Moment inequalities for nonnegative random variables

• Autorzy: Castañeda-Leyva Netzahualcóyotl , Rodríguez-Narciso Silvia , Hernández-Quintero Angélika , Pérez Aroldo

Identyfikatory

DOI

10.37190/0208-4147.00106

• Języki publikacji: EN

Abstrakty

EN

We give reciprocal versions of the Sclove et al. and Feller inequalities for moments of nonnegative random variables. Our results apply to any nonnegative random variable. The strongest assumption is that the moments involved must be finite. Thus, the results obtained also hold for any empirical distribution with nonnegative data. These facts allow potential applications in numerical analysis, probability, and statistical inference, among other disciplines. Moreover, the proposed methodology offers an alternative approach to obtain new inequalities and even to improve some known inequalities. For instance, we give new inequalities for the ratio of gamma functions. In this context, we also improve an inequality by Bustoz and Ismail and some cases of inequalities due to Gurland and Dragomir et al. Additionally, we present a new inequality for finite sums of nonnegative or nonpositive numbers. For some cases, this relation improves even the Cauchy-Bunyakovsky-Schwarz inequality.

Słowa kluczowe

EN

moment inequalities; ratio of gamma functions; alternative expectation formula; alternative covariance formula

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2023
• Tom: Vol. 43, Fasc. 1
• Strony: 41--61
• Opis fizyczny: Bibliogr. 41 poz.

Twórcy

autor

Castañeda-Leyva Netzahualcóyotl

• Departamento de Estadística Universidad Autónoma de Aguascalientes Aguascalientes, Ags., México

autor

Rodríguez-Narciso Silvia

• Departamento de Estadística Universidad Autónoma de Aguascalientes Aguascalientes, Ags., México

autor

Hernández-Quintero Angélika

• Departamento de Estadística Universidad Autónoma de Aguascalientes Aguascalientes, Ags., México

autor

Pérez Aroldo

• División Académica de Ciencias Básicas Universidad Juárez Autónoma de Tabasco Cunduacán, Tab., México

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).