A new generalization of the beta distribution

Sankhya B, 2014

A new family of skewed distributions referred to as modified beta distributions is presented. Some properties of the new family including estimation procedures are derived. A real data application as well as simulation studies are described to show superior performance versus known models.

Journal of Modern Applied Statistical Methods Jmasm, 2004

The beta-normal distribution is characterized by four parameters that jointly describe the location, the scale and the shape properties. The beta-normal distribution can be unimodal or bimodal. This paper studies the bimodality properties of the beta-normal distribution. The region of bimodality in the parameter space is obtained. The beta-normal distribution is applied to fit a numerical bimodal data set. The beta-normal fits are compared with the fits of mixture-normal distribution through simulation.

Communications in Statistics - Theory and Methods, 2002

Journal of Modern Applied Statistical Methods

The beta-normal distribution is characterized by four parameters that jointly describe the location, the scale and the shape properties. The beta-normal distribution can be unimodal or bimodal. This paper studies the bimodality properties of the beta-normal distribution. The region of bimodality in the parameter space is obtained. The beta-normal distribution is applied to fit a numerical bimodal data set. The beta-normal fits are compared with the fits of mixture-normal distribution through simulation.

2007

In this paper, we discuss a novel class of skewed multivariate distributions and, more generally, a method of building such a class on the basis of univariate skewed distributions. The method is based on a general linear transformation of a multidimensional random variable with independent components, each with a skewed distribution. The proposed class of multivariate skewed distributions has a simple form for the pdf, and moment existence only depends on that of the underlying symmetric univariate distributions. In addition, we can freely allow for any mean and covariance structure in combination with any magnitude and direction of skewness. In order to deal with both skewness and fat tails, we introduce multivariate skewed regression models with fat tails based on Student distributions. We present two main classes of such distributions, one of which is novel even under symmetry. Under standard non-informative priors on both regression and scale parameters, we derive conditions for propriety of the posterior and for existence of posterior moments. We describe MCMC samplers for Bayesian inference and analyse an application to biomedical data.

Brazilian Journal of Probability and Statistics, 2014

A new continuous distribution, so-called the beta log-logistic distribution, that extends the log-logistic distribution and some other distributions is proposed and studied. The new model is quite flexible to analyze positive data. Various structural properties of the new distribution are derived, including explicit expressions for the moments, mean deviations and Rényi and Shannon entropies. The score function is derived and the estimation of the model parameters is performed by maximum likelihood. We also determine the expected information matrix. The usefulness of the new model is illustrated by means of two real data sets. We hope that the new distribution proposed here will serve as an alternative model to other models available in the literature for modeling positive real data in many areas.

Mathematics

Several papers on distributions to model rates and proportions have been recently published; their fitting in numerous instances is better than the alternative beta distribution, which has been the distribution to follow when it is necessary to quantify the average of a response variable based on a set of covariates. Despite the great usefulness of this distribution to fit the responses on the (0,1) unit interval, its relevance loses objectivity when the interest is quantifying the influence of these covariates on the quantiles of the variable response in (0,1); being the most critical situation when the distribution presents high asymmetry and/or kurtosis. The main objective of this work is to introduce a distribution for modeling rates and proportions. The introduced distribution is obtained from the alpha-power extension of the skew–normal distribution, which is known in the literature as the power–skew–normal distribution.

Journal of Statistical Computation and Simulation, 2013

For the first time, we introduce the beta log-normal distribution for which the log-normal distribution is a special case. Various properties of the new distribution are discussed. Expansions for the cumulative distribution and density functions that do not involve complicated functions are derived. We obtain expressions for its moments and for the moments of order statistics. The estimation of parameters is approached by the method of maximum likelihood and the expected information matrix is derived. The new model is quite flexible in analyzing positive data as an important alternative to the gamma, Weibull, generalized exponential, beta exponential and Birnbaum-Saunders distributions. The flexibility of the new distribution is illustrated in an application to a real data set.

1979

Studia Scientiarum Mathematicarum Hungarica, 2013

The beta generalized half-normal distribution is commonly used to model lifetimes. We propose a new wider distribution called the beta generalized half-normal geometric distribution, whose failure rate function can be decreasing, increasing or upside-down bathtub. Its density function can be expressed as a linear combination of beta generalzed half-normal density functions. We derive quantile function, moments and generating unction. We characterize the proposed distribution using a simple relationship between wo truncated moments. The method of maximum likelihood is adapted to estimate the model parameters and its potentiality is illustrated with an application to a real fatigue data set. Further, we propose a new extended regression model based on the logarithm of the new distribution. This regression model can be very useful for the analysis of real data and provide more realistic fits than other special regression models.