Measurement and comparison of distributional shift with applications to ecology, economics, and image analysis
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912427570888704 |
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| author | Locey, Kenneth J. Stein, Brian D. |
| author_facet | Locey, Kenneth J. Stein, Brian D. |
| contents | The concentration of a distribution toward a lower bound is a conceptually simple property that closely relates to concepts of rarity and poverty, but that lacks a global descriptive statistic. We term this property 'shift' and define it as the distance of a central tendency from an upper bound, expressed as a proportion of a finite range. We derive a flexible, low complexity measure of shift and demonstrate its properties, its use with theoretical distributions, and its relation to skewness. We then use shift as the basis for a directional difference measure and as the basis for a formal distance metric that closely approximates the behavior of metrics having greater complexity (e.g., Wasserstein distance). Using simulated datasets and comparisons to system-specific measures, we demonstrate shift as a measure of species rarity and as a measure of poverty. We then apply our shift statistics to the analysis of image data. The shift statistics presented have a high degree of potential use across disciplines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11119 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Measurement and comparison of distributional shift with applications to ecology, economics, and image analysis Locey, Kenneth J. Stein, Brian D. Methodology The concentration of a distribution toward a lower bound is a conceptually simple property that closely relates to concepts of rarity and poverty, but that lacks a global descriptive statistic. We term this property 'shift' and define it as the distance of a central tendency from an upper bound, expressed as a proportion of a finite range. We derive a flexible, low complexity measure of shift and demonstrate its properties, its use with theoretical distributions, and its relation to skewness. We then use shift as the basis for a directional difference measure and as the basis for a formal distance metric that closely approximates the behavior of metrics having greater complexity (e.g., Wasserstein distance). Using simulated datasets and comparisons to system-specific measures, we demonstrate shift as a measure of species rarity and as a measure of poverty. We then apply our shift statistics to the analysis of image data. The shift statistics presented have a high degree of potential use across disciplines. |
| title | Measurement and comparison of distributional shift with applications to ecology, economics, and image analysis |
| topic | Methodology |
| url | https://arxiv.org/abs/2401.11119 |