What will be the statistical properties of the error present in the signal?
It depends on how "raw" your raw data is. The number of triggers received in a given time period will be Poisson distributed. This is true for most kinds of cuts you have on your data; for example, an energy threshold. If you have downstream non-linear data processing or electronics effects, you can push this off Poisson, but it's pretty robust. Now, the measured energy is a different beast, which will be entirely detector dependent. If you have a measured energy dispersion function (ideally but rarely measured by shooting a known monoenergetic beam into the detector, and measuring the distribution of the reported energy) your on-orbit data will be the true energy spectrum convolved with your energy dispersion function.
See Gregory and Loredo, ApJ 398, 146, 1992, or Feigelson and Babu, "Promise of Bayesian Inference for Astrophysics" (a book of articles), or WF Tompkins, "Applications of LIkelihood Analysis in Gamma-Ray Astrophysics," a PhD thesis from Stanford -- pretty sure it's on arXiv.
Biplob,
My comment is not directly concerning your question, but I hope it will be usefull to known some new information about a background noise caused by the magnetospheric electrons at heights 30 keV were revealed at longitudes outside the South Atlantic Anomaly region during the geomagnetic disturbances (storms and substorms).
See details in the paper Suvorova et.al., TEC evidence for near-equatorial energy deposition by 30 keV electrons in the topside ionosphere, JGR-Space Physics, 2013, doi:10.1002/jgra.50439.
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