How Do the Schechter Function and Maximum Likelihood Method Differ?

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The Schechter Function is a model that describes the luminosity function of galaxies, while the Maximum Likelihood Method and 1/Vmax method are statistical techniques used to fit functions like the Schechter function to observational data. These methods are not the same as the Schechter function but are tools for analyzing data related to it. The 1/Vmax method may not be suitable for galaxy groups with similar distances, as it relies on varying distances for accurate application. The choice of fitting method can vary based on specific circumstances and data characteristics. Understanding these distinctions is crucial for effective analysis in astrophysics.
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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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