Accurate Goodness of Fit tests for the extreme tails of empirical distributions is a very important issue, relevant in many contexts, including geophysics, insurance  and finance. We have derived exact asymptotic results for a generalization of the  Kolmogorov-Smirnov test, well suited to test these extreme tails. In passing, we have rederived and made more precise the result of [   P. L. Krapivsky and S. Redner, Am. J. Phys. 64  ( 5):546, 1996  ] concerning the survival probability of a diffusive particle in an expanding cage .
Accurate goodness-of-fit tests for the extreme tails of empirical distributions is a very important issue, relevant in many contexts, including geophysics, insurance , and finance. We have derived exact asymptotic results for a generalization of the large-sample Kolmogorov-Smirnov test, well suited to testing these extreme tails. In passing, we have rederived and made more precise the approximate limit solutions found originally in unrelated fields, first in [ L. Turban, J. Phys. A 25, 127 (1992) and later in P. L. Krapivsky and S. Redner, Am. J. Phys. 64 , 546 ( 1996 ) ] .
R
Goodness of Fit
goodness-of-fit
A
,
A
large-sample
R
test
testing
R
result of
approximate limit solutions found originally in unrelated fields, first in
A
L. Turban, J. Phys. A 25, 127 (1992)
A
and later in
A
, 546
D
5):546,
A
)
D
concerning the survival probability of a diffusive particle in an expanding cage