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.

我们提出了两种分析稀疏随机数据的方法，它们表现出它们的第一矩和第二矩之间的幂律关系（泰勒定律），以及当其值介于1和2之间时确定各自的幂指数。它们是基于分析Haar小波展开的成分。第一种方法使用平均系数和小波系数的第一次迭代之间的相关性，随后研究线路上零填充的统计信息，这对应于分析分布的两个第一时刻之间的线性相关性。第二种方法是指由全套小波系数形成的泰勒图。讨论的是，此类表示形式还提供了检查分析数据的时间尺度稳定性并区分Tweedie概率分布的特殊情况的机会。以太平洋五个空间区域的模拟系列和真实海洋物种丰度数据为例，说明了这些方法的适用性。