Analytic derivation of the statistical error in the Feynman-αmethod

Experimental validation of analytic formulas for the statistical uncertainty in the Feynman-αmethod

“…Clearly, since the two moments are sampled from the same distribution they are correlated, and thus the formalism introduced in Cramer (1962) depends on the covariance of the two moments. The approach taken in Dubi and Kolin (2016) is a bit different, and geometric by nature. Consider YðTÞ ¼ YðM 1 ðTÞ; M 2 ðTÞÞ as a general differential function of the first two moments.…”

“…The main theme of the present study is the experimental validation of the analytic formulas introduced in Dubi and Kolin (2016). A full description of the construction and the implementation of the formulas is given in Dubi and Kolin (2016), but for sake of completeness, a short description is added.…”

“…The values for M i ; i ¼ 1; 2; 3; 4 can either sampled, or estimated through analytic formulas introduced in Dubi and Kolin (2016). Since the formulas are very lengthy, they will not be repeated here, and the reader is referred to Dubi and Kolin (2016).…”

“…A full description of the construction and the implementation of the formulas is given in Dubi and Kolin (2016), but for sake of completeness, a short description is added.…”

“…. T N , once r YðT j Þ is evaluated, the statistical uncertainty on a is given by Dubi and Kolin (2016):…”