Bounded distributions place limits on skewness and larger moments.
Distributions of strictly positive numbers are common and can be characterized by standard statistical measures such as mean, standard deviation, and skewness. We demonstrate that for these distributions the skewness D3 is bounded from below by a function of the coefficient of variation (CoV) δ as D...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2024-01-01
|
| Series: | PLoS ONE |
| Online Access: | https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0297862&type=printable |
| _version_ | 1797304778218274816 |
|---|---|
| author | David J Meer Eric R Weeks |
| author_facet | David J Meer Eric R Weeks |
| author_sort | David J Meer |
| collection | DOAJ |
| description | Distributions of strictly positive numbers are common and can be characterized by standard statistical measures such as mean, standard deviation, and skewness. We demonstrate that for these distributions the skewness D3 is bounded from below by a function of the coefficient of variation (CoV) δ as D3 > δ - 1/δ. The results are extended to any distribution that is bounded with minimum value xmin and/or bounded with maximum value xmax. We build on the results to provide bounds for kurtosis D4, and conjecture analogous bounds exists for higher statistical moments. |
| first_indexed | 2024-03-08T00:15:23Z |
| format | Article |
| id | doaj.art-aae1ec5f34da41a2a8364cb06ec6b575 |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-03-08T00:15:23Z |
| publishDate | 2024-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-aae1ec5f34da41a2a8364cb06ec6b5752024-02-17T05:32:48ZengPublic Library of Science (PLoS)PLoS ONE1932-62032024-01-01192e029786210.1371/journal.pone.0297862Bounded distributions place limits on skewness and larger moments.David J MeerEric R WeeksDistributions of strictly positive numbers are common and can be characterized by standard statistical measures such as mean, standard deviation, and skewness. We demonstrate that for these distributions the skewness D3 is bounded from below by a function of the coefficient of variation (CoV) δ as D3 > δ - 1/δ. The results are extended to any distribution that is bounded with minimum value xmin and/or bounded with maximum value xmax. We build on the results to provide bounds for kurtosis D4, and conjecture analogous bounds exists for higher statistical moments.https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0297862&type=printable |
| spellingShingle | David J Meer Eric R Weeks Bounded distributions place limits on skewness and larger moments. PLoS ONE |
| title | Bounded distributions place limits on skewness and larger moments. |
| title_full | Bounded distributions place limits on skewness and larger moments. |
| title_fullStr | Bounded distributions place limits on skewness and larger moments. |
| title_full_unstemmed | Bounded distributions place limits on skewness and larger moments. |
| title_short | Bounded distributions place limits on skewness and larger moments. |
| title_sort | bounded distributions place limits on skewness and larger moments |
| url | https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0297862&type=printable |
| work_keys_str_mv | AT davidjmeer boundeddistributionsplacelimitsonskewnessandlargermoments AT ericrweeks boundeddistributionsplacelimitsonskewnessandlargermoments |