In many situations the values that a random variable, X, can take on is restricted, for example precipitation data [0,inf), that is f(x) = 0 for x < 0. We say that the support of f(x) is [0,inf).

We need to be modified when f(x) has bounded support. The simplest method of solving this problem is use a log transformation.

The idea is to estimate the probability density function (PDF) of a transformed random variable Y = t(X) which has unbounded support.

I have carries out the following steps:

(a) Transform the observations yi = t(xi), i = 1, 2,... , n.

(b) Apply the kernel method to estimate the PDF g(y) that is the density of Y = log(X).

My problem is how to estimate f(x) via kernel smooth of log(values) by using R?


  • $\begingroup$ Is this a question about the mathematical relationship between the distributions of $X$ and $\log(X)$, or is there more to it? If there's more, could you describe explicitly what you are looking for? $\endgroup$
    – whuber
    Feb 7 '18 at 14:17
  • $\begingroup$ This question ask about how to estimate density function for bounded variable [0,inf) by using Gaussian kernel. $\endgroup$
    – Rosbert
    Feb 8 '18 at 0:00
  • $\begingroup$ Please edit your post to include that information. Currently it does not articulate any clear question. In the meantime, I have found a thread that asks and answers the question you pose in your comment. The answer by Gavin Simpson is particularly good. $\endgroup$
    – whuber
    Feb 8 '18 at 14:23