Open AccessOn new stability estimations in Ramachandran–Rao characterization
Author(s) -
Romanas Januškevičius,
Olga Januškevičienė
Publication year - 2008
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.2008.18127
Subject(s) - mathematics , cauchy distribution , bar (unit) , combinatorics , monomial , ramachandran plot , function (biology) , characterization (materials science) , distribution (mathematics) , stability (learning theory) , mathematical analysis , metric (unit) , physics , nuclear magnetic resonance , protein structure , operations management , evolutionary biology , machine learning , meteorology , computer science , optics , economics , biology
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.