How to explain exponential plus Gaussian noise

I have some noisy signal. When I substract real (for calibration it is known) or filtered signal I get residuals. When I plot distribution of these residuals I see that it is sum of exponential and Gaussian distributions. Is it possible to speculate about what does it means? Maybe it is common situation? Could you help me with explanation?

UPDATE:

Blue is RAW signal, red- filtered. Distribution of residuals:

Distribution of abs(residuals):

Distribution near 0:

• How can you tell for sure that it's the sum of an exponential and Gaussian rather than (say) a gamma distribution or a Weibull distribution or some other moderately right skew distribution? May 4, 2017 at 2:46
• It has maximum on 0. In reality it is symmetrical over 0. I just use absolute values.
– zlon
May 4, 2017 at 5:49
• I don't follow this at all. Why would having a mode at 0 imply exponential + Gaussian? If its symmetrical about 0, how does that imply exponential + Gaussian? May 4, 2017 at 8:56
• Ok, it is not exponential it is something very skewed. Is it important for the explanation which 2 sources of noise I have?
– zlon
May 4, 2017 at 8:58
• A. I'm just trying to understand (i) what your actual claim about your data actually is, and (ii) what the basis for the claim is. B. Thanks for the picture; that's potentially quite useful. If that's the absolute value of residuals, how did you decide the residuals were actually symmetric about 0? May 4, 2017 at 11:21

1 Answer

Your side-lobes appear to be approximately at +/- twice your signal amplitude, i.e. when the two signals are 180 degrees out of phase (peak of one = trough of the other). The prevalence likely arises because the blue signal is much higher frequency than the red, so the blue signal goes through several cycles over any interval where the slower red signal is near a peak/trough.