Mathematics – Probability
Scientific paper
Dec 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007agufmsh13a1102c&link_type=abstract
American Geophysical Union, Fall Meeting 2007, abstract #SH13A-1102
Mathematics
Probability
2101 Coronal Mass Ejections (7513), 7513 Coronal Mass Ejections (2101)
Scientific paper
On January 20, 2005, 7:02-7:05 UT the Aragats Multidirectional Muon Monitor (AMMM) located at 3200 m a.s.l. registered enhancement of the high energy secondary muon flux (threshold 5 GeV). The enhancement, lasting for three minutes, has statistical significance of ~4σ and is related to the X7.1 flare seen by the GOES, and very fast (2500 km/s) CME seen by SOHO, and the Ground Level Enhancements (GLE) N 69 detected by the world-wide network of neutron monitors and muon detectors. The energetic and temporal characteristics of the muon signal from the AMMM are compared with the characteristics of other monitors located at the Aragats Space-Environmental Center (ASEC) and with other neutron and muon detectors. Since secondary muons with energies above 5 GeV are corresponding to solar proton primaries with energies 20-30 GeV we conclude that in the episode of the particle acceleration at 7:02 - 7:05 UT 20 January 2005 solar protons were accelerated up to energies in excess of 20 GeV. To prove that detected peaks in the time-series are not only background flux (Galactic Cosmic Rays) fluctuations, but signal candidate (Solar Cosmic Rays), we perform additional investigations of the detectors count rates at 20 January. When calculated the chance probability we have to take into account the experimental procedures we use to reveal the signal. We made 3-minute time series from the 1 minute ones. The re-binning of time series is ordinary operation used by the all groups running the particle solar monitors. However, it has to be taken into account in calculating of the chance probability. Different attempts to obtain "best signal" considering different re- binning cannot be treated by standard Gaussian distribution, but can be considered by implementing Chapman statistics. To check this assumption and demonstrate the influence of the re-binning procedure we perform simulations with simple model of time series. Our numerical modeling confirm that when testing different data binning the probability of obtaining "fake" signal during a given time period increases proportional to number of tests and should be corrected with tuning of parameters of Chapman statistics. Simple Gaussian statistics gives positively biased estimates of chance probability.
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