random variable of desired pdf

Started by nammi sairamesh October 26, 2004

Arun,
f= a*f1+b*f2, ya, u guessed right! f1 na df2
have noramla distribution , but not different means
and variances, and now i wanna generate a random
variable with pdf of f. This is the question i asked
initially!
Regards,
-SaiRamesh.

--- wrote:

> Hi Sai
> A few clarifications:
> Please see the 2 paras below:
> 1. > >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).
>
> 2.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).
>
> There is some discrepancy here. Since the mean of
> the two pdfs are same and variance is also same, the
> only way you can have f(x) = a1*f1(x)+a2*f2(x),
> where f1(x) and f2(x) are normally distributed, is
> that a2+a1 =1. In other words, since both components
> have same variance and mean, the resultant should be
> a a normal distribution. Hence, this is a trivial
> case.
>
> In other words, if f1(x) =
> 1/sqrt(2*pi*sigma1^2)*exp(-(x-mu1)^2/(2*sigma1^2))
> and
>
f2(x)=1/sqrt(2*pi*sigma2^2)*exp(-(x-mu2)^2/(2*sigma2^2)),
> where mu1!=mu2 and/or variances are different, the
> pdf f(x)*f1(x)+a2*f2(x) should be such that total
> area under the composite curve should be 1. If this
> is what you are referring to, then I don't know how
> to simulate the pdf for such a case(when mu1!=mu2
> and/or sigma1 != sigma2)
>
> regards
> arun
>
> -----Original Message-----
> From: arun d naik (WT01 - EMBEDDED & PRODUCT
> ENGINEERING SOLUTIONS)
> Sent: Tue 10/26/2004 16:05
> To: nammi sairamesh; tArAng
> Cc: ;
> Subject: RE: RE: [matlab] random variable of
> desired pdf > 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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