Bimodal and nultimodal extensions of the normal and skew normal distributions
Copyright policy )Bimodal and nultimodal 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 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.
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- University of Melbourne Australia
- CUNEF Universidad Spain
- University of Cantabria Spain
- University of Las Palmas de Gran Canaria Spain
old faithful geyser data, Statistics, skewness, Skewness, Univariate distribution, QA273-280, HA1-4737, Unimodality, univariate distribution, Characterization and structure theory of statistical distributions, Old faithful geyser data, unimodality, 5302 Econometría, Old Faithful Geyser Data, Probability distributions: general theory, Univariate Distribution, Probabilities. Mathematical statistics, multimodality, Multimodality
old faithful geyser data, Statistics, skewness, Skewness, Univariate distribution, QA273-280, HA1-4737, Unimodality, univariate distribution, Characterization and structure theory of statistical distributions, Old faithful geyser data, unimodality, 5302 Econometría, Old Faithful Geyser Data, Probability distributions: general theory, Univariate Distribution, Probabilities. Mathematical statistics, multimodality, Multimodality
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