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. 2022 Sep 20;12:15687. doi: 10.1038/s41598-022-19365-4

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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The three main categories for synthetic data generation in a simulation study. (1) The synthetic data with different spatial structures were generated using different input in variogram function (spatial data1: range1 = 20, range2 = 20, sill1 = 0.1, sill2 = 0.3; spatial data2: range1 = 20, range2 = 10, sill1 = 0.1, sill2 = 0.1; spatial data3: range1 = 20, range2 = 10, sill1 = 0.1, sill2 = 0.3). (2) The variables in synthetic data are derived from different statistical distributions: normal, non-normal, bimodal, and all combined. (3) The synthetic data was modified by increasing the mean value for a certain number of variables and adding the noise.