Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions
A transformation of a density function is introduced to derive two families of continuous densities, the first symmetric and the second not-necessarily symmetric, exhibiting both unimodality and bimodality. Their respective density functions are provided in closed form, allowing us to simply obtain...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Instituto Nacional de Estatística | Statistics Portugal
2025-05-01
|
| Series: | Revstat Statistical Journal |
| Subjects: | |
| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/563 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849328016063201280 |
|---|---|
| author | Emilio Gómez-Déniz Enrique Calderín-Ojeda José M. Sarabia |
| author_facet | Emilio Gómez-Déniz Enrique Calderín-Ojeda José M. Sarabia |
| author_sort | Emilio Gómez-Déniz |
| collection | DOAJ |
| description |
A transformation of a density function is introduced to derive two families of continuous densities, the first symmetric and the second not-necessarily symmetric, exhibiting both unimodality and bimodality. Their respective density functions are provided in closed form, allowing us to simply obtain moments and related quantities. We focus on the case where the normal distribution is considered, although it can be applied to other models, such as the logistic and Cauchy distributions. This transformation is also extended to derive a family of asymmetric unimodal and bimodal distributions via Azzalini’s scheme. An example related to environmental science illustrate these models’ practical performance.
|
| format | Article |
| id | doaj-art-0db232b60aae464dac3702e16b5c6107 |
| institution | Kabale University |
| issn | 1645-6726 2183-0371 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj-art-0db232b60aae464dac3702e16b5c61072025-08-20T03:47:41ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712025-05-0123210.57805/revstat.v23i2.563Bimodal and Multimodal Extensions of the Normal and Skew Normal DistributionsEmilio Gómez-Déniz0Enrique Calderín-Ojeda1José M. Sarabia2University of Las Palmas de Gran CanariaUniversity of MelbourneCUNEF Universidad A transformation of a density function is introduced to derive two families of continuous densities, the first symmetric and the second not-necessarily symmetric, exhibiting both unimodality and bimodality. Their respective density functions are provided in closed form, allowing us to simply obtain moments and related quantities. We focus on the case where the normal distribution is considered, although it can be applied to other models, such as the logistic and Cauchy distributions. This transformation is also extended to derive a family of asymmetric unimodal and bimodal distributions via Azzalini’s scheme. An example related to environmental science illustrate these models’ practical performance. https://revstat.ine.pt/index.php/REVSTAT/article/view/563multimodalityold faithful geyser dataskewnessunimodalityunivariate distribution |
| spellingShingle | Emilio Gómez-Déniz Enrique Calderín-Ojeda José M. Sarabia Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions Revstat Statistical Journal multimodality old faithful geyser data skewness unimodality univariate distribution |
| title | Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions |
| title_full | Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions |
| title_fullStr | Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions |
| title_full_unstemmed | Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions |
| title_short | Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions |
| title_sort | bimodal and multimodal extensions of the normal and skew normal distributions |
| topic | multimodality old faithful geyser data skewness unimodality univariate distribution |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/563 |
| work_keys_str_mv | AT emiliogomezdeniz bimodalandmultimodalextensionsofthenormalandskewnormaldistributions AT enriquecalderinojeda bimodalandmultimodalextensionsofthenormalandskewnormaldistributions AT josemsarabia bimodalandmultimodalextensionsofthenormalandskewnormaldistributions |