How to find the quantiles of the estimated distribution.

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 ?

Answer 1

[the cyclist]

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.

[Bo]

Thanks for your answer! Follow your method,I just can get a approximate quantile among the given vector e and that is not enough.

• My question is How I can get some more accuracy quantiles of the variable, just like "quantile"function in Matlab which is using Linear interpolation method to find the quantiles not included in the vector e*.

 And if the elements in vector e are much more in some content, the numerals in vector P are unregular, such as P=[0.12,0.003,0.008....].what should I do to get the (1-A)/2 and (1+A)/2 quantiles of the random variable E, where A is a selected confidence parameter.

Would you please tell me how to do the interpolation? Should I do some random generating or simulation first?

[the cyclist]

I'm a little bit confused by your response. You said in your original question that P is the cumulative distribution function (cdf). So, I would expect it to be monotonically increasing. Are you sure that P is not the probability distribution function (pdf)? How do you get P?

Is there some reason you cannot apply the quantile() function directly to e? Why is it preferable to use P?

Are you able to post a small example of your vectors e and P?

[Bo]

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]

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]

Thanks for your help ~!:P