# Thread: Calculate SD, Skewness and Kurtosis for PDF

1. ## Calculate SD, Skewness and Kurtosis for PDF

Hello everybody

How can I calculate standard deviation, skewness and kurtosis once I
know the PDF of a distribution?

Thanx

Sidiras Chris

2. ## Re: Calculate SD, Skewness and Kurtosis for PDF

Hey csidiras.

You can either calculated the moment generating function of the PDF and then use the derivative rules to calculate all the individual moments or you can calculate the individual moments using the expectation formula.

Recall that E[g(X)] = Integral (over the real line) g(x)f(x)dx where f(x) is the PDF function.

If the distribution is not continuous, then replace an integral with a sigma (i.e. summation).

3. ## Re: Calculate SD, Skewness and Kurtosis for PDF

Hi Chiro

I know I am inexcusable but what stands for g(x)?
I am familiar with the formula
E(x)= Integral x f(x) dx

Sidiras Chris

4. ## Re: Calculate SD, Skewness and Kurtosis for PDF

g(x) is any function of x and when g(x) = x, then you are calculating the mean of the random variable X.