MATLAB: What assumptions are made in computing Bit Error Rate (BER) and confidence intervals with the BERCONFINT function in Communications System Toolbox

algorithmberconfint

I am looking to use the BERCONFINT function to calculate confidence intervals and Bit Error Rate for signals I am working with.

In order to publish my results, I would like to know what algorithm or general assumptions about these calculations are made by the BERCONFINT function before I use it.

Best Answer

The BERCONFINT function calls the BINOFIT function, which uses the Clopper-Pearson interval to calculate confidence intervals. This is shown at the following link:

 <http://www.mathworks.com/help/toolbox/stats/binofit.html>

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MATLAB: Confidence interval using binofit

The binofit function computes confidence intervals using the Clopper-Pearson method.

I believe what you're seeing is because the distribution is very coarse for N*p values on the order of 1. With N=1000 and p=1/500,

>> binocdf(4:5,1000,1/500)
ans =
    0.9475    0.9835

So in order for the confidence interval to have at least a 95% chance of including p=1/500, the intervals based on x=4 and x=5 would both have to include p. So the coverage probability will be over 98%.

Try increasing to N=100000 in your example and see if the results match.

MATLAB: Confidence Interval

The confidence of what ?

Do you perhaps mean the confidence that the generated numbers really are representative of the normal distribution, then consider (for example) using http://www.mathworks.com/help/toolbox/stats/ttest.html

Keep in mind, of course, that low confidence is not disproof. With the normal distribution you could end up with 15000 copies of the number -42: such a thing is not impossible, just low probability.

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Related Solutions

MATLAB: Confidence interval using binofit

MATLAB: Confidence Interval

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