Any difference in their basic mathematical formula ? Like p= Cov (X,Y)/ ((var X * var Y)^1/2)?
No, Cross correlation is another name of the Pearson correlation coefficient.
Seyed Mahdi Amir Jahanshahi Unfortunately you are incorrect. A correlation coefficient measures correlation between two ordinary variables say x, y. A cross correlation coefficient usually measures the correlation between two time series say x(t), y(t). full details at https://www.google.com/search?q=correlation&rlz=1C1CHBF_enUS874US874&oq=correlation&aqs=chrome..69i57.8275j0j1&sourceid=chrome&ie=UTF-8
and
https://www.google.com/search?rlz=1C1CHBF_enUS874US874&ei=lKg-XslpyNW0BvuFk4AI&q=cross+correlation&oq=cross+correlation&gs_l=psy-ab.3..0l3j0i7i30j0l6.156025.159162..162671...0.2..0.308.684.5j3-1......0....1..gws-wiz.......0i71j0i13.tj0BSOoOXGo&ved=0ahUKEwjJg7K--cHnAhXIKs0KHfvCBIAQ4dUDCAs&uact=5
Please notice that t can be more general than time as we think of it in most time series applications. Best, David Booth
Dear David
You are right. Since Ismail asked a simple question, I tried to write a simple answer for better understanding the correlation notion without considering time series situation. As you mentioned correctly, a cross correlation coefficient usually measures the correlation between two time series say x(t), y(t).
Thank you so much for your explanation. David Eugene Booth and Seyed Mahdi Amir Jahanshahi, I am done with it. I have another small issue. I hope you might help. Kindly Read it is really interesting specially for you stat people.
I am working on an equation where i need E[H^4]
They have given in paper that E[H] = 0 , E[H^2] = N/2 now how do I find E[H^4] =? I don't know Pdf too, They say it Channel gains H follows zero mean complex Gaussian random variables with variance of N/2 per real dimension.
I found this on Wikipedia, In middle of this page we have E[Z^4] = var [Z^2] + E[Z^2]? May be this helps me. How do I find var[Z^2] ? https://en.wikipedia.org/wiki/Kurtosis
Isn't that interesting to find Var[X^2] ? Not many people in literature know about what variance to the second power actually mean.
PS: Nevertheless My aim is E[X^4] ...
https://en.wikipedia.org/wiki/Kurtosis
E[X^4] = var [Z^2] + E[Z^2]? How do I find var[Z^2] ?
Isn't that quite interesting for stats people.
Look at this link: https://www.google.com/search?q=Moments+of+X%5E4&oq=Moments+of+X%5E4&aqs=chrome..69i57j33.172660j0j8&sourceid=chrome&ie=UTF-8 This answer box doesn't let me write math notation. Somewhere in your university is a mathematical statistician. Take this question and answer to that persion along with the above link and ask him/her what to do. This is not something that I would expect someone without a course entitled, Mathematical Statistics I to be able to do. If you cannot find such a person see this link: https://b-ok.cc/book/1226537/9bcd1a
This link gives you a free pdf reader: https://get.adobe.com/reader/
Start by looking up the term MOMENTS
May the force be with you. David Booth PS all of this assumes Mathematics thru Calculus II. Whoever told you to read what ever you are reading without this background is an idiot. You may quote me. David Booth
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