Compute conditional mean from distribution

How do I compute a conditional mean of a distribution in Matlab (e.g. between the 1st and 5th percentiles)? Right now, I am thinking of using integral, but I'm guessing that there is a smarter way.

pd = makedist('Lognormal', 5, 0.5);

[Fredrik P]

https://en.wikipedia.org/wiki/Log-normal_distribution#Conditional_expectation

Answer 1

[Jeff Miller]

Another approach:

pd = makedist('Lognormal', 5, 0.5);
lb = icdf(pd,0.01);  % find scores at 1% and 5%
ub = icdf(pd,0.05);
td = truncate(pd,lb,ub);  % truncate the distribution between those bounds
m = mean(td);
[lb, ub, m]
% ans =
%        46.378       65.207       57.298

Answer 2

[Julian]

Is one of these conditional mean models fit you?

Answer 3

[Paul]

Hi Fredrik,

If you just want to compute the conditional mean, why not just use the third expression for Conditional Expectation in the link you've provided? In Matlab, that PHI function is implemented with normcdf.

If you want a quick, numerical approximation to your answer you can always do something like this:

mu = 5; sigma = 0.5;
pd = makedist('Lognormal', mu, sigma);
plot(0:.1:500,pdf(pd,0:.1:500))  % plot to see what we're working with

rng(100)
r = random(pd,[1e6 1]);  % generate random numbers from the distribution
r(r<200 | r>300) = [];   % throw away values outside of 200 < X < 300
conditionalmean = mean(r)% mean conditioned on X being in the specified range

conditionalmean = 240.2054