Reply by Nishit Jain March 6, 20062006-03-06
      Thankyou so much. I have got the answer to both of ours problems. 
    You are correct, its simply the convolution of the two pdf's. Also for  the
problem of a^4, the derivation for its pdf is given in the book  called :
"Probability with Random Processes with Applications to Signal 
Processing" by Henry Stark and John W. Woods on page 131.
  
    Thankyou once again for your response.
    
    Nishit
Nandan Das <nandan@nand...> wrote:In  general, if Z = X + Y and X and Y
are independent, then pdf Z is the  convolution of the pdfs of X and Y.  Is that
easy to find for your  distributions of chi-sq and GAussian?  I don't know..but
you can  (in theory) find it.  

Nandan

On 3/5/06, Nishit Jain <bignishit@bign...> wrote:  Thanks for the reply
but not exactly I am looking for that !! I  am  looking for a case where X is
chi square and Y is  gaussian distributed  and I want the distribution of
Z(=X+Y).  And my colleague Vimal is  looking for a case of X^4 where X  is
Gaussian.  

    Can you give me some reference where I may find any similar discussion?

    Nishit

Bavithi <bavithi@bavi...>  wrote:If  X & Y are gaussian distributed,
their envolopes  are Rayleigh  distributed & variance of Z(=X+Y) should
be  exponential. Is this  what you are looking for?  

  On 3/3/06, Nishit Jain <bignishit@bign...> wrote:       Hi Vimal and
all,

  I  am  also dealing with a similar  problem, but my problem  is  slightly
different. I have a function of  RV  (Random  Variable) which is sum of squares
of  the Gaussian RV.  

   In literature I have found that the sum  of  squares of Gaussian RV is a 
Chi-Square  Distribution. I dont  exactly know about the fourth power  of 
Gaussian !!!

   Now my problem is I have a random variable Z :  

   Z = X + Y, where X = Non-zero mean Chi-Square and Y = non-zero mean Gaussian
RV.

   Now I am wondering, what would be the distribution of Z ?

   Can anybody help us out in this matter?

   Thanks and regards,  
   Nishit

Vimal <vimal125@vima...> wrote:  Dear All,
	In my work I am using MATLAB function RANDN to generate zero mean and
variance 1 random numbers. I know the PDF for this is Gaussian which  
is well defined in literature and I can find loads of information on it.

But in my work I happened to get four different Gaussian numbers
multiplied together i.e.:

a4 = a*a*a*a (where a is a Complex Gaussian number)  

I am interested in analyzing the statistics of a4. Can anyone please
tell me what would be the PDF of such random numbers i.e. a4.

The shape I am getting for PDF from MATLAB looks similar to CHI-SQUARE
    and RAYLIEGH DISTRIBUTION. But I had a look into CHI-SQUARE and
RAYLEIGH distributions and not completely convinced that a4 is
CHI-SQUARE or RAYLEIGH distributed.

Could someone please help me out here, I would really appreciate it.  

Thank you.
	
Reply by Nandan Das March 6, 20062006-03-06
In general, if Z = X + Y and X and Y are independent, then pdf Z is the
convolution of the pdfs of X and Y.  Is that easy to find for your
distributions of chi-sq and GAussian?  I don't know..but you can (in theory)
find it.

Nandan

On 3/5/06, Nishit Jain <bignishit@bign...> wrote:
>
> Thanks for the reply but not exactly I am looking for that !! I
> am  looking for a case where X is chi square and Y is gaussian
> distributed  and I want the distribution of Z(=X+Y). And my colleague
Vimal
> is  looking for a case of X^4 where X is Gaussian.
>
>     Can you give me some reference where I may find any similar
> discussion?
>
>     Nishit
>
> Bavithi <bavithi@bavi...> wrote:If  X & Y are gaussian
distributed,
> their envolopes are Rayleigh  distributed & variance of Z(=X+Y)
should be
> exponential. Is this  what you are looking for?
>
>   On 3/3/06, Nishit Jain <bignishit@bign...> wrote:       Hi Vimal
and
> all,
>
>   I  am also dealing with a similar  problem, but my problem is  slightly
> different. I have a function of RV  (Random  Variable) which is sum of
> squares of the Gaussian RV.
>
>    In literature I have found that the sum of  squares of Gaussian RV is
> a  Chi-Square Distribution. I dont  exactly know about the fourth power
> of  Gaussian !!!
>
>    Now my problem is I have a random variable Z :
>
>    Z = X + Y, where X = Non-zero mean Chi-Square and Y = non-zero mean
> Gaussian RV.
>
>    Now I am wondering, what would be the distribution of Z ?
>
>    Can anybody help us out in this matter?
>
>    Thanks and regards,
>    Nishit
>
> Vimal <vimal125@vima...> wrote:  Dear All,
>
>
> In my work I am using MATLAB function RANDN to generate zero mean and
> variance 1 random numbers. I know the PDF for this is Gaussian which
> is well defined in literature and I can find loads of information on it.
>
> But in my work I happened to get four different Gaussian numbers
> multiplied together i.e.:
>
> a4 = a*a*a*a (where a is a Complex Gaussian number)
>
> I am interested in analyzing the statistics of a4. Can anyone please
> tell me what would be the PDF of such random numbers i.e. a4.
>
> The shape I am getting for PDF from MATLAB looks similar to CHI-SQUARE
>   and RAYLIEGH DISTRIBUTION. But I had a look into CHI-SQUARE and
> RAYLEIGH distributions and not completely convinced that a4 is
> CHI-SQUARE or RAYLEIGH distributed.
>
> Could someone please help me out here, I would really appreciate it.
>
> Thank you.
>
	
Reply by Nishit Jain March 6, 20062006-03-06
Thanks for the reply but not exactly I am looking for that !! I am  looking
for a case where X is chi square and Y is gaussian distributed  and I want the
distribution of Z(=X+Y). And my colleague Vimal is  looking for a case of
X^4 where X is Gaussian.
    
    Can you give me some reference where I may find any similar discussion? 
    
    Nishit

Bavithi <bavithi@bavi...> wrote:If  X & Y are gaussian distributed,
their envolopes are Rayleigh  distributed & variance of Z(=X+Y) should
be exponential. Is this  what you are looking for? 

  On 3/3/06, Nishit Jain <bignishit@bign...> wrote:       Hi Vimal and
all,

  I  am also dealing with a similar  problem, but my problem is  slightly
different. I have a function of RV  (Random  Variable) which is sum of squares
of the Gaussian RV.  

   In literature I have found that the sum of  squares of Gaussian RV is a 
Chi-Square Distribution. I dont  exactly know about the fourth power of 
Gaussian !!!

   Now my problem is I have a random variable Z :  

   Z = X + Y, where X = Non-zero mean Chi-Square and Y = non-zero mean Gaussian
RV.

   Now I am wondering, what would be the distribution of Z ?

   Can anybody help us out in this matter?

   Thanks and regards,  
   Nishit

Vimal <vimal125@vima...> wrote:  Dear All,
	In my work I am using MATLAB function RANDN to generate zero mean and
variance 1 random numbers. I know the PDF for this is Gaussian which  
is well defined in literature and I can find loads of information on it.

But in my work I happened to get four different Gaussian numbers
multiplied together i.e.:

a4 = a*a*a*a (where a is a Complex Gaussian number)  

I am interested in analyzing the statistics of a4. Can anyone please
tell me what would be the PDF of such random numbers i.e. a4.

The shape I am getting for PDF from MATLAB looks similar to CHI-SQUARE
  and RAYLIEGH DISTRIBUTION. But I had a look into CHI-SQUARE and
RAYLEIGH distributions and not completely convinced that a4 is
CHI-SQUARE or RAYLEIGH distributed.

Could someone please help me out here, I would really appreciate it.  

Thank you.
	
Reply by Bavithi March 5, 20062006-03-05
If X & Y are gaussian distributed, their envolopes are Rayleigh
distributed
& variance of Z(=X+Y) should be exponential. Is this what you are
looking
for?

On 3/3/06, Nishit Jain <bignishit@bign...> wrote:
>
>      Hi Vimal and all,
>
>   I am also dealing with a similar  problem, but my problem is slightly
> different. I have a function of RV  (Random Variable) which is sum of
> squares of the Gaussian RV.
>
>    In literature I have found that the sum of squares of Gaussian RV is
> a  Chi-Square Distribution. I dont exactly know about the fourth power
> of  Gaussian !!!
>
>    Now my problem is I have a random variable Z :
>
>    Z = X + Y, where X = Non-zero mean Chi-Square and Y = non-zero mean
> Gaussian RV.
>
>    Now I am wondering, what would be the distribution of Z ?
>
>    Can anybody help us out in this matter?
>
>    Thanks and regards,
>    Nishit
>
> Vimal <vimal125@vima...> wrote:  Dear All,
>
>
> In my work I am using MATLAB function RANDN to generate zero mean and
> variance 1 random numbers. I know the PDF for this is Gaussian which
> is well defined in literature and I can find loads of information on it.
>
> But in my work I happened to get four different Gaussian numbers
> multiplied together i.e.:
>
> a4 = a*a*a*a (where a is a Complex Gaussian number)
>
> I am interested in analyzing the statistics of a4. Can anyone please
> tell me what would be the PDF of such random numbers i.e. a4.
>
> The shape I am getting for PDF from MATLAB looks similar to CHI-SQUARE
> and RAYLIEGH DISTRIBUTION. But I had a look into CHI-SQUARE and
> RAYLEIGH distributions and not completely convinced that a4 is
> CHI-SQUARE or RAYLEIGH distributed.
>
> Could someone please help me out here, I would really appreciate it.
>
> Thank you.
>
	
Reply by Nandan Das March 3, 20062006-03-03
If they are four independent Gaussians, then the pdf is the product of 4
Gaussian pdfs

Nandan

On 3/3/06, Vimal <vimal125@vima...> wrote:
>
> Dear All,
>
>
> In my work I am using MATLAB function RANDN to generate zero mean and
> variance 1 random numbers. I know the PDF for this is Gaussian which
> is well defined in literature and I can find loads of information on it.
>
> But in my work I happened to get four different Gaussian numbers
> multiplied together i.e.:
>
> a4 = a*a*a*a (where a is a Complex Gaussian number)
>
> I am interested in analyzing the statistics of a4. Can anyone please
> tell me what would be the PDF of such random numbers i.e. a4.
>
> The shape I am getting for PDF from MATLAB looks similar to CHI-SQUARE
> and RAYLIEGH DISTRIBUTION. But I had a look into CHI-SQUARE and
> RAYLEIGH distributions and not completely convinced that a4 is
> CHI-SQUARE or RAYLEIGH distributed.
>
> Could someone please help me out here, I would really appreciate it.
>
> Thank you.
>
>
	
Reply by Nishit Jain March 3, 20062006-03-03
      Hi Vimal and all,
    
   I am also dealing with a similar  problem, but my problem is slightly
different. I have a function of RV  (Random Variable) which is sum of squares of
the Gaussian RV.
    
    In literature I have found that the sum of squares of Gaussian RV is a 
Chi-Square Distribution. I dont exactly know about the fourth power of  Gaussian
!!!
    
    Now my problem is I have a random variable Z :
  
    Z = X + Y, where X = Non-zero mean Chi-Square and Y = non-zero mean Gaussian
RV.
    
    Now I am wondering, what would be the distribution of Z ?
    
    Can anybody help us out in this matter?
    
    Thanks and regards,
    Nishit

Vimal <vimal125@vima...> wrote:  Dear All,
	In my work I am using MATLAB function RANDN to generate zero mean and
variance 1 random numbers. I know the PDF for this is Gaussian which
is well defined in literature and I can find loads of information on it. 

But in my work I happened to get four different Gaussian numbers
multiplied together i.e.:

a4 = a*a*a*a (where a is a Complex Gaussian number)

I am interested in analyzing the statistics of a4. Can anyone please
tell me what would be the PDF of such random numbers i.e. a4. 

The shape I am getting for PDF from MATLAB looks similar to CHI-SQUARE
and RAYLIEGH DISTRIBUTION. But I had a look into CHI-SQUARE and
RAYLEIGH distributions and not completely convinced that a4 is
CHI-SQUARE or RAYLEIGH distributed.

Could someone please help me out here, I would really appreciate it. 

Thank you.
	
Reply by Vimal March 3, 20062006-03-03
Dear All,
	In my work I am using MATLAB function RANDN to generate zero mean and
variance 1 random numbers. I know the PDF for this is Gaussian which
is well defined in literature and I can find loads of information on it. 

But in my work I happened to get four different Gaussian numbers
multiplied together i.e.:

a4 = a*a*a*a (where a is a Complex Gaussian number)

I am interested in analyzing the statistics of a4. Can anyone please
tell me what would be the PDF of such random numbers i.e. a4. 

The shape I am getting for PDF from MATLAB looks similar to CHI-SQUARE
and RAYLIEGH DISTRIBUTION. But I had a look into CHI-SQUARE and
RAYLEIGH distributions and not completely convinced that a4 is
CHI-SQUARE or RAYLEIGH distributed.

Could someone please help me out here, I would really appreciate it. 

Thank you.