How to integrate with distribution function?

I have a situation in Magnetisation where i am required to find .

Available data for variables: M and H. (1*350 each)

Constants:

where

Taking σ and as symbolic variables, i need to evaluate the integral which will be then used to fit available M-H data to estimate σ and .

I tried integrating but couldn't get any result.

Can someone point out what to be done?

Answer 1

[Star Strider]

That looks like a version of the Lognormal Distribution. It would likely be best to code the ‘M’ result as a function of ‘H’, and then use one of the optimisation routines to solve for the ‘D_m’ as a parameter.

Code it, then first experiment with lsqcurvefit or another routine. If that approach has problems, consider using a Global Optimization Toolbox function such as ga to see if it can be estimated.

[Musthafa Anwar]

Thanks for your suggestion. I'll try it out and get back.

[Star Strider]

My pleasure!

Since I do not have any of the constants, or the data, I did not pursue this myself. It should be relatively straightforward to code and estimate ‘D_m’. Consider using the integral funciton. It may be necessary to use 'ArrayValued' as well.