Any solution to quasi-gaussian integral ?

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In summary, a quasi-gaussian integral is a type of integral used in statistics and probability to approximate the area under a non-Gaussian curve. It can be solved using various methods, such as Gaussian quadrature or numerical integration, and has applications in physics, engineering, and finance. In most cases, these integrals cannot be solved analytically and instead rely on numerical approximations. The accuracy of the results depends on the method used and the complexity of the function.
  • #1
nlama
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Hello everybody,

Do you know if the following integral has an analytical solution ?

\int^{}_{} \exp{(x-\frac{(x-\mu)^2}{\sigma})} dx

Thanks in advance for your help.

Nicola
 
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  • #2
[tex]\int^{}_{} \exp{\left[x-\frac{(x-\mu)^2}{\sigma}\right]} \ dx [/tex]

This you mean?Try the Mathematica integrator from the wolfram site.

Daniel.
 
  • #3
There it is

[tex] \int \exp\left[x-\frac{(x-a)^{2}}{b}}\right] \ dx =-\frac{\sqrt{b}}{2}e^{a+\frac{b}{4}} \sqrt{\pi} \ \mbox{erf}\left[\frac{b+2(a-x)}{2\sqrt{b}}\right] +C [/tex]

Daniel.
 

1. What is a quasi-gaussian integral?

A quasi-gaussian integral is a type of integral that involves a function with a shape similar to a Gaussian curve. It is often used in statistics and probability to calculate the area under a curve that is not exactly Gaussian, but close enough to approximate using the Gaussian function.

2. How is a quasi-gaussian integral solved?

A quasi-gaussian integral can be solved using various techniques such as the Gaussian quadrature method, numerical integration, or special functions like the error function. The method used depends on the complexity of the function and the desired level of accuracy.

3. What are some applications of quasi-gaussian integrals?

Quasi-gaussian integrals are commonly used in physics, engineering, and finance to model and analyze data that follows a non-Gaussian distribution. They are also useful in signal processing, image analysis, and pattern recognition.

4. Can quasi-gaussian integrals be solved analytically?

In most cases, quasi-gaussian integrals cannot be solved analytically, meaning there is no closed-form solution. Instead, numerical methods are used to approximate the integral.

5. How accurate are the results obtained from solving a quasi-gaussian integral?

The accuracy of the results depends on the method used to solve the integral and the complexity of the function. In general, the results obtained from numerical methods are close to the exact solution, but may have a small margin of error.

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