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How to find the quantiles of the estimated distribution.

Asked by Bo on 6 May 2013

I have a random variable E follows a estimated distribution.Now I put the values of E in a vector,for example e=[-1:1], and the cumulative probability of each element in vector e is filled in vector P. How can I find the 95% quantile of E ?

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Bo

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1 Answer

Answer by the cyclist on 6 May 2013
Accepted answer

So, if I understand, the vector P is effectively the cumulative distribution function (CDF). So, you just need to find which value of P is closest to 0.95. You could this this with

[~,idx95] = min(abs(P-0.95));

Then, to find the corresponding value of e, you could do

e_95 = e(idx95);

If P is not fine-grained enough, you may need to do some kind of interpolation as well.

5 Comments

Bo on 7 May 2013

Thanks for your response and patience

I thought I did not articulate the problem well and my awkward English made you confused.

My work flow was follow:firstly,I got a range of values of ε and formed a unsorted vector E. Since the vector just include the values of random variable ε and the vector couldn't present the probability characteristics of the variable, So I couldn't apply the quantile() function directly to E to get the quantiles I need.

Secondly, I apply a cumulative function whose form was given(not included in Matlab) to E and calculate the cumulative probability values refer to each element of E, then form another vector P in which the order of elements is as the same as in E.

Right now what I am wanna figure out is that, the vector P could be sorted automatically after I sorted the vector E? when I got the two sorted vectors how can I calculate the (1-A)/2 and (1+A)/2 quantiles of the random variable ε? For example:E=[3,4,2,1]; P=[0.75,0.92,0.3,0.1] Each element in E may be different.

Postscripts:

You may ask me "why don't you sort the vector E first then calculate the vector P ?" because I a newcomer and have just started to learn how use the Matlab to do calculating So I am wanna know that : If I have two vectors or matrixes with the same column dimensions, when I sort one of them,is there a method or process can rearrange the other one with the same order along the column direction

the cyclist on 7 May 2013

Just commenting on your last question (then I will try to give the broader problem some thought). There are a couple ways to do what you want, I think.

One way is to use the second index of the sort command:

[sorted_x, index] = sort(x);

The index will give the ordering, which could then be used for other vectors.

You could also put the vectors into one matrix, and use the sortrows() function.

doc sortrows

for details.

Bo on 7 May 2013

Thanks for your help ~!:P

the cyclist

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