How to pick the j-th percentile of a distribution?

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pietro 2014-6-6

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https://ww2.mathworks.cn/matlabcentral/answers/132661-how-to-pick-the-j-th-percentile-of-a-distribution

评论： Marco Soldati 2018-4-4

采纳的回答： Star Strider

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Hi all,

I have some data and I want to pick the j-th percentile of the distribution.

Here an example:

a=2000;
b=300;
c=a+(b)*randn(100,1);
cdfval = fitdist(arg_1, 'normal');

So how can I get the 50° percentile of the distribution, that it is 2000?

thanks

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Answer 1

Star Strider 2014-6-6

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Since you have the Statistics Toolbox, use the prctile function.

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Star Strider 2014-6-6

编辑：Star Strider 2014-6-6

在 MATLAB Online 中打开

Change this line to:

pctval = prctile(pdfval,95)

to get the 95th percentile.

If you want to get every percentile from the 5th to the 95th, put the call in a loop:

a=2000;
b=300;
pdfval = a + b*randn(100000,1);
pctl = 5:5:95;
for k1 = 1:length(pctl)
    pctval(k1,:) = [pctl(k1) prctile(pdfval,pctl(k1))];
end

The pctval array now has the information as:

pctval =
       5.0000e+000     1.5063e+003
      10.0000e+000     1.6155e+003
      15.0000e+000     1.6915e+003
                  . . .

with the percentile in the first column and the percentile value for your data in the second column.

Take out these lines:

prova=fitdist(c,'normal');
pdfval=pdf(prova,linspace(a-4*b,a+4*b,100));

and just use the code I included here. These lines will simply make things more complicated and will give you wrong answers if your actual data are not normally distributed. The prctile function does everything you need.

Marco Soldati 2018-4-4

Hi all, do you know how to get the confidence interval for a given percentile?

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Answer 2

pietro 2014-6-6

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You're on right, Thanks

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pietro 2014-6-7

Supposing I have few numbers got by experiment that I know from a theory they are distributed according to a specific distribution. If I'm not lucky to get spread values using prctile(numbers) I'll never get the real percentile of the distribution because the percentiles are limited by the experimental data. Therefore I need to compute the percentiles from a distribution. In this case, how can I compute them? Generating casual numbers according to the fitted distribution and then using prctile?

Star Strider 2014-6-7

If you know the distribution, then estimate its parameters from your experimental data (the fitdist function is probably best here) and calculate the percentiles from the cumulative distribution function for that distribution. Use the icdf function for the appropriate distribution, Don’t use prctile in that situation.

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