Hello, I am facing problem in finding the pdf of Z= AB+CD, where A, B, C, D are independent normal random variables with zero mean and uneqaul variances. I could bale to find out the pdf's of each term (i.e. AB or CD). It is a well known result that AB has a pdf of modified Bessel function of the second kind. If we add two random variables having the pdf of " modified Bessel function of the second kind.", assuming both are independent, I am unable to get the final expression . Since it involves the convolution of two " modified Bessel function of the second kind.". Is there any standard expression for finding the pdf of z= AB+CD? Best Regards, -SaiRamesh.
pdf of product of two dependent rv
Started by ●August 24, 2006
Reply by ●August 25, 20062006-08-25
sairamesh@gmail.com wrote:> Hello, > I am facing problem in finding the pdf of Z= AB+CD, > where A, B, C, D are independent normal random variables with zero > mean and uneqaul variances. > I could bale to find out the pdf's of each term (i.e. AB or CD). It is > a well known result that AB has a pdf of modified Bessel function of > the second kind. > If we add two random variables having the pdf of " modified Bessel > function of the second kind.", assuming both are independent, I am > unable to get the final expression . Since it involves the convolution > of two " modified Bessel function of the second kind.". > Is there any standard expression for finding the pdf of > z= AB+CD? > Best Regards, > -SaiRamesh.I think you can numerically obtain the pdf of z (by plotting in matlab) but I do not think any analytical result can be obtained by convolving 2 Bessel functions