1
$\begingroup$

Basically the title. I can't seem to find any solution for this.

I have the mean, variance or the second central moment and third central moment and third raw moment. I need to find the fourth raw moment.

$\endgroup$
2
  • $\begingroup$ There are universal inequalities among these moments but that's all one can say. $\endgroup$
    – whuber
    Commented Apr 3 at 21:25
  • $\begingroup$ Microsoft's beta version of its "Copilot" chatbot includes in its response (using your full title as the prompt) this passage: "Unfortunately, there isn’t a direct formula to calculate the fourth raw moment from the variance and the third central moment. These are different statistical measures that capture different aspects of the data distribution. " $\endgroup$
    – whuber
    Commented Apr 3 at 21:34

1 Answer 1

1
$\begingroup$

Unfortunately this is not possible. For example, consider $X_1$ a unit normal distribution (zero mean, and variance=1) and $X_2$ a distribution which is $\pm 1$ with probability 50 percent. Both of these have the same mean, second moment, and third moment, but the 4th moment of $X_1$ is equal to 3, while the 4th moment of $X_2$ is equal to 1.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.