Does a bad powerlaw fit not even be closer to the data points??

[Nixon Raj]

I am trying to fit a data with power law, to show it is a scale free network.

When i use powerlaw, i could able to get a better fit with alpha=2.03 and xmin 3.52 (please check the attached figure 1). 

So extracted the values less than 3.5 as separate dataset and wanted to know the alpha value for that dataset. This is just to differentiate how scale free the higher values that had a power law fit is from the lower values. (In other words, the better fit should have alpha between 2 to 3 and the lower values with bad fit should have alpha value very low.)

So i tried to power law fit the lower values, ie dataset with values less than 3.5, i get a weird fit, which is away from the data points. (please check the attached figure 2).

Figure 3, shows the overall power law fit (ignore the lomax fit in it)

Questions:

1. Why is the power_law.plot_pdf is very away from the data points?

2. Why is it even not in the trendline of the data? Any reasons.

3. The lower value data points visually looks very linear, so atleast i should have got a line trend through the data points even if it is a bad poer law fit right!! May be i'm wrong. Please help me sort this out.

Figure 1: The tail region (alpha:2.03, amin:3.52)

Figure 2: Values < 3.52

Figure 3: (All data)

[Jeff Alstott]

Thanks for using powerlaw!

You've created an xmax in the data. Do you get the same effect if when you fit with powerlaw you add xmax=3.5?

I dimly recall there *might* be some issue with values smaller than 1, but I doubt it. Worth trying multiplying all the data by the smallest value, just in case. But I apologize that I haven't maintained powerlaw in years.

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[Nixon Raj]

Adding 3.5 as xmax does not help either. And multiplying the smallest value with the data also didn't help. 

I have attached the data along with this mail, can you check it. I just need a better fit and the alpha value of it. Please help me.

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Regards 

Nixon Raj N

Department of Biological Science and Technology
Institute of Bioinformatics and Systems Biology
National Chiao Tung University
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