# Calculate SD, Skewness and Kurtosis for PDF

• Mar 10th 2013, 03:09 PM
csidiras
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
• Mar 10th 2013, 10:50 PM
chiro
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).
• Mar 11th 2013, 11:16 AM
csidiras
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
• Mar 11th 2013, 07:38 PM
chiro
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.