A wavelet-based approach to revealing the Tweedie distribution type in sparse data

• Published in: Physica A Vol. 553; p. 124653
• Main Authors: Khalin, Andrey A., Postnikov, Eugene B.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2020
• Subjects: Fishery; Haar wavelet; Species abundance; Taylor’s law; Tweedie distribution; Fishery; Species abundance; Tweedie distribution; Taylor’s law; Haar wavelet
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2020.124653

We propose two approaches to the analysis of sparse stochastic data, which exhibit a power-law dependence between their first and second moments (Taylor’s law), and determining the respective power index, when it has a value between 1 and 2. They are based on the analysis of components of the Haar wavelet expansion. The first method uses a dependence between the first iterations of averaging and wavelet coefficients with the subsequent studying the statistics of zero paddings on the line, which corresponds the linear dependence between two first moments of the analysed distributions. The second method refers to Taylor’s plot formed by the full set of wavelet coefficients. It is discussed that such representations provide also an opportunity to check time–scale stability of analysed data and distinguish between particular cases of the Tweedie probabilistic distribution. Both simulated series and real marine species abundance data for five spatial regions of the Pacific are used as example illustrating an applicability of these approaches. •The Haar wavelet transform allow calculating the Tweedie power index.•Taylor(Tweedie)’s law can be distinguished from the Gamma-distributed data with zeros.•Real fish abundance data are analysed as an example.