Related papers: A new generalization of the beta distribution

Beta regression is used routinely for continuous proportional data, but it often encounters practical issues such as a lack of robustness to misspecification of the beta distribution and sensitivity to outliers. We develop an improved class…

This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian…

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…

Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…

A six parameter distribution so-called the McDonald modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the beta…

In this paper, we introduce the BMT distribution as an unimodal alternative to continuous univariate distributions supported on a bounded interval. The ideas behind the mathematical formulation of this new distribution come from computer…

The Weibull distribution can be obtained using a power transformation from the standard exponential distribution. In this article, we will consider a symmetrized power transformation of a random variable with the standard normal…

This paper generalizes beta divergence beyond its classical form associated with power variance functions of Tweedie models. Generalized form is represented by a compact definite integral as a function of variance function of the…

A new generalization of the family of Poisson-G is called beta Poisson-G family of distribution. Useful expansions of the probability density function and the cumulative distribution function of the proposed family are derived and seen as…

Percentiles and more generally, quantiles are commonly used in various contexts to summarize data. For most distributions, there is exactly one quantile that is unbiased. For distributions like the Gaussian that have the same mean and…

Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…

A new distribution is introduced, which we call the twin-t distribution. This distribution is heavy-tailed like the t distribution, but closer to normality in the central part of the curve. Its properties are described, e.g. the pdf, the…

The beta Weibull distribution was introduced by Famoye et al. (2005) and studied by these authors. However, they do not give explicit expressions for the moments. We now derive explicit closed form expressions for the cumulative…

This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context. The proof leverages a…

We introduce beta diffusion, a novel generative modeling method that integrates demasking and denoising to generate data within bounded ranges. Using scaled and shifted beta distributions, beta diffusion utilizes multiplicative transitions…

In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…

The Gutenberg-Richter power law distribution of earthquake sizes is one of the most famous example illustrating self-similarity. It is well-known that the Gutenberg-Richter distribution has to be modified for large seismic moments, due to…

A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…

The modality is important topic for modelling. Using parametric models is an efficient way when real data set shows trimodality. In this paper we propose a new class of trimodal probability distributions, that is, probability distributions…

In this paper, we introduce a new probability distribution, the Lasso distribution. We derive several fundamental properties of the distribution, including closed-form expressions for its moments and moment-generating function.…