On new stability estimations in Ramachandran–Rao characterization
Romanas Januševičius
Vilniaus pedagoginis universitetas
Olga Januševičienė
Matematikos ir informatikos institutas
Published 2008-12-21


Cauchy distribution
sample mean
identically distributed statistics
stability estimations

How to Cite

Januševičius R. and Januševičienė O. (2008) “On new stability estimations in Ramachandran–Rao characterization”, Lietuvos matematikos rinkinys, 48(proc. LMS), pp. 386–388. doi: 10.15388/LMR.2008.18127.


B. Ramachandran and C.R. Rao have proved that if X, X1, X2, . . ., Xn are i.i.d. random variables and if distributions of sample mean \bar X = \bar X(n) = (X1 + ··· + Xn)/n and monomial X are coincident at least at two points n = j1 and n = j2 such that log j1/ log j2 is irrational, then X follows a Cauchy law. Assuming that condition of coincidence of \bar X(n) and X are fulfilled at least for two n values, but only approximately, with some error ε in metric λ, we prove that, in certain sense, characteristic function of X is close to the characteristic function of the Cauchy distribution and construct stability estimation.

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