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Breakdown coefficient statistics in binary multiplicative cascades

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Abstract

Given the use of multiplicative cascades for the construction of multifractal measures, combined with the difficulty of obtaining the probability distribution function of a cascade generator from a realization thereof, it becomes important to develop mathematical tools to estimate the generator distributions. We are herein devising a method of obtaining the probability distribution of weights in a one-dimensional, binary multiplicative cascade, using its binary breakdown coefficients. Confirmation is provided by numerical simulations, and the method is applied to rainfall intensity time series.

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Data availability

Rainfall data were collected at the Hydrometeorology Lab of the Iowa Institute of Hydraulic Research (now IIHR – Hydroscience & Engineering), under the supervision of Konstantine Georgakakos.

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Acknowledgements

The authors would like to acknowledge the constructive observations and suggestions of the Associate Editor and Reviewers.

Funding

César Aguilar Flores was supported by CONACyT scholarship 485991. Alin Carsteanu was supported by Grant SIP-IPN 20202012.

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Authors and Affiliations

  1. Escuela Superior de Física y Matemáticas – Instituto Politécnico Nacional, Mexico City, Mexico

    César Aguilar-Flores, José-María Rocha-Martínez & Alin-Andrei Carsteanu

Authors
  1. César Aguilar-Flores
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  2. José-María Rocha-Martínez
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  3. Alin-Andrei Carsteanu
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Correspondence to Alin-Andrei Carsteanu.

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Aguilar-Flores, C., Rocha-Martínez, JM. & Carsteanu, AA. Breakdown coefficient statistics in binary multiplicative cascades. Stoch Environ Res Risk Assess 35, 1681–1687 (2021). https://doi.org/10.1007/s00477-021-01975-5

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