Hi!
I'm using the fitdist() function from the package fitdistrplus.
It works great and estimates the parameters needed.
But what if I want to estimate the mathematical expectation of the random variable? How to process the results of the fitdist() function to estimate the mathematical expectation? I would be extremely grateful if someone could provide me with the R code for that.
Thanks a lot!
Dear Andrey Davydenko,
From your question it is not entirely clear what you want to achieve. Is it what I show in the example code below? Maybe you can refine your question?
Kind regards,
Pepijn
require(fitdistrplus)
# generate some normally distributed data
data
Dear Pepijn de Vries,
Thank you for your answer. You're right - it may be not very clear as to what needs to be found.
The problem is that sometimes you have distributions (e.g., Weibull) where the mean is not exactly described by some parameter, but instead it is found using some expression that is specific to the distribution under interest.
I'd like to have a more general code that will work with any distribution (if its mean is defined).
Your code works great. But suppose we have the following code:
fit
I think I already answered this in another post, but well...
E(X) = intergal of x*p(x) dx
So all you need is to integrate the product x*p(x) over the domain of X. You can use the R-function integrate(.) for this purpose.
Thanks a lot - I got the general idea. The question is how it would be better to implement it in R - how many bins to use, etc?
Read the documentation about the function integrate(.) and how it does numerical integration. There is no need to specify bins:
from R help ?integrate:
If one or both limits are infinite, the infinite range is mapped onto a finite interval.
For a finite interval, globally adaptive interval subdivision is used in connection with extrapolation by Wynn's Epsilon algorithm, with the basic step being Gauss–Kronrod quadrature.
So further you may have a look at
Hazewinkel, Michiel, ed. (2001), "Gauss–Kronrod quadrature formula", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
Piessens, R; Branders, M (1974), "A Note on the Optimal Addition of Abscissas to Quadrature Formulas of Gauss and Lobatto", Mathematics of Computation, 28(125): 135–139
and
R. Piessens, E. deDoncker–Kapenga, C. Uberhuber, D. Kahaner (1983) Quadpack: a Subroutine Package for Automatic Integration; Springer.
Thanks! I see that it can integrate some abstract function.
But how to extract the function I need to integrate from the output of the fitdist() function? How to find the x*p(x) in order to specify it as the input parameter for the integrate() function?
Would it be easy to write an R code to solve the task specified in the question?
# use the parameter estimates from the fitdist() function and calculate the mean
# i.e.
# # the Weibull distribution has parameters : h = shape, s = scale and l = location
# its mean is:
fit
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