How can I calculate vector relative errors in percent?

I have to calculated for each vector sample mean ms and variance vs and for

each calculated ms and vs calculate their relative errors in percent. How can I calculate their relative errors in percent?

It would be great if somebody give some examples.

Answer 1

[Image Analyst]

You need to have a reference signal. Note: variance of a signal is not the error of a signal unless the true signal is a constant, which would be a true variance of zero. For example a true noiseless sine wave would have a variance but that is not an error -- it's the true signal.

You can compute the percentage error from your reference signal like this

pctMeans = 100 * abs(refSignal - testSignal) ./ refSignal;

[Image Analyst]

Is your mean and variance over the whole signal, or is a locally varying one by sliding a window along?

Note the signal is either the mean or the variance in my above equation, so

pctMeans = 100 * abs(refSignal - testSignal) ./ refSignal; % On your vector itself
pctVar = 100 * abs(refSignalVar - testSignalVar) ./ refSignalVar; % On the variance of your signal vector.

[Ihor]

Thank you so much!

Answer 2

[Torsten]

x = rand(100,1);
ms = mean(x);
vs = var(x);
relative_error_ms_in_percent = abs(ms-0.5)/0.5 * 100

relative_error_ms_in_percent = 0.0043

relative_error_vs_in_percent = abs(vs-1/12)/(1/12) * 100

relative_error_vs_in_percent = 4.9800

[Ihor]

Thank you so much!