Thread Subject: convolve 2 probability distributions

Hi - probably an easy one:

How do I nummerically convolve 2 probability distributions
and see the resulting distribution?

i.e.
P = [(0+eps):0.01:(1-eps)];
normint = norminv(P,0.05,0.005)
lognint = logninv(P,log(0.05),3);
X = lognpdf(lognint,log(0.05),3);
Y = normpdf(normint,0.05,0.005);
total = conv(X,Y);
figure,hist(total)

Leads not really to the result... Any help?

Patric

"Patrice Tscherrig" <patrice.tscherrig@gmx.ch> wrote in
message <g3ra0s$g8k$1@fred.mathworks.com>...
> Hi - probably an easy one:
>
> How do I nummerically convolve 2 probability distributions
> and see the resulting distribution?
>
> i.e.
> P = [(0+eps):0.01:(1-eps)];
> normint = norminv(P,0.05,0.005)
> lognint = logninv(P,log(0.05),3);
> X = lognpdf(lognint,log(0.05),3);
> Y = normpdf(normint,0.05,0.005);
> total = conv(X,Y);
> figure,hist(total)
>
> Leads not really to the result... Any help?
>
> Patric


Wouldn't it be easier to just sample from X and Y and do
hist(x+y)?

"matt dash" <n.a@mail.com> wrote in message <g3rjm6
$79h$1@fred.mathworks.com>...
> "Patrice Tscherrig" <patrice.tscherrig@gmx.ch> wrote in
> message <g3ra0s$g8k$1@fred.mathworks.com>...
> > Hi - probably an easy one:
> >
> > How do I nummerically convolve 2 probability
distributions
> > and see the resulting distribution?
> >
> > i.e.
> > P = [(0+eps):0.01:(1-eps)];
> > normint = norminv(P,0.05,0.005)
> > lognint = logninv(P,log(0.05),3);
> > X = lognpdf(lognint,log(0.05),3);
> > Y = normpdf(normint,0.05,0.005);
> > total = conv(X,Y);
> > figure,hist(total)
> >
> > Leads not really to the result... Any help?
> >
> > Patric
>
>
> Wouldn't it be easier to just sample from X and Y and do
> hist(x+y)?

Matt,

Well, Don't think that leads to what I want to achive.
Given an empirical pdf1 and pdf2 I want to get out the
empirical convolution of pdf1 and pdf2. With your
suggestion:
x=X(randint(1,1000,[1 100]));
y=Y(randint(1,1000,[1 100]));
figure,hist(x+y)

And looking at the empirial means and std's - not really
what I expect after convolving the above two distributions.

Any help?

Patrice Tscherrig <patrice.tscherrig@gmx.ch> wrote:
> Hi - probably an easy one:
>
> How do I nummerically convolve 2 probability distributions
> and see the resulting distribution?
> P = [(0+eps):0.01:(1-eps)];
> normint = norminv(P,0.05,0.005)
> lognint = logninv(P,log(0.05),3);
> X = lognpdf(lognint,log(0.05),3);
> Y = normpdf(normint,0.05,0.005);
> total = conv(X,Y);
> figure,hist(total)

1) conv works on equidistant points
2) if you have pdf dont use hist but plot

You need do it like this:

x=(-1:.001:1);
l=lognpdf(x,log(0.05),3);
n=normpdf(x,0.05,0.005);
ln=conv(l,n)*(x(2)-x(1));
plot( x,n, x,l, x*2,ln(1:2:end) );
xlim([.0,.3]);ylim([0,100]);

pisz_na.mirek@dionizos.zind.ikem.pwr.wroc.pl wrote in
message <g3tg6p$cdg$1@z-news.pwr.wroc.pl>...
> Patrice Tscherrig <patrice.tscherrig@gmx.ch> wrote:
> > Hi - probably an easy one:
> >
> > How do I nummerically convolve 2 probability
distributions
> > and see the resulting distribution?
> > P = [(0+eps):0.01:(1-eps)];
> > normint = norminv(P,0.05,0.005)
> > lognint = logninv(P,log(0.05),3);
> > X = lognpdf(lognint,log(0.05),3);
> > Y = normpdf(normint,0.05,0.005);
> > total = conv(X,Y);
> > figure,hist(total)
>
> 1) conv works on equidistant points
> 2) if you have pdf dont use hist but plot
>
> You need do it like this:
>
> x=(-1:.001:1);
> l=lognpdf(x,log(0.05),3);
> n=normpdf(x,0.05,0.005);
> ln=conv(l,n)*(x(2)-x(1));
> plot( x,n, x,l, x*2,ln(1:2:end) );
> xlim([.0,.3]);ylim([0,100]);
>
>
Hi

Thanks for the hint - very useful! could you however
elaborate on why to use:
 x*2
and
ln(1:2:end)
?

regards,

Patrice

pisz_na.mirek@dionizos.zind.ikem.pwr.wroc.pl wrote in
message <g3tg6p$cdg$1@z-news.pwr.wroc.pl>...
> Patrice Tscherrig <patrice.tscherrig@gmx.ch> wrote:
> > Hi - probably an easy one:
> >
> > How do I nummerically convolve 2 probability
distributions
> > and see the resulting distribution?
> > P = [(0+eps):0.01:(1-eps)];
> > normint = norminv(P,0.05,0.005)
> > lognint = logninv(P,log(0.05),3);
> > X = lognpdf(lognint,log(0.05),3);
> > Y = normpdf(normint,0.05,0.005);
> > total = conv(X,Y);
> > figure,hist(total)
>
> 1) conv works on equidistant points
> 2) if you have pdf dont use hist but plot
>
> You need do it like this:
>
> x=(-1:.001:1);
> l=lognpdf(x,log(0.05),3);
> n=normpdf(x,0.05,0.005);
> ln=conv(l,n)*(x(2)-x(1));
> plot( x,n, x,l, x*2,ln(1:2:end) );
> xlim([.0,.3]);ylim([0,100]);
>
>
Hi

Thanks for the hint - very useful! could you however
elaborate on why to use:
 x*2
and
ln(1:2:end)
?

regards,

Patrice

pisz_na.mirek@dionizos.zind.ikem.pwr.wroc.pl wrote in
message <g3tg6p$cdg$1@z-news.pwr.wroc.pl>...
> Patrice Tscherrig <patrice.tscherrig@gmx.ch> wrote:
> > Hi - probably an easy one:
> >
> > How do I nummerically convolve 2 probability
distributions
> > and see the resulting distribution?
> > P = [(0+eps):0.01:(1-eps)];
> > normint = norminv(P,0.05,0.005)
> > lognint = logninv(P,log(0.05),3);
> > X = lognpdf(lognint,log(0.05),3);
> > Y = normpdf(normint,0.05,0.005);
> > total = conv(X,Y);
> > figure,hist(total)
>
> 1) conv works on equidistant points
> 2) if you have pdf dont use hist but plot
>
> You need do it like this:
>
> x=(-1:.001:1);
> l=lognpdf(x,log(0.05),3);
> n=normpdf(x,0.05,0.005);
> ln=conv(l,n)*(x(2)-x(1));
> plot( x,n, x,l, x*2,ln(1:2:end) );
> xlim([.0,.3]);ylim([0,100]);
>
>
Hi

Thanks for the hint - very useful! could you however
elaborate on why to use:
 x*2
and
ln(1:2:end)
?

regards,

Patrice

Thanks for posting this question.

I'm trying to use convolve to use probability generating
functions in a branching process. So my example is not
empirical.

I used

s = 1
p = [p2 p1 p0]

conv(p,p) ...

using this with varargout and varargin to iterate on conv
so result is like conv(p,p), conv(p,p,p) conv(p,p,...,p)

I replicated a result in demography text successfully.

But wheh I use a compound distribution like Poisson and
Bernoulli, I'm not getting a result that makes sense

When I figure this out, I'll email

Nancy Hammond
Chicago
"Patrice Tscherrig" <Patrice_Tscherrig@rcomext.com> wrote
in message <g4aqsq$gar$1@fred.mathworks.com>...
> pisz_na.mirek@dionizos.zind.ikem.pwr.wroc.pl wrote in
> message <g3tg6p$cdg$1@z-news.pwr.wroc.pl>...
> > Patrice Tscherrig <patrice.tscherrig@gmx.ch> wrote:
> > > Hi - probably an easy one:
> > >
> > > How do I nummerically convolve 2 probability
> distributions
> > > and see the resulting distribution?
> > > P = [(0+eps):0.01:(1-eps)];
> > > normint = norminv(P,0.05,0.005)
> > > lognint = logninv(P,log(0.05),3);
> > > X = lognpdf(lognint,log(0.05),3);
> > > Y = normpdf(normint,0.05,0.005);
> > > total = conv(X,Y);
> > > figure,hist(total)
> >
> > 1) conv works on equidistant points
> > 2) if you have pdf dont use hist but plot
> >
> > You need do it like this:
> >
> > x=(-1:.001:1);
> > l=lognpdf(x,log(0.05),3);
> > n=normpdf(x,0.05,0.005);
> > ln=conv(l,n)*(x(2)-x(1));
> > plot( x,n, x,l, x*2,ln(1:2:end) );
> > xlim([.0,.3]);ylim([0,100]);
> >
> >
> Hi
>
> Thanks for the hint - very useful! could you however
> elaborate on why to use:
> x*2
> and
> ln(1:2:end)
> ?
>
> regards,
>
> Patrice