how to create Chi squared distribution using mean and variance?

Hello,

I have the mean and the variance for a Chi squared distribution.

I want to create this Chi squared distribution using the mean and the variance that I have, can I ?

Thank you.

Answer 1

[Vladimir Sovkov]

see https://www.mathworks.com/help/stats/chi-square-distribution-1.html

[Khoder Makkawi]

Thanks Vladimir but I already tried all of this equations and I am not able to use the mean to create the Chi squared distribution. The only way that I can do it with these equations by using the degree of freedom which is the variance/2.

But I need to use the mean for my Chi squared distribution.

[Vladimir Sovkov]

Why "variance/2"? The variance must be equal to the number of the degrees of freedom in , isn't it?

[Khoder Makkawi]

Sorry I am not sure. But the variance that I have is 0.01 for my data so the number of degree of freedom in my data is 0.01 !!!!

[Vladimir Sovkov]

You probably mean the variance of the normally distributed variable x. Then , , and its variance is the number of the degrees of freedom (number of independent measurements of x) n, which is the integer number. What do you really have, and what do you want?

[Khoder Makkawi]

What I have is the mean and the variance of the distributed variable x.

What I want is to plot the Chi squared distribution that represents these data.

But I don't know how to do that using the mean and the variance.

[Vladimir Sovkov]

If you want to approximate your x with the variance of 0.01 via chi^2, then it is quite impossible--the variance of chi^2 must be integer. If you want to construct the new chi^2 variable based on your x implying it is normally distributed - see my earlier comment.