Bibcode
Asensio Ramos, A.
Bibliographical reference
Astronomy and Astrophysics, Volume 472, Issue 1, September II 2007, pp.293-298
Advertised on:
9
2007
Journal
Citations
15
Refereed citations
14
Description
Aims:We investigate the statistical properties of the extreme events of
the solar cycle as measured by the sunspot number. Methods: The
recent advances in the methodology of the theory of extreme values are
applied to the maximal extremes of the time series of sunspots. We focus
on the extreme events that exceed a carefully chosen threshold and a
generalized Pareto distribution is fitted to the tail of the empirical
cumulative distribution. A maximum likelihood method is used to estimate
the parameters of the generalized Pareto distribution and confidence
levels are also given to the parameters. Due to the lack of an automatic
procedure for selecting the threshold, we analyze the sensitivity of the
fitted generalized Pareto distribution to the exact value of the
threshold. Results: According to the available data, which only
span the previous ~250 years, the cumulative distribution of the time
series is bounded, yielding an upper limit of 324 for the sunspot
number. We also estimate that the return value for each solar cycle is
~188, while the return value for a century increases to ~228. Finally,
the results also indicate that the most probable return time for a large
event such as the maximum at solar cycle 19, happens once every ~700
years and that the probability of finding such a large event with a
frequency smaller than ~50 years is very small. In spite of the
essentially extrapolative character of these results, their statistical
significance is very large.