**integration over a Gaussian density #2**in matlab, how to get the integration of xf(x) from t1 to t2
where f(x) is a Gaussian (or Normal) density function with
known mean and variance parameters? thanks!
"Jerry " <mricad@yahoo.no000spppam.com> wrote in message
<foau82$cqb$1@fred.mathworks.com>...
> in matlab, how to get the integration of xf(x) from t1 to t2
> where f(x) is a Gaussian (or Normal) density function with
> known mean and variance parameters? thanks!
normcdf, if you have the statistics toolbox.
If not, then its a simple transformation of
erf or erfc.
John
"John D'Errico"...

**How can i calculate a double density gaussian defined integral**Hi,
I am developing a tool with Matlab of statistical type and i have to
calculate the integral of this function:
f1=( r/(2*pi*(sigma)^2)) * exp( -(
(r)^2/(2*(1-(correlationCoefficent)^2)*(sigma)^2 ) * (
1-2*correlationCoefficent*cos(t)*sin(t) ) ) );
i tried with this Matlab functions:
int
dblquad
and other...
but the result is always the same, Matlab communicate me that it
can't resolve the integral. There aren't error message because the
code is exact simply it can't find a solution for this type of
integral, and the value that return int or the oder functions isn't a
n...

**integration of a gaussian**Hi!
I need to integrate a gaussian plot between two bounds 'a' and 'b' (for
example: -5, +5) .
I'm trying to use the snipped code below:
a=quadl(normpdf,-5,5,0,0,0,1)
but once executed Matlab send me the message:
??? Error using ==> normpdf
Requires at least one input argument.
Any idea?
Many thanks in advance,
Paolo.
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Paolo Giai Miniet wrote
>[...]
> I need to integrate a gaussian plo...

**Complex Gaussian integral**Hi.
I am using version 9.03.
I tried
int(exp(-I*x^2),x=-infinity..infinity);
and received the correct answer: (1/2-1/2*I)*2^(1/2)*Pi^(1/2)
(which is equivalent to sqrt(Pi/I)).
However
int(exp(I*x^2),x=-infinity..infinity);
yields the incorrect result: infinity
rather than the complex conjugate of the first integral.
Is this a known bug?
Inf.
Introducing a parameter 'a' seems to reveal the problem:
> int(exp(a*x^2),x=-infinity..infinity);
/ (1/2)
| Pi
| --------- -csgn(a) = 1
...

**Problem with Simplify and Integrating a gaussian**Hello,
I encountered a very strange behaviour of Mathematica and would like to
ask if this is a bug or if I am doing something incredible wrong. I hope
this list is the right place to do so.
Please find below the contents of my notebook:
In[27]:= v[x_]=If[x<a,0,Exp[- ((x-a)/1.)^2]]
u[x_]=Simplify[v[x]]
Out[27]= If[x<a,0,Exp[-((x-a)/1.)^2]]
Out[28]= \[Piecewise]E^(-1. (a-1. x)^2) a<=x
0 True
In[29]:= Refine[Integrate[u[x],{x,d,\[Infinity]}],{d>a,a>0}]
Refine[Integrate[v[x],{x,d,\[Infinity]}],{d>a,a>0}]
Out[29]= 0.886227 (1.+Erf[a-1. d])
During evaluation ...

**How to get this gaussian integral result?** Integrate[
x1^(n1) x2^(n2) x3^(n3) Exp[
a x1 x1 + b x2 x2 + c x3 x3 + d12 x1 x2 + d23 x2 x3 + d13 x1 x3 +
d], {x1, -Infinity, Infinity}, {x2, -Infinity,
Infinity}, {x3, -Infinity, Infinity}]. n1,n2,n3 are Natural numbers. I still cannot get the general result ,although mathematica takes so much time. Can you help me about this?
simplerbysimpler@gmail.com writes:
> Integrate[
> x1^(n1) x2^(n2) x3^(n3) Exp[
> a x1 x1 + b x2 x2 + c x3 x3 + d12 x1 x2 + d23 x2 x3 + d13 x1 x3 +
> d], {x1, -Infinity, Infinity}, {x2, -Infinity,
> Infinity}, {x3, ...

**integral inside an integral**
Does anyone know how to make the following work using pure functions in Mathematica? Given two functions f and g compute and for a fixed k[x]
h[f_,g_,alpha]:=NIntegrate[f[alpha-x]*k[x]/NIntegrate[g[alpha-x-y]*k[y],{y,-Infinity,Infinity}],{x,-Infinity,Infinity}]
I want to put arbitrary functions f and g into h and get an answer.
Charles
In your definition of h, alpha must be a pattern, and since you are using numerical techniques alpha should be restricted to a numeric value.
Clear[h, h2]
k[x_] := Exp[-x^2/3]
h[f_, g_, alpha_?NumericQ] :=
NIntegrate[f[alpha - x...

**integrating within an integral**Hi,
I am looking to integrate a function within another integral. My
problems is that the variable of integration for the outer integral
is a variable in the inner intergral.
For example in pseudo-code:
int(x^2 - int(c^2-x^2)dc )dx
I was suggested the use of a separate function and putting the quad
command in a loop. So I would call the inner integral from this:
function res = G2(xv,lambda10)
res = zeros(size(xv));
for i=1:length(xv)
x = xv(i);
res(i) = (2./lambda10) .* quad(@(c) c.^2./sqrt...
(c.^2-x.^2), x.*(1+eps), lambda10.*(1-eps));
end
end
wher...

**how to integrate this double integral?**Hello everyone.
I'm trying to integrate the below double integral using Monte Carlo
integration:
h = int(from 0 to infinity) int(from 0 to infinity) g(x,y) f_1(x)f_2(y)
dxdy
where f_1 is Gamma function with parameters alpha1 and beta1, f_2 is
Gamma function with parameters alpha1 and beta2. Here g(x,y) is not
provided as a closed form, but it can be evaluated through my m
function.
Since g(x,y) is not closed form, the best way may use Monte Carlo
integration as follows:
h^ = sum(from 1 to n) g(U1_i, U2_i) f_1(U1_i) f_2(U2_i) / n
The problem is that I have to multiply two intervals o...

**Rapid execution of gaussian integrals**I recently posted about very slow execution of infinite symbolic
integrals of the general form
Integrate[const * Exp[-A x^2 + 2 B x], {x, -Infinity, Infinity},]
when A and B are constant-valued expressions of even modest complexity,
even when one inserts the necessary Assumptions to make the integral
convergent.
Daniel Lichtbau replied with some helpful suggestions on how to speed
things up a bit; but to really speed things up I've since been using the
brute force approach
gaussianIntegral[func_, x_] : = Module[ {exp, A, B, C, const},
exp = Exp...

**Integral of square of integral**Hi All,
I need to calculate numerically nested integrals of the form
I = integral f(t)dt (between constant limits)
where
f(t) = [integral of g(x,t)dx (between constant limits)]^2.
Because the result of the innermost integral is squared, the form of
the nested integrals does fit the nested quadrature functions dblquad
and quad2d. In addition, the integrand g(x,t) of the innermost
integral has two problems 1) it is highly oscillatory -so I was trying
the Gauss-Kronrod method (MATLAB's quadgk) and 2) it includes a
expressions of the form v(x) + u(t) (where u and v are wel...

**Integration of Elliptic Integral**One of the (many!) advantages of the CAS Mathematica is how quickly
known bugs and deficiencies in general, of an earlier version are
fixed in the next (if possibly!) version of it.
I know some bugs (especially regarding Integration) in other CAS which
are not fixed even 3 or 4 versions later!
It is very pleasant to search in the archives of MathGroup forum and
see old posts mentioning bugs or bad behavior of e.g. Integrate
command which in the later version(s).were corrected.
Nevertheress, sometimes you see old versions to work and give
desirable results and on the contrary the new...

**Integrating a quadruple integral**Dear all,
I need to numerically evaluate a quadrauple integral; however, to my best
knowledge, Matlab doesn't offer any bulit in functions for this type of situation.
Can someone please give me some advice on how I can solve this problem?
Any input is appreciated.
Thank you.
David
Den Mon, 01 Oct 2007 21:41:59 +0000 skrev David :
> Dear all,
>
> I need to numerically evaluate a quadrauple integral; however, to my best
> knowledge, Matlab doesn't offer any bulit in functions for this type of situation.
> Can someone please give me some advice on how I can solve...

**Gaussian integration broken**
Abother bug concerning gaussian integration:
In:= Integrate[Exp[-{x, y}.{{a, b}, {c, d}}.{x, y}],
{x, -Infinity, Infinity}, {y, -Infinity, Infinity}]
Out:= 0
...

**Exponential integration with normal density function**Hello,
I need to evaluate an exponential integral over a positive range. The integrand is of the following form:
(1/x)*pdf(X)
where pdf(X) is the Normal(mu,sigma^2) probability density function.
Which integral approximation method (quad, quadgk, etc.) is the best to evaluate this integral in terms of time and least error?
Thank you,
A.
On May 5, 5:05=A0pm, "Angie" <angie1...@yahoo.com> wrote:
> Hello,
>
> I need to evaluate an exponential integral over a positive range. The int=
egrand is of the following form:
>
> (1/x)*pdf(X)
>
> wher...

**L_{p} norm for gaussian density**Dear all,
Hi, I am a newbie in this newsgroup, my name's Andrew Au. Nice to see
you all. I am recently studying in speech recognition. I am wondering can I
replace the Mahalanobis distance, used by the Gaussian density, by any other
norm, is it still a probability density, can it help by consider choosing
different metric...?
It seems that wasn't many post about probability model here, I am really
interested in those method for knowledge representation. For example,
Bayesian Network, Hidden Markov Model, Kalman Filter as so on. Are there any
newsgroup talk about all these... ?
...

**Gaussian probability density function in Matlab?**Hello all,
I am wondering if there is Gaussian probability density function(pdf)
and Gaussian cumulative density function (cdf) in matlab?
Thanks!
Davy
zhushenli@gmail.com wrote:
> I am wondering if there is Gaussian probability density function(pdf)
> and Gaussian cumulative density function (cdf) in matlab?
If you have the Statstics Toolbox, they are NORMPDF and NORMCDF. If not, it's
easy enough to code them up; the CDF uses ERF or ERFC.
Hope this helps.
- Peter Perkins
The MathWorks, Inc.
...

**Numerical Integration of a Density a various point**Hello,
I have a density (2-dimensional function) that is not symbolically
integrable. Therefore I would
like to numerically integrate this function at different points, e.g.
100-500.
Is there a way to compute the numerical integral at various point
simultaneously? I tried to
use quad2d with vectors, but it doesn't work.
Do you an idea how to solve this?
Best regards,
Ralf
"Ralf Heimrich" <blowfinger@gmx.net> wrote in message
news:f22bfd39-a28a-4b32-b9a5-611a6def6ee4@w31g2000yqk.googlegroups.com...
> Hello,
>
> I have a density (2-dimensional function) that ...

**How to normalize the Gaussian distribution integration to 1**I have a gaussian distribution as the following;
FWHM=50000;
a=FWHM/1.7;
x=linspace(-2*a,2*a,161);
p2=(1/(sqrt(pi)*a))*exp(-.5*(x./a).^2);
i have to do the following;
normalize the gaussian distribution so that when the sum is calculated and each divsion is divided by the sum, the result gives 1.
is this correct?
g=sum(p2);
for o=1:length(p2)
YY(o)=p2(o)/g;
end
any other suggestion is appreciated. thanks alot
On 8 Nov., 12:09, "salman " <salmanabdull...@gmail.com> wrote:
> I have a gaussian distribution as the following;
>
> FWHM=3D50000;
> ...

**Three-dimensional Gaussian Probability Density Function**Hi all,
I am working on a research,I want to define a 3-Dimensional Gaussian
Probability function on YUV color space.. But I dont know how to
calculate 3-D Gauss PDF?
Can someone help me?
Thanks in Advance
Student-Yeditepe University
Shlomo
shlomo wrote:
> Hi all,
>
> I am working on a research,I want to define a 3-Dimensional Gaussian
> Probability function on YUV color space.. But I dont know how to
> calculate 3-D Gauss PDF?
>
> Can someone help me?
>
I assume that the 3-D refers to (Y, U, V). Have you plenty of examples
of the vector (Y, U, V)? Let us nam...

**plotting the probability density for multivariate gaussian mixture**Hi,
I have a multivariate gaussian mixture distribution(a mixture of two gaussians). For each gaussian in the mixture, the mean MU is a 3 dimensional vector, and the covariance matrix is a 3 by 3 matrix.
I want to project the probability densities onto their best-fit hyperplane for the visualization purpose, so could you please help me out?
Thanks a tonne!
Manjari
On Wed, 06 Feb 2013 17:17:08 +0000, Manjari wrote:
> Hi,
> I have a multivariate gaussian mixture distribution(a mixture of two
> gaussians). For each gaussian in the mixture, the mean MU is a 3
> dimensional...

**SMS Gateways Integration | Payment Gateways Integration | API integration and development**http://www.rankingofuniversity.com/show.php?c=9&ARTID=188
...

**SMS Gateways Integration | Payment Gateways Integration | API integration and development**http://www.rankingofuniversity.com/show.php?c=9&ARTID=188
...

**polar transformation to integrate double integral using Monte Carlo Integration**Hello everyone.
I'm trying to integrate the below double integral using Monte Carlo integration:
h = int(from 0 to infinity) int(from 0 to infinity) g(x,y) f_1(x)f_2(y)dxdy
where f_1 is Gamma function with parameters alpha1 and beta1, f_2 is Gamma function with parameters alpha1 and beta2. Here g(x,y) is not provided as a closed form, but it can be evaluated through my m function.
Since g(x,y) is not closed form, the best way may use Monte Carlo integration as follows:
h^ = sum(from 1 to n) g(U1_i, U2_i) f_1(U1_i) f_2(U2_i) / n
The problem is that I have to multiply two intervals o...