English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

This contribution aims at studying the behaviour of the classical samplemoment estimator, $S(n,q)= \sum_{k=1}^n X_k^{q}/n $, as a function of thenumber of available samples $n$, in the case where the random variables $X$ arepositive, have finite moments at all orders and are naturally of the form $X=\exp Y$ with the tail of $Y$ behaving like $e^{-y^\rho}$. This class of lawsencompasses and generalizes the classical example of the log-normal law. Thisform is motivated by a number of applications stemming from modern statisticalphysics or multifractal analysis. Borrowing heuristic and analytical resultsfrom the analysis of the Random Energy Model in statistical physics, a criticalmoment $q_c(n)$ is defined as the largest statistical order $q$ up to which thesample mean estimator $S(n,q)$ correctly accounts for the ensemble average $\EX^q$, for a given $n$. A practical estimator for the critical moment $q_c(n)$is then proposed. Its statistical performance are studied analytically andillustrated numerically in the case of \emph{i.i.d.} samples. A simplemodification is proposed to explicitly account for correlation amongst theobserved samples. Estimation performance are then carefully evaluated by meansof Monte-Carlo simulations in the practical case of correlated time series.

Critical moment definition and estimation, for finite size observation of log-exponential-power law random variables