How I accept generated [x,y] samples that fall into a probability density function or an equivalent area?

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DIMITRIS GEORGIADIS 2017-10-14

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I generate samples in 2-d space, i.e. x,y coordinates. I have a normal pdf and I want to keep/accept the samples that fall inside the pdf. Let as denote this area W. Is there a specific command for this? How can I implement it? I found in Matlab inpolygon command , but it works only for polygonal region and not on curves, such as pdf .

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Star Strider 2017-10-14

The normal distribution extends from -Inf to +Inf. All the real values you create are by definition ‘inside the PDF’.

DIMITRIS GEORGIADIS 2017-10-15

Maybe I was not clear. Please see my comment below and the .m file.

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Answer 1

Image Analyst 2017-10-14

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I'm not sure you mean "fall inside the pdf" since, of course, all values generated must come from the PDF. I think you mean "fall inside the area", presumably one defined by some limits on x and y

% Get x and y somehow
if x < x1 || x > x2 || y < y1 || y > y2
    % Coordinate is out of bounds.  Skip this one.
    continue;
end
% Else do something with it.

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DIMITRIS GEORGIADIS 2017-10-15

编辑：DIMITRIS GEORGIADIS 2017-10-15

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My fault. Maybe I was not clear. I need a simple rejection sampling algorithm, such as the following:

1. K=200 %number of simulations
2. k=1 % first iteration
3. Generate a sample x (for k=1) from f(x) % prior pdf
4. Generate a sample p from the standard uniform distribution in [0,1].
5. if [x,p] ε (i.e. belong) W-space
    a. Accept x
    b. k=k+1
6. Stop if k=K, else go to 3.
Here is my .m file for the above. My question is HOW I express the if condition? The accepted samples must fall inside W-space (the shaded area).