rdistributionvarianceskewkurtosis

Estimating moments from a distribution function

I have a non-normal distribution function which I want to calculate it's moments (mean, variance, skewness, and kurtosis). The packages I know are e1071 and moments which calculate the moments for a vector of discrete values. Is there a package that estimates moments for a continuous distribution function? As an example assume I have this distribution:

tmp <- runif(100,-10,10)
PDFdata <- density(tmp , kernel = "gaussian")
PDF <- splinefun(PDFdata$x , PDFdata$y)

Now I want to calculate:

enter image description here

Solution

  • You can use function integrate to compute the moments.
    All you need is to define an integrand, which I call int in the code below.

    First, I will make the results reproducible by setting the RNG seed.

    set.seed(6126)    # Make the results reproducible

tmp <- runif(100,-10,10)
PDFdata <- density(tmp , kernel = "gaussian")
PDF <- splinefun(PDFdata$x , PDFdata$y)

int <- function(x, c = 0, g = PDF, n = 1) (x - c)^n * g(x)

integrate(int, lower = -15, upper = 15, n = 1)
#-0.3971095 with absolute error < 7.8e-06

integrate(int, lower = -15, upper = 15, n = 2)
#35.76295 with absolute error < 0.0012

plot(PDFdata)
curve(PDF, -15, 15, add = TRUE, col = "blue", lty = "dashed")

    density plot