How to get upper and lower bounds values from an empirical cumulative distribution?

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Hamish Cavaye 2020-10-20

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评论： Star Strider 2020-10-20

Hi, thanks for looking at my question. I've been googling, looking on here, and reading the Matlab documentation all afternoon and I can't work this out. I'm sure it's very simple, but I'm new to Matlab syntax so I need some help please!

I have a vector, which is a list of parameters from some data fitting. Specifically it's 250 values.

I want to find the 95% confidence bounds for the numbers in this vector. I can plot an ecdf:

I can also get the [x,y] values for this ECDF using:

[cdf_x,cdf_y] = ecdf(data_vector)
cdf = [cdf_x,cdf_y]

Where I am struggling is I cannot work out how to get the 95% upper and lower values from the array "cdf" (or any of the previous variables I've generated along the way). It's all empirical, so I just want to know the two values of cdf_y where cdf_x equals 0.025 and 0.975.

How can I do this?

NB. cdf_x doesn't have values specifically at 0.025 or 0.975 so it needs to either interpolate or give the closest result if possible.

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采纳的回答

Star Strider 2020-10-20

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https://ww2.mathworks.cn/matlabcentral/answers/620213-how-to-get-upper-and-lower-bounds-values-from-an-empirical-cumulative-distribution#answer_519343

编辑：Star Strider 2020-10-20

Using the prctile funciton on ‘cdf_y’ may work to calculate the percentiles (that appear to be what you want). To get the approximate ‘cdf_x’ values that are associated with them, use the interp1 function.

The code would go something like this:

prctv = prctile(cdf_y, [2.5 97.5]);
xval = interp1(cdf_y, cdf_x, prctv);

I cann ot write exact code since I do not have your data.

EDIT — (20 Oct 2020 at 15:42)

Corrected typographical error.

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Hamish Cavaye 2020-10-20

Thanks a lot for your help. I will give this a try and if I need to come back to you I'll attach some files so you've got something specific to work with!