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.
PDF for four Gaussian Distributed numbers multipiled together (a^4)
Started by ●March 3, 2006
Reply by ●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 ●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 ●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 ●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 ●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 ●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.
