Reply by nammi sairamesh ●November 29, 20042004-11-29

Hi Ashok,
Thank you very much for response. Yes,
the proof is correct and makes sense. I also did in
the same manner with little more steps involved.
Thanks for your help.

Regards,
-SaiRamesh.
--- wrote:

>
> Hi Sai
>
> I tried to post this proof to you earlier, but it
> bounced due.
>
> Hemant,
>
> What do you say about this? The proof is very simple
> and there is not
> much jugglery required.
>
> Regards
>
> arun >
> -----Original Message-----
> From: arun d naik (WT01 - EMBEDDED & PRODUCT
> ENGINEERING SOLUTIONS)
> Sent: Tuesday, November 16, 2004 6:28 PM
> To: 'nammi sairamesh'; Nilay Shah; hemanth kumar
> Cc:
> Subject: RE: RE: [matlab] random variable of desired
> pdf >
> Hi Sai
>
> Here is my explanation:
>
> Let Z be the RV which is an experiment in which we
> choose Z =
> {-(inf<=X1<=+inf) or (inf<=X2<=+inf)}.
>
> Let U be another RV, P(U=X1) = alpha and
> P(X2=x)=(1-alpha). > pdf fZ(z) = partial derivative wrt z of {P(Z<=z)}
>
> = partial derivative wrt z of {P(Z<=z|(U=X1)P(U=X1)+
> P(Z<=z|(U=X2)P(U=X2)}
>
> (This follows from the fact that X1 and X2 are
> mutually exclusive events
> and hence in such a case, the respective
> probabilities can be added.
> P(AUB) = P(A) + P(B) when intersection of A and B is
> null.) >
> = partial derivative wrt z of {FX1(x1)*alpha+
> FX2(x2)*(1-alpha)}
>
> ( for first term z=x1 and second term, z=x2)
>
> = alpha* fX1(x1) + (1-alpha)*fX2(x2) > I am afraid, there may be lack of some rigour in
> this explanation. I
> feel that I might have hurried through steps? >
> By the way, how did you verify the experiment
> statistically? >
> Regards
>
> arun > -----Original Message-----
> From: nammi sairamesh [mailto:]
> Sent: Thursday, November 04, 2004 1:06 PM
> To: Nilay Shah; hemanth kumar; arun d naik (WT01 -
> EMBEDDED & PRODUCT
> ENGINEERING SOLUTIONS)
> Cc:
> Subject: RE: RE: [matlab] random variable of desired
> pdf >
>
> Thanks Nilay! Infact i would like say thanks for
> Arun
>
> and Hemanth for their excellent ideas.
>
> I generated the random variable with pdf
>
> f= a*f1+b*f2, where a+b = 1;
>
> So i got the sequence(with the pdf as GMM) as
> Hemanth
>
> suggested, Now my problem is how to verify this, the
>
> pdf is equal to f?
>
> I mean mathematically?
>
> Is there any book talks about this? >
> Thanks,
>
> -SaiRamesh. >
> __________________________________
>
>



Reply by ●November 22, 20042004-11-22

Hi Sai

I tried to post this proof to you earlier, but it bounced due.

Hemant,

What do you say about this? The proof is very simple and there is not much jugglery required.

Regards

arun

 

-----Original Message-----
From: arun d naik (WT01 - EMBEDDED & PRODUCT ENGINEERING SOLUTIONS)
Sent: Tuesday, November 16, 2004 6:28 PM
To: 'nammi sairamesh'; Nilay Shah; hemanth kumar
Cc: m...@yahoogroups.com
Subject: RE: RE: [matlab] random variable of desired pdf

 

Hi Sai

Here is my explanation:

Let Z be the RV which is an experiment in which we choose Z = {-(inf<=X1<=+inf) or (inf<=X2<=+inf)}.

Let U be another RV, P(U=X1) = alpha and P(X2=x)=(1-alpha).

 

 

pdf fZ(z)   = partial derivative wrt z of {P(Z<=z)}

= partial derivative wrt z of {P(Z<=z|(U=X1)P(U=X1)+ P(Z<=z|(U=X2)P(U=X2)}

(This follows from the fact that X1 and X2 are mutually exclusive events and hence in such a case, the respective probabilities can be added. P(AUB) = P(A) + P(B) when intersection of A and B is null.)

 

= partial derivative wrt z of {FX1(x1)*alpha+ FX2(x2)*(1-alpha)}

( for first term z=x1 and second term, z=x2)

= alpha* fX1(x1) + (1-alpha)*fX2(x2)

 

space.gif

I am afraid, there may be lack of some rigour in this explanation. I feel that I might have hurried through steps?

 

By the way, how did you verify the experiment statistically?

 

Regards

arun

  

 

-----Original Message-----
From: nammi sairamesh [mailto:s...@yahoo.com]
Sent: Thursday, November 04, 2004 1:06 PM
To: Nilay Shah; hemanth kumar; arun d naik (WT01 - EMBEDDED & PRODUCT ENGINEERING SOLUTIONS)
Cc: m...@yahoogroups.com
Subject: RE: RE: [matlab] random variable of desired pdf

 

 

 

Thanks Nilay! Infact i would like  say thanks for Arun

and Hemanth for their excellent ideas.

I generated the random variable with pdf

f= a*f1+b*f2,  where a+b = 1;

So i got the sequence(with the pdf as GMM) as Hemanth

suggested, Now my problem is how to verify this, the

pdf is equal to f?

I mean mathematically?

Is there any book talks about this?

 

Thanks,

-SaiRamesh.

 

 

 

           

__________________________________


Reply by nammi sairamesh ●November 4, 20042004-11-04

Thanks Nilay! Infact i would like say thanks for Arun
and Hemanth for their excellent ideas.
I generated the random variable with pdf
f= a*f1+b*f2, where a+b = 1;
So i got the sequence(with the pdf as GMM) as Hemanth
suggested, Now my problem is how to verify this, the
pdf is equal to f?
I mean mathematically?
Is there any book talks about this?

Thanks,
-SaiRamesh.

__________________________________


Reply by Nilay Shah ●October 29, 20042004-10-29

Hi all,

I think random variable Sai is talking about is
defined as Gaussian Mixture random Variable having pdf
which is combination of weighted sum of two Gaussian
PDF's. The Characteristic of weights in Gaussian
Mixture is that Addition of it is 1. ( so here a+b
=1).

Now as far as generation of it has concern,what u can
do is generate two Gaussina Pdf's with their means and
variance...

Add them point by point.. I am sure when u would see
this for only two pdf's your curve would not be
guassian anymore ,but having some different shape
depending on the values of coefficients.

Also, this is gaussian Mixture..
Does anyone has think.. how u can defined
mutlivariable Gaussian Mixrture Random Vector having
its pdf as addition of two Multivariate Gaussian
vector once again weighted by some values whose
addition is 1.

Interesting problem to look at and this has
application in every wireless projects, if u want to
dump few assumptions we make every time..

I hope this helps sai.. and would, like to know your
thoughts about Multivariate case of Gaussian Mixture.

Regards,
Nilay

-----
Ph.D Student
Stevens Institute of Technology. --- hemanth kumar <> wrote:
>
>
> Hi arun,
>
> This is the only and actual definition of GMM.
>
> regards
> -Hemanth
>
> --- wrote:
> >
> > Hi
> > A small correction:
> > Prob(Z=x0) = Prob(X1=x0|X1)Prob(X1)+
> > Prob(X2=x0|X2)Prob(X2).
> > Regards
> > arun
> >
> > -----Original Message-----
> > From: arun d naik (WT01 - EMBEDDED & PRODUCT
> > ENGINEERING SOLUTIONS)
> > Sent: Wednesday, October 27, 2004 5:55 PM
> > To: 'nammi sairamesh'; hemanth kumar
> > Cc:
> > Subject: RE: RE: [matlab] random variable of
> desired
> > pdf
> >
> > Sai
> > Hemant is right.
> > The fact that we can easily decompose f as a
> linear
> > combination of f1
> > and f2 (where each is a normally distributed rv),
> > can be made use of in
> > simulating the composite pdf by means of
> individual
> > normally distributed
> > rvs.
> >
> > Hemant is not suggesting x = ax1+bx2. It is
> actually
> > a switch between
> > the two rvs at any instant.
> >
> > Remember the two hypothesis problem.
> > Suppose X1 and X2 are 2 rvs. And you generate a
> new
> > rv, Z by picking one
> > of the two rvs and let the probability of X1 being
> > selected is a and X2
> > being selected is b=1-a.
> > Then Prob(Z=x0) = Prob(X=x0|X1)Prob(Z=X1)+
> > Prob(X=x0|X2)Prob(Z=X2).
> > This is intuitively(to me) easiest way of
> generating
> > your random
> > variable.
> >
> > Regards
> > arun
> >
> > -----Original Message-----
> > From: nammi sairamesh
> [mailto:]
> > Sent: Wednesday, October 27, 2004 1:53 PM
> > To: hemanth kumar
> > Cc:
> > Subject: RE: RE: [matlab] random variable of
> desired
> > pdf
> >
> >
> >
> > Hi,
> > Thanks for your response! But
> > if f= a*f1+b*f2, then is x= a*x1+b*x2??? No know!
> > where x has a pdf of f, x1 has pdf of f1, and x2
> has
> > pdf of f2.
> > -SaiRamesh.
> > --- hemanth kumar <> wrote:
> >
> > > Hi Sai,
> > > Let me write an anology of GMM first then I will
> > > mention How
> > > to generate the sequence.
> > >
> > > Let us assume that there are 2 machines
> producing
> > > same type of toys
> > > with the hieght of the toys as random variable
> > > (For example
> > > Machine1 - Mean 4 and variance 3
> > > Machine 2 - mean 5 and variance 2)
> > > and the probability that machine 1 is selected
> > > machine 1 is 'a'
> > > and machine 2 is 'b' (Where a and b are the same
> > as
> > > the constants
> > > in the equation f = a*f1+b*f2)
> > >
> > > So If you want to generate total 1000 toys
> > > (samples).
> > > 1. Generate 'a' times 1000 toys using random
> > > varaible f1
> > > (for example a =0.6 this becomes 600)
> > > 2. Generate 'b' times 1000 toys using randome
> > > variable f2
> > > (for example b =0.4 this becomes 400)
> > >
> > > I hope this helps
> > >
> > >
> > > nammi sairamesh <> wrote:
> > > Hi,
> > > For my problem f1 and f2 are normal
> distributions
> > > ! As Arun wrote they have different mean and
> > > variance,!
> > > if they have same mean and variance , the f is
> not
> > a
> > > pdf! at all!
> > > -SaiRamesh.
> > >
> > >
> > > --- hemanth kumar wrote:
> > >
> > > > hi sai,
> > > > could u be a little specific about the pdf of
> > the
> > > > random sequences u want to generate...
> > > >
> > > > do u have any particular pdf's(f1 and f2) in
> > mind?
> > > >
> > > > - Hemanth
> > > >
> > > >
> > > > --- wrote:
> > > > > Sai
> > > > > I think had understood your requirements.
> > > > > I vaguely remember that the convolution of
> two
> > > > > guassian functions is also a guassian(but I
> am
> > > not
> > > > > confirming this; please refer to papoulis's
> > > book).
> > > >
> > > > > If the two rvs are independent, the variance
> > of
> > > > the
> > > > > sum of 2 rvs is given by sum of variances.
> > hence
> > > > in
> > > > > your case var = a1^2*sigma1+a2^2*sigma2.
> > > > > If the facts in the above 2 paras are true
> it
> > > can
> > > > > help you to make use of randn in your case.
> > > > > Hope I understood your requirements
> correctly
> > > and
> > > > > this helps you.
> > > > > regadrs
> > > > > arun
> > > > >
> > > > >
> > > > > -----Original Message-----
> > > > > From: nammi sairamesh
> > > > > [mailto:]
> > > > > Sent: Mon 10/25/2004 22:04
> > > > > To: tArAng; arun d naik (WT01 - EMBEDDED &
> > > > PRODUCT
> > > > > ENGINEERING SOLUTIONS)
> > > > > Cc: ;
> > >
> > > >
> > > > > Subject: Re: RE: [matlab] random variable of
> > > > > desired pdf
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > > Hi,
> > > > > Thanks for your responses.! But I guess, u
> > > > > misunderstood my problem!
> > > > > My problem is to generate a random variable
> > > > whose
> > > > > pdf
> > > > > is given! not the other way!
> > > > > for example: we know normal distribution so
> > with
> > > > > randn
> > > > > we can generate a random variable with
> normal
> > > > > distribution!
> > > > > In similar way, i want to write a function
>
=== message truncated ===

________________________________________________________________________
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Reply by hemanth kumar ●October 27, 20042004-10-27

Hi arun,

This is the only and actual definition of GMM.

regards
-Hemanth

--- wrote:
>
> Hi
> A small correction:
> Prob(Z=x0) = Prob(X1=x0|X1)Prob(X1)+
> Prob(X2=x0|X2)Prob(X2).
> Regards
> arun
>
> -----Original Message-----
> From: arun d naik (WT01 - EMBEDDED & PRODUCT
> ENGINEERING SOLUTIONS)
> Sent: Wednesday, October 27, 2004 5:55 PM
> To: 'nammi sairamesh'; hemanth kumar
> Cc:
> Subject: RE: RE: [matlab] random variable of desired
> pdf
>
> Sai
> Hemant is right.
> The fact that we can easily decompose f as a linear
> combination of f1
> and f2 (where each is a normally distributed rv),
> can be made use of in
> simulating the composite pdf by means of individual
> normally distributed
> rvs.
>
> Hemant is not suggesting x = ax1+bx2. It is actually
> a switch between
> the two rvs at any instant.
>
> Remember the two hypothesis problem.
> Suppose X1 and X2 are 2 rvs. And you generate a new
> rv, Z by picking one
> of the two rvs and let the probability of X1 being
> selected is a and X2
> being selected is b=1-a.
> Then Prob(Z=x0) = Prob(X=x0|X1)Prob(Z=X1)+
> Prob(X=x0|X2)Prob(Z=X2).
> This is intuitively(to me) easiest way of generating
> your random
> variable.
>
> Regards
> arun
>
> -----Original Message-----
> From: nammi sairamesh [mailto:]
> Sent: Wednesday, October 27, 2004 1:53 PM
> To: hemanth kumar
> Cc:
> Subject: RE: RE: [matlab] random variable of desired
> pdf >
> Hi,
> Thanks for your response! But
> if f= a*f1+b*f2, then is x= a*x1+b*x2??? No know!
> where x has a pdf of f, x1 has pdf of f1, and x2 has
> pdf of f2.
> -SaiRamesh.
> --- hemanth kumar <> wrote:
>
> > Hi Sai,
> > Let me write an anology of GMM first then I will
> > mention How
> > to generate the sequence.
> >
> > Let us assume that there are 2 machines producing
> > same type of toys
> > with the hieght of the toys as random variable
> > (For example
> > Machine1 - Mean 4 and variance 3
> > Machine 2 - mean 5 and variance 2)
> > and the probability that machine 1 is selected
> > machine 1 is 'a'
> > and machine 2 is 'b' (Where a and b are the same
> as
> > the constants
> > in the equation f = a*f1+b*f2)
> >
> > So If you want to generate total 1000 toys
> > (samples).
> > 1. Generate 'a' times 1000 toys using random
> > varaible f1
> > (for example a =0.6 this becomes 600)
> > 2. Generate 'b' times 1000 toys using randome
> > variable f2
> > (for example b =0.4 this becomes 400)
> >
> > I hope this helps
> >
> >
> > nammi sairamesh <> wrote:
> > Hi,
> > For my problem f1 and f2 are normal distributions
> > ! As Arun wrote they have different mean and
> > variance,!
> > if they have same mean and variance , the f is not
> a
> > pdf! at all!
> > -SaiRamesh.
> >
> >
> > --- hemanth kumar wrote:
> >
> > > hi sai,
> > > could u be a little specific about the pdf of
> the
> > > random sequences u want to generate...
> > >
> > > do u have any particular pdf's(f1 and f2) in
> mind?
> > >
> > > - Hemanth
> > >
> > >
> > > --- wrote:
> > > > Sai
> > > > I think had understood your requirements.
> > > > I vaguely remember that the convolution of two
> > > > guassian functions is also a guassian(but I am
> > not
> > > > confirming this; please refer to papoulis's
> > book).
> > >
> > > > If the two rvs are independent, the variance
> of
> > > the
> > > > sum of 2 rvs is given by sum of variances.
> hence
> > > in
> > > > your case var = a1^2*sigma1+a2^2*sigma2.
> > > > If the facts in the above 2 paras are true it
> > can
> > > > help you to make use of randn in your case.
> > > > Hope I understood your requirements correctly
> > and
> > > > this helps you.
> > > > regadrs
> > > > arun
> > > >
> > > >
> > > > -----Original Message-----
> > > > From: nammi sairamesh
> > > > [mailto:]
> > > > Sent: Mon 10/25/2004 22:04
> > > > To: tArAng; arun d naik (WT01 - EMBEDDED &
> > > PRODUCT
> > > > ENGINEERING SOLUTIONS)
> > > > Cc: ;
> >
> > >
> > > > Subject: Re: RE: [matlab] random variable of
> > > > desired pdf
> > > >
> > > >
> > > >
> > > >
> > > >
> > > > Hi,
> > > > Thanks for your responses.! But I guess, u
> > > > misunderstood my problem!
> > > > My problem is to generate a random variable
> > > whose
> > > > pdf
> > > > is given! not the other way!
> > > > for example: we know normal distribution so
> with
> > > > randn
> > > > we can generate a random variable with normal
> > > > distribution!
> > > > In similar way, i want to write a function
> which
> > > > generates a random varibale with the desired
> pdf
> > > > (f_desired= a*f1+b*f2, where f1 and f2 are the
> > > > given
> > > > pdfs not random numbers).
> > > > I hope now u understood the actual problem!
> > > > Regards,
> > > > -SaiRamesh.
> > > >
> > > >
> > > > --- tArAng wrote:
> > > >
> > > > > Arun, Sairamesh,
> > > > >
> > > > > I think Arun you are correct. The resultant
> > pdf
> > > > will
> > > > > be Gaussian by Central Limit Theorum.
> > > > >
> > > > > I think what Sairamesh is doing is adding
> two
> > > > > Gaussian Random Variables with different
> > > > variances (
> > > > > var1 = a^2 and var2 = b^2).
> > > > > Correct me if I am wrong.
> > > > >
>
=== message truncated ===

________________________________________________________________________
Yahoo! India Matrimony: Find your life partner online
Go to: http://yahoo.shaadi.com/india-matrimony




Reply by ●October 27, 20042004-10-27

Sai
Hemant is right.
The fact that we can easily decompose f as a linear combination of f1
and f2 (where each is a normally distributed rv), can be made use of in
simulating the composite pdf by means of individual normally distributed
rvs.

Hemant is not suggesting x = ax1+bx2. It is actually a switch between
the two rvs at any instant.

Remember the two hypothesis problem.
Suppose X1 and X2 are 2 rvs. And you generate a new rv, Z by picking one
of the two rvs and let the probability of X1 being selected is a and X2
being selected is b=1-a.
Then Prob(Z=x0) = Prob(X=x0|X1)Prob(Z=X1)+ Prob(X=x0|X2)Prob(Z=X2).
This is intuitively(to me) easiest way of generating your random
variable.

Regards
arun

-----Original Message-----
From: nammi sairamesh [mailto:]
Sent: Wednesday, October 27, 2004 1:53 PM
To: hemanth kumar
Cc:
Subject: RE: RE: [matlab] random variable of desired pdf
Hi,
Thanks for your response! But
if f= a*f1+b*f2, then is x= a*x1+b*x2??? No know!
where x has a pdf of f, x1 has pdf of f1, and x2 has
pdf of f2.
-SaiRamesh.
--- hemanth kumar <> wrote:

> Hi Sai,
> Let me write an anology of GMM first then I will
> mention How
> to generate the sequence.
>
> Let us assume that there are 2 machines producing
> same type of toys
> with the hieght of the toys as random variable
> (For example
> Machine1 - Mean 4 and variance 3
> Machine 2 - mean 5 and variance 2)
> and the probability that machine 1 is selected
> machine 1 is 'a'
> and machine 2 is 'b' (Where a and b are the same as
> the constants
> in the equation f = a*f1+b*f2)
>
> So If you want to generate total 1000 toys
> (samples).
> 1. Generate 'a' times 1000 toys using random
> varaible f1
> (for example a =0.6 this becomes 600)
> 2. Generate 'b' times 1000 toys using randome
> variable f2
> (for example b =0.4 this becomes 400)
>
> I hope this helps > nammi sairamesh <> wrote:
> Hi,
> For my problem f1 and f2 are normal distributions
> ! As Arun wrote they have different mean and
> variance,!
> if they have same mean and variance , the f is not a
> pdf! at all!
> -SaiRamesh. > --- hemanth kumar wrote:
>
> > hi sai,
> > could u be a little specific about the pdf of the
> > random sequences u want to generate...
> >
> > do u have any particular pdf's(f1 and f2) in mind?
> >
> > - Hemanth
> >
> >
> > --- wrote:
> > > Sai
> > > I think had understood your requirements.
> > > I vaguely remember that the convolution of two
> > > guassian functions is also a guassian(but I am
> not
> > > confirming this; please refer to papoulis's
> book).
> >
> > > If the two rvs are independent, the variance of
> > the
> > > sum of 2 rvs is given by sum of variances. hence
> > in
> > > your case var = a1^2*sigma1+a2^2*sigma2.
> > > If the facts in the above 2 paras are true it
> can
> > > help you to make use of randn in your case.
> > > Hope I understood your requirements correctly
> and
> > > this helps you.
> > > regadrs
> > > arun
> > >
> > >
> > > -----Original Message-----
> > > From: nammi sairamesh
> > > [mailto:]
> > > Sent: Mon 10/25/2004 22:04
> > > To: tArAng; arun d naik (WT01 - EMBEDDED &
> > PRODUCT
> > > ENGINEERING SOLUTIONS)
> > > Cc: ;
>
> >
> > > Subject: Re: RE: [matlab] random variable of
> > > desired pdf
> > >
> > >
> > >
> > >
> > >
> > > Hi,
> > > Thanks for your responses.! But I guess, u
> > > misunderstood my problem!
> > > My problem is to generate a random variable
> > whose
> > > pdf
> > > is given! not the other way!
> > > for example: we know normal distribution so with
> > > randn
> > > we can generate a random variable with normal
> > > distribution!
> > > In similar way, i want to write a function which
> > > generates a random varibale with the desired pdf
> > > (f_desired= a*f1+b*f2, where f1 and f2 are the
> > > given
> > > pdfs not random numbers).
> > > I hope now u understood the actual problem!
> > > Regards,
> > > -SaiRamesh.
> > >
> > >
> > > --- tArAng wrote:
> > >
> > > > Arun, Sairamesh,
> > > >
> > > > I think Arun you are correct. The resultant
> pdf
> > > will
> > > > be Gaussian by Central Limit Theorum.
> > > >
> > > > I think what Sairamesh is doing is adding two
> > > > Gaussian Random Variables with different
> > > variances (
> > > > var1 = a^2 and var2 = b^2).
> > > > Correct me if I am wrong.
> > > >
> > > >
> > > > Tarang
> > > >
> > > >
> > > > On Mon, 25 Oct 2004 wrote
> :
> > > > >Hi
> > > > >Are the 2 rvs are independent? I assume you
> > are
> > > > generating a new rv by
> > > > >linear combination of the 2 rvs.
> > > > >When pdf of 2 independent rvs are added, the
> > > > resultant pdf is
> > > > >convolution of the 2 pdfs. Hence, you should
> > be
> > > > able to calculate closed
> > > > >form of the resultant pdf. I guess(I may be
> > > wrong)
> > > > that the resultant
> > > > >pdf also may be a guassian rv.
> > > > >Regards
> > > > >arun
> > > > >-----Original Message-----
> > > > > From: nammi sairamesh
> > > > [mailto:]
> > > > >Sent: Saturday, October 23, 2004 8:29 AM
> > > > >To:
> > > > >Subject: [matlab] random variable of desired
> > pdf
> > > > >Hi,
> > > > > I am modelling a wireless channel, I
> > want
> > > to
> > > > >model the channel as mixture of two guassians
> > > which
> > > > is
> > > > >suitable for my applications.
> > > > >i.e. f= a*f1+b*f2;
> > > > >where f is the pdf of the noise signal.
> > > > >f1 and f2 are gaussian pdfs with mean 0 and
> > > > variance
> > > > >=1, a and b are some constants>0,
> > > > >Now i want to generate a random variable in
> > > matlab
> > > > >whose pdf is f(=a*f1+b*f2).
> > > > >But how to genearte a random variable with
> pdf
> > > of
> > > > f.
> > > > >Help in this regard is highly appreciated.
> > > > >Regards,
> > > > >-SaiRamesh.
> > > > >
> > > > >_______________________________
> > > > >
 _____________________________________
Note: If you do a simple "reply" with your email client, only the author
of this message will receive your answer. You need to do a "reply all"
if you want your answer to be distributed to the entire group.

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Reply by hemanth kumar ●October 27, 20042004-10-27

Hi,
yes, thats right..
try this small peice of code,

x1 = randn(1,600);
x2 = randn(1,400;
% here modifide the mean and std dev of x1 and x2. %
x1 = 0.5*x1 + 1;
x2 = 0.25*x2 - 1;
x = [ x1 x2];
h = hist(x,100);
n = min(x):(max(x) - min(x))/100:max(x);
n = n(1:100);
plot(n,h);

hope it helps.

- Hemanth
--- nammi sairamesh <> wrote:
> Hi,
> Thanks for your response! But
> if f= a*f1+b*f2, then is x= a*x1+b*x2??? No know!
> where x has a pdf of f, x1 has pdf of f1, and x2 has
> pdf of f2.
> -SaiRamesh.
> --- hemanth kumar <> wrote:
>
> > Hi Sai,
> > Let me write an anology of GMM first then I will
> > mention How
> > to generate the sequence.
> >
> > Let us assume that there are 2 machines producing
> > same type of toys
> > with the hieght of the toys as random variable
> > (For example
> > Machine1 - Mean 4 and variance 3
> > Machine 2 - mean 5 and variance 2)
> > and the probability that machine 1 is selected
> > machine 1 is 'a'
> > and machine 2 is 'b' (Where a and b are the same
> as
> > the constants
> > in the equation f = a*f1+b*f2)
> >
> > So If you want to generate total 1000 toys
> > (samples).
> > 1. Generate 'a' times 1000 toys using random
> > varaible f1
> > (for example a =0.6 this becomes 600)
> > 2. Generate 'b' times 1000 toys using randome
> > variable f2
> > (for example b =0.4 this becomes 400)
> >
> > I hope this helps
> >
> >
> > nammi sairamesh <> wrote:
> > Hi,
> > For my problem f1 and f2 are normal distributions
> > ! As Arun wrote they have different mean and
> > variance,!
> > if they have same mean and variance , the f is not
> a
> > pdf! at all!
> > -SaiRamesh.
> >
> >
> > --- hemanth kumar wrote:
> >
> > > hi sai,
> > > could u be a little specific about the pdf of
> the
> > > random sequences u want to generate...
> > >
> > > do u have any particular pdf's(f1 and f2) in
> mind?
> > >
> > > - Hemanth
> > >
> > >
> > > --- wrote:
> > > > Sai
> > > > I think had understood your requirements.
> > > > I vaguely remember that the convolution of two
> > > > guassian functions is also a guassian(but I am
> > not
> > > > confirming this; please refer to papoulis's
> > book).
> > >
> > > > If the two rvs are independent, the variance
> of
> > > the
> > > > sum of 2 rvs is given by sum of variances.
> hence
> > > in
> > > > your case var = a1^2*sigma1+a2^2*sigma2.
> > > > If the facts in the above 2 paras are true it
> > can
> > > > help you to make use of randn in your case.
> > > > Hope I understood your requirements correctly
> > and
> > > > this helps you.
> > > > regadrs
> > > > arun
> > > >
> > > >
> > > > -----Original Message-----
> > > > From: nammi sairamesh
> > > > [mailto:]
> > > > Sent: Mon 10/25/2004 22:04
> > > > To: tArAng; arun d naik (WT01 - EMBEDDED &
> > > PRODUCT
> > > > ENGINEERING SOLUTIONS)
> > > > Cc: ;
> >
> > >
> > > > Subject: Re: RE: [matlab] random variable of
> > > > desired pdf
> > > >
> > > >
> > > >
> > > >
> > > >
> > > > Hi,
> > > > Thanks for your responses.! But I guess, u
> > > > misunderstood my problem!
> > > > My problem is to generate a random variable
> > > whose
> > > > pdf
> > > > is given! not the other way!
> > > > for example: we know normal distribution so
> with
> > > > randn
> > > > we can generate a random variable with normal
> > > > distribution!
> > > > In similar way, i want to write a function
> which
> > > > generates a random varibale with the desired
> pdf
> > > > (f_desired= a*f1+b*f2, where f1 and f2 are the
> > > > given
> > > > pdfs not random numbers).
> > > > I hope now u understood the actual problem!
> > > > Regards,
> > > > -SaiRamesh.
> > > >
> > > >
> > > > --- tArAng wrote:
> > > >
> > > > > Arun, Sairamesh,
> > > > >
> > > > > I think Arun you are correct. The resultant
> > pdf
> > > > will
> > > > > be Gaussian by Central Limit Theorum.
> > > > >
> > > > > I think what Sairamesh is doing is adding
> two
> > > > > Gaussian Random Variables with different
> > > > variances (
> > > > > var1 = a^2 and var2 = b^2).
> > > > > Correct me if I am wrong.
> > > > >
> > > > >
> > > > > Tarang
> > > > >
> > > > >
> > > > > On Mon, 25 Oct 2004
> wrote
> > :
> > > > > >Hi
> > > > > >Are the 2 rvs are independent? I assume you
> > > are
> > > > > generating a new rv by
> > > > > >linear combination of the 2 rvs.
> > > > > >When pdf of 2 independent rvs are added,
> the
> > > > > resultant pdf is
> > > > > >convolution of the 2 pdfs. Hence, you
> should
> > > be
> > > > > able to calculate closed
> > > > > >form of the resultant pdf. I guess(I may be
> > > > wrong)
> > > > > that the resultant
> > > > > >pdf also may be a guassian rv.
> > > > > >Regards
> > > > > >arun
> > > > > >-----Original Message-----
> > > > > > From: nammi sairamesh
> > > > > [mailto:]
> > > > > >Sent: Saturday, October 23, 2004 8:29 AM
> > > > > >To:
> > > > > >Subject: [matlab] random variable of
> desired
> > > pdf
> > > > > >Hi,
> > > > > > I am modelling a wireless channel, I
> > > want
> > > > to
> > > > > >model the channel as mixture of two
> guassians
> > > > which
> > > > > is
> > > > > >suitable for my applications.
> > > > > >i.e. f= a*f1+b*f2;
> > > > > >where f is the pdf of the noise signal.
> > > > > >f1 and f2 are gaussian pdfs with mean 0 and
> > > > > variance
> > > > > >=1, a and b are some constants>0,
> > > > > >Now i want to generate a random variable in
> > > > matlab
> > > > > >whose pdf is f(=a*f1+b*f2).
> > > > > >But how to genearte a random variable with
> > pdf
> > > > of
> > > > > f.
> > > > > >Help in this regard is highly appreciated.
> > > > > >Regards,
>
=== message truncated ===

________________________________________________________________________
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Reply by nammi sairamesh ●October 27, 20042004-10-27

Hi,
Thanks for your response! But
if f= a*f1+b*f2, then is x= a*x1+b*x2??? No know!
where x has a pdf of f, x1 has pdf of f1, and x2 has
pdf of f2.
-SaiRamesh.
--- hemanth kumar <> wrote:

> Hi Sai,
> Let me write an anology of GMM first then I will
> mention How
> to generate the sequence.
>
> Let us assume that there are 2 machines producing
> same type of toys
> with the hieght of the toys as random variable
> (For example
> Machine1 - Mean 4 and variance 3
> Machine 2 - mean 5 and variance 2)
> and the probability that machine 1 is selected
> machine 1 is 'a'
> and machine 2 is 'b' (Where a and b are the same as
> the constants
> in the equation f = a*f1+b*f2)
>
> So If you want to generate total 1000 toys
> (samples).
> 1. Generate 'a' times 1000 toys using random
> varaible f1
> (for example a =0.6 this becomes 600)
> 2. Generate 'b' times 1000 toys using randome
> variable f2
> (for example b =0.4 this becomes 400)
>
> I hope this helps > nammi sairamesh <> wrote:
> Hi,
> For my problem f1 and f2 are normal distributions
> ! As Arun wrote they have different mean and
> variance,!
> if they have same mean and variance , the f is not a
> pdf! at all!
> -SaiRamesh. > --- hemanth kumar wrote:
>
> > hi sai,
> > could u be a little specific about the pdf of the
> > random sequences u want to generate...
> >
> > do u have any particular pdf's(f1 and f2) in mind?
> >
> > - Hemanth
> >
> >
> > --- wrote:
> > > Sai
> > > I think had understood your requirements.
> > > I vaguely remember that the convolution of two
> > > guassian functions is also a guassian(but I am
> not
> > > confirming this; please refer to papoulis's
> book).
> >
> > > If the two rvs are independent, the variance of
> > the
> > > sum of 2 rvs is given by sum of variances. hence
> > in
> > > your case var = a1^2*sigma1+a2^2*sigma2.
> > > If the facts in the above 2 paras are true it
> can
> > > help you to make use of randn in your case.
> > > Hope I understood your requirements correctly
> and
> > > this helps you.
> > > regadrs
> > > arun
> > >
> > >
> > > -----Original Message-----
> > > From: nammi sairamesh
> > > [mailto:]
> > > Sent: Mon 10/25/2004 22:04
> > > To: tArAng; arun d naik (WT01 - EMBEDDED &
> > PRODUCT
> > > ENGINEERING SOLUTIONS)
> > > Cc: ;
>
> >
> > > Subject: Re: RE: [matlab] random variable of
> > > desired pdf
> > >
> > >
> > >
> > >
> > >
> > > Hi,
> > > Thanks for your responses.! But I guess, u
> > > misunderstood my problem!
> > > My problem is to generate a random variable
> > whose
> > > pdf
> > > is given! not the other way!
> > > for example: we know normal distribution so with
> > > randn
> > > we can generate a random variable with normal
> > > distribution!
> > > In similar way, i want to write a function which
> > > generates a random varibale with the desired pdf
> > > (f_desired= a*f1+b*f2, where f1 and f2 are the
> > > given
> > > pdfs not random numbers).
> > > I hope now u understood the actual problem!
> > > Regards,
> > > -SaiRamesh.
> > >
> > >
> > > --- tArAng wrote:
> > >
> > > > Arun, Sairamesh,
> > > >
> > > > I think Arun you are correct. The resultant
> pdf
> > > will
> > > > be Gaussian by Central Limit Theorum.
> > > >
> > > > I think what Sairamesh is doing is adding two
> > > > Gaussian Random Variables with different
> > > variances (
> > > > var1 = a^2 and var2 = b^2).
> > > > Correct me if I am wrong.
> > > >
> > > >
> > > > Tarang
> > > >
> > > >
> > > > On Mon, 25 Oct 2004 wrote
> :
> > > > >Hi
> > > > >Are the 2 rvs are independent? I assume you
> > are
> > > > generating a new rv by
> > > > >linear combination of the 2 rvs.
> > > > >When pdf of 2 independent rvs are added, the
> > > > resultant pdf is
> > > > >convolution of the 2 pdfs. Hence, you should
> > be
> > > > able to calculate closed
> > > > >form of the resultant pdf. I guess(I may be
> > > wrong)
> > > > that the resultant
> > > > >pdf also may be a guassian rv.
> > > > >Regards
> > > > >arun
> > > > >-----Original Message-----
> > > > > From: nammi sairamesh
> > > > [mailto:]
> > > > >Sent: Saturday, October 23, 2004 8:29 AM
> > > > >To:
> > > > >Subject: [matlab] random variable of desired
> > pdf
> > > > >Hi,
> > > > > I am modelling a wireless channel, I
> > want
> > > to
> > > > >model the channel as mixture of two guassians
> > > which
> > > > is
> > > > >suitable for my applications.
> > > > >i.e. f= a*f1+b*f2;
> > > > >where f is the pdf of the noise signal.
> > > > >f1 and f2 are gaussian pdfs with mean 0 and
> > > > variance
> > > > >=1, a and b are some constants>0,
> > > > >Now i want to generate a random variable in
> > > matlab
> > > > >whose pdf is f(=a*f1+b*f2).
> > > > >But how to genearte a random variable with
> pdf
> > > of
> > > > f.
> > > > >Help in this regard is highly appreciated.
> > > > >Regards,
> > > > >-SaiRamesh.
> > > > >
> > > > >_______________________________
> > > > >


Reply by hemanth kumar ●October 27, 20042004-10-27
Hi Sai,
Let me write an anology of GMM first then I will mention How
to generate the sequence.
 
Let us assume that there are 2 machines producing same type of toys
with the hieght of the toys as random variable
(For example
 Machine1 - Mean 4 and variance 3
 Machine 2 - mean 5 and variance 2)
and the probability that machine 1 is selected machine 1 is 'a'
and machine 2 is 'b' (Where a and b are the same as the constants
in the equation f = a*f1+b*f2)
 
So If you want to generate total 1000 toys (samples).
1. Generate 'a' times 1000 toys using random varaible f1
    (for example a =0.6 this becomes 600)
2. Generate 'b' times 1000 toys using randome variable f2
     (for example b =0.4 this becomes 400)
 
I hope this helps


nammi sairamesh <s...@yahoo.com> wrote:
Hi,
For my problem f1 and f2 are normal distributions
! As Arun wrote they have different mean and
variance,!
if they have same mean and variance , the f is not a
pdf! at all!
-SaiRamesh.--- hemanth kumar wrote:

> hi sai,
> could u be a little specific about the pdf of the
> random sequences u want to generate...
>
> do u have any particular pdf's(f1 and f2) in mind?
>
> - Hemanth> --- a...@wipro.com wrote:
> > Sai
> > I think had understood your requirements.
> > I vaguely remember that the convolution of two
> > guassian functions is also a guassian(but I am not
> > confirming this; please refer to papoulis's book).
>
> > If the two rvs are independent, the variance of
> the
> > sum of 2 rvs is given by sum of variances. hence
> in
> > your case var = a1^2*sigma1+a2^2*sigma2.
> > If the facts in the above 2 paras are true it can
> > help you to make use of randn in your case.
> > Hope I understood your requirements correctly and
> > this helps you.
> > regadrs
> > arun
> >
> >
> > -----Original Message-----
> > From: nammi sairamesh
> > [mailto:s...@yahoo.com]
> > Sent: Mon 10/25/2004 22:04
> > To: tArAng; arun d naik (WT01 - EMBEDDED &
> PRODUCT
> > ENGINEERING SOLUTIONS)
> > Cc: s...@yahoo.com; m...@yahoogroups.com
>
> > Subject: Re: RE: [matlab] random variable of
> > desired pdf
> >
> >
> >
> >
> >
> > Hi,
> > Thanks for your responses.! But I guess, u
> > misunderstood my problem!
> > My problem is to generate a random variable
> whose
> > pdf
> > is given! not the other way!
> > for example: we know normal distribution so with
> > randn
> > we can generate a random variable with normal
> > distribution!
> > In similar way, i want to write a function which
> > generates a random varibale with the desired pdf
> > (f_desired= a*f1+b*f2, where f1 and f2 are the
> > given
> > pdfs not random numbers).
> > I hope now u understood the actual problem!
> > Regards,
> > -SaiRamesh.
> >
> >
> > --- tArAng wrote:
> >
> > > Arun, Sairamesh,
> > >
> > > I think Arun you are correct. The resultant pdf
> > will
> > > be Gaussian by Central Limit Theorum.
> > >
> > > I think what Sairamesh is doing is adding two
> > > Gaussian Random Variables with different
> > variances (
> > > var1 = a^2 and var2 = b^2).
> > > Correct me if I am wrong.
> > >
> > >
> > > Tarang
> > >
> > >
> > > On Mon, 25 Oct 2004 a...@wipro.com wrote :
> > > >Hi
> > > >Are the 2 rvs are independent? I assume you
> are
> > > generating a new rv by
> > > >linear combination of the 2 rvs.
> > > >When pdf of 2 independent rvs are added, the
> > > resultant pdf is
> > > >convolution of the 2 pdfs. Hence, you should
> be
> > > able to calculate closed
> > > >form of the resultant pdf. I guess(I may be
> > wrong)
> > > that the resultant
> > > >pdf also may be a guassian rv.
> > > >Regards
> > > >arun
> > > >-----Original Message-----
> > > > From: nammi sairamesh
> > > [mailto:s...@yahoo.com]
> > > >Sent: Saturday, October 23, 2004 8:29 AM
> > > >To: m...@yahoogroups.com
> > > >Subject: [matlab] random variable of desired
> pdf
> > > >Hi,
> > > > I am modelling a wireless channel, I
> want
> > to
> > > >model the channel as mixture of two guassians
> > which
> > > is
> > > >suitable for my applications.
> > > >i.e. f= a*f1+b*f2;
> > > >where f is the pdf of the noise signal.
> > > >f1 and f2 are gaussian pdfs with mean 0 and
> > > variance
> > > >=1, a and b are some constants>0,
> > > >Now i want to generate a random variable in
> > matlab
> > > >whose pdf is f(=a*f1+b*f2).
> > > >But how to genearte a random variable with pdf
> > of
> > > f.
> > > >Help in this regard is highly appreciated.
> > > >Regards,
> > > >-SaiRamesh.
> > > >
> > > >_______________________________
> > > >
> > > >_____________________________________
> > > >Note: If you do a simple "reply" with your
> email
> > > client, only the author
> > > >of this message will receive your answer. You
> > need
> > > to do a "reply all"
> > > >if you want your answer to be distributed to
> the
> > > entire group.
> > > >_____________________________________
> > > >About this discussion group:
> > > >To Join: m...@yahoogroups.com
> > > >To Post: m...@yahoogroups.com
> > > >To Leave: m...@yahoogroups.com
> > > >Archives:
> > > >http://www.yahoogroups.com/group/matlab
> > > >More DSP-Related Groups:
> > > >http://www.dsprelated.com/groups.php3
> > > >Yahoo! Groups Links
> > > >_____________________________________
> > > >Note: If you do a simple "reply" with your
> email
> > > client, only the author of this message will
> > receive
> > > your answer. You need to do a "reply all" if
> you
> > > want your answer to be distributed to the
> entire
> > > group.
> > > >_____________________________________
> > > >About this discussion group:
> > > >To Join: m...@yahoogroups.com
> > > >To Post: m...@yahoogroups.com
> > > >To Leave: m...@yahoogroups.com
> > > >Archives:
> > > >http://www.yahoogroups.com/group/matlab
> > > >More DSP-Related Groups:
> > > >http://www.dsprelated.com/groups.php3
> > > >
> > > >Yahoo! Groups Links
> > > >To
Reply by nammi sairamesh ●October 27, 20042004-10-27

Hi,
For my problem f1 and f2 are normal distributions
! As Arun wrote they have different mean and
variance,!
if they have same mean and variance , the f is not a
pdf! at all!
-SaiRamesh. --- hemanth kumar <> wrote:

> hi sai,
> could u be a little specific about the pdf of the
> random sequences u want to generate...
>
> do u have any particular pdf's(f1 and f2) in mind?
>
> - Hemanth > --- wrote:
> > Sai
> > I think had understood your requirements.
> > I vaguely remember that the convolution of two
> > guassian functions is also a guassian(but I am not
> > confirming this; please refer to papoulis's book).
>
> > If the two rvs are independent, the variance of
> the
> > sum of 2 rvs is given by sum of variances. hence
> in
> > your case var = a1^2*sigma1+a2^2*sigma2.
> > If the facts in the above 2 paras are true it can
> > help you to make use of randn in your case.
> > Hope I understood your requirements correctly and
> > this helps you.
> > regadrs
> > arun
> >
> >
> > -----Original Message-----
> > From: nammi sairamesh
> > [mailto:]
> > Sent: Mon 10/25/2004 22:04
> > To: tArAng; arun d naik (WT01 - EMBEDDED &
> PRODUCT
> > ENGINEERING SOLUTIONS)
> > Cc: ;
>
> > Subject: Re: RE: [matlab] random variable of
> > desired pdf
> >
> >
> >
> >
> >
> > Hi,
> > Thanks for your responses.! But I guess, u
> > misunderstood my problem!
> > My problem is to generate a random variable
> whose
> > pdf
> > is given! not the other way!
> > for example: we know normal distribution so with
> > randn
> > we can generate a random variable with normal
> > distribution!
> > In similar way, i want to write a function which
> > generates a random varibale with the desired pdf
> > (f_desired= a*f1+b*f2, where f1 and f2 are the
> > given
> > pdfs not random numbers).
> > I hope now u understood the actual problem!
> > Regards,
> > -SaiRamesh.
> >
> >
> > --- tArAng <> wrote:
> >
> > > Arun, Sairamesh,
> > >
> > > I think Arun you are correct. The resultant pdf
> > will
> > > be Gaussian by Central Limit Theorum.
> > >
> > > I think what Sairamesh is doing is adding two
> > > Gaussian Random Variables with different
> > variances (
> > > var1 = a^2 and var2 = b^2).
> > > Correct me if I am wrong.
> > >
> > >
> > > Tarang
> > >
> > >
> > > On Mon, 25 Oct 2004 wrote :
> > > >Hi
> > > >Are the 2 rvs are independent? I assume you
> are
> > > generating a new rv by
> > > >linear combination of the 2 rvs.
> > > >When pdf of 2 independent rvs are added, the
> > > resultant pdf is
> > > >convolution of the 2 pdfs. Hence, you should
> be
> > > able to calculate closed
> > > >form of the resultant pdf. I guess(I may be
> > wrong)
> > > that the resultant
> > > >pdf also may be a guassian rv.
> > > >Regards
> > > >arun
> > > >-----Original Message-----
> > > > From: nammi sairamesh
> > > [mailto:]
> > > >Sent: Saturday, October 23, 2004 8:29 AM
> > > >To:
> > > >Subject: [matlab] random variable of desired
> pdf
> > > >Hi,
> > > > I am modelling a wireless channel, I
> want
> > to
> > > >model the channel as mixture of two guassians
> > which
> > > is
> > > >suitable for my applications.
> > > >i.e. f= a*f1+b*f2;
> > > >where f is the pdf of the noise signal.
> > > >f1 and f2 are gaussian pdfs with mean 0 and
> > > variance
> > > >=1, a and b are some constants>0,
> > > >Now i want to generate a random variable in
> > matlab
> > > >whose pdf is f(=a*f1+b*f2).
> > > >But how to genearte a random variable with pdf
> > of
> > > f.
> > > >Help in this regard is highly appreciated.
> > > >Regards,
> > > >-SaiRamesh.
> > > >
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> > > >To br> > > > >.
> > > >
> > >
> > >
> > > Tarang Dadia
> > > Graduate Student
> > > Wireless Networking Lab
> > > University of Texas at Arlington.
> > >
> >
> >
> >
>
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