How Do the Schechter Function and Maximum Likelihood Method Differ?

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Discussion Overview

The discussion revolves around the differences between the Schechter Function and the Maximum Likelihood Method, including the 1/Vmax method. Participants explore whether these methods are related or serve different purposes in calculating luminosity functions in astronomy.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the relationship between the Schechter Function and the Maximum Likelihood Method, questioning whether they are applied to the same context or are entirely different approaches.
  • Another participant clarifies that the Schechter Function describes the luminosity function of galaxies, while the Maximum Likelihood and 1/Vmax methods are statistical techniques used to fit functions to data.
  • A participant inquires about the best method for fitting the Schechter Function specifically for Galaxy Groups, suggesting that the 1/Vmax method may not be suitable due to similar distances among the galaxies.
  • Another participant acknowledges uncertainty about the best fitting method, indicating that the choice may depend on specific circumstances and noting variability in the implementation of the Maximum Likelihood Method.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method for fitting the Schechter Function, and there are differing views on the applicability of the 1/Vmax method in certain scenarios.

Contextual Notes

The discussion highlights the potential limitations of the 1/Vmax method based on distance assumptions and the variability in implementing the Maximum Likelihood Method, but these aspects remain unresolved.

jl294
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Schechter Function...

I''m very confused with what the difference is between the Schechter Function and 'Maximum likelihood method' or 1/Vmax method? Are the later two methods to be applied to the Schechter or are they completely different functions to calculate LF altogether?

Cheers
 
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These are completely different things. The Schechter function describes the luminosity function of galaxies [see: http://en.wikipedia.org/wiki/Luminosity_function_(astronomy ) ]; while the maximum likelihood and 1/vmax methods are statistical methods of fitting a function (e.g. the Schechter function) to a set of data [see: http://en.wikipedia.org/wiki/Maximum_likelihood ]
 
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OK. What do you think is the best method for fitting Schechter function for Galaxy Groups? The distance is roughly similar for these galaxies, so 1/Vmax method wouldn't be applicable right?

Cheers
 


I'm not sure, I've never done it myself. I'm sure it depends on the situation---and I'm sure you're right, if the distances are comparable, 1/Vmax isn't doing much.
I think there is also a lot of variety on how to implement a maximum likelihood method---I don't think its a specific algorithm.
 

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