How can I fit a flexible distribution to a set of percentiles?
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I want to estimate a distribution for test scores however the only data available is in percentile scores {10,25,50,75,90}. I can measure skew and kurtosis from these percentiles but how can I fit the percentile scores into a continuous distribution while preserving the shape. here is some example data:
Test_Score_Data = [352, 410, 478, 543, 597]
Percentiles = [10, 25, 50, 75, 90]
Thanks
2 Comments
Jeff Miller
on 27 Oct 2020
Do you want to fit particular continuous distribution shapes (e.g., normal, gamma), or do you want to fit the percentiles into some generic, unspecified continuous distribution?
Accepted Answer
Jeff Miller
on 28 Oct 2020
A normal distribution fits very well: see attached for a figure and the matlab code to generate it.
There is no obvious skew (543-478 is nearly equal to 478-410), and I think you would need wider percentiles to get much information about kurtosis.
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