Topic
Beta distribution
About: Beta distribution is a research topic. Over the lifetime, 1191 publications have been published within this topic receiving 21351 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: The authors present maximum-likelihood regression models assuming that the dependent variable is conditionally beta distributed rather than Gaussian, and approach models both means and variances with their own distinct sets of predictors, thereby modeling heteroscedasticity.
Abstract: Uncorrectable skew and heteroscedasticity are among the “lemons” of psychological data, yet many important variables naturally exhibit these properties. For scales with a lower and upper bound, a suitable candidate for models is the beta distribution, which is very flexible and models skew quite well. The authors present maximum-likelihood regression models assuming that the dependent variable is conditionally beta distributed rather than Gaussian. The approach models both means (location) and variances (dispersion) with their own distinct sets of predictors (continuous and/or categorical), thereby modeling heteroscedasticity. The location submodel link function is the logit and thereby analogous to logistic regression, whereas the dispersion submodel is log linear. Real examples show that these models handle the independent observations case readily. The article discusses comparisons between beta regression and alternative techniques, model selection and interpretation, practical estimation, and software.
1,560 citations
TL;DR: A survey of general properties of normal variance-mean mixtures, including various new results, is given in this article, where it is shown that the class of self-reciprocal normal variance mixtures is rather wide, and some Tauberian results are established from which relations between the tail behaviour of a normal variance -mean mixture and its mixing distribution may be deduced.
Abstract: A survey is given of general properties of normal variance-mean mixtures, including various new results. In particular, it is shown that the class of self-reciprocal normal variance mixtures is rather wide, and some Tauberian results are established from which relations between the tail behaviour of a normal variance-mean mixture and its mixing distribution may be deduced. The generalized hyperbolic distributions and the modulated normal distributions provide examples of normal variance-mean mixtures whose densities can be given in terms of well-known functions, and it is proved that also the z distributions, i.e. the class of distributions generated from the beta distribution through logistic transformation followed by introduction of location and scale parameters, are normal variance-mean mixtures. (The z distributions include the hyperbolic cosine distribution and the logistic distribution.) Some properties of the associated mixing distributions are derived, and the z distributions are shown to be self-decomposable.
515 citations
TL;DR: A comprehensive treatment of the mathematical properties of the beta exponential distribution generated from the logit of a beta random variable is provided and an expression for the Fisher information matrix is provided.
504 citations
Journal Article•
418 citations
TL;DR: In this paper, the authors considered the issue of modeling fractional data observed in the interval [0, 1], (0,1] or [0.1] and proposed mixed continuous-discrete distributions.
Abstract: This paper considers the issue of modeling fractional data observed in the interval [0,1), (0,1] or [0,1]. Mixed continuous-discrete distributions are proposed. The beta distribution is used to describe the continuous component of the model since its density can have quite diferent shapes depending on the values of the two parameters that index the distribution. Properties of the proposed distributions are examined. Also, maximum likelihood and method of moments estimation is discussed. Finally, practical applications that employ real data are presented.
363 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 18 |
| 2024 | 33 |
| 2023 | 30 |
| 2022 | 54 |
| 2021 | 71 |
| 2020 | 64 |