since p[[1]] = 0 does not exist.

Examples

### Example 1 ###
helperTrapezoidRule(c(1,2,3,3,3,4,5,9,3,0,1))
# 0.00 0.15 0.40 0.70 1.00 1.35 1.80 2.50 3.10 3.25 3.30

RVCompare documentation built on Aug. 21, 2023, 5:13 p.m.