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In the analysis of count data often the equidispersion assumption is not suitable, hence the Poisson regression model is inappropriate. As a generalization of the Poisson distribution, the COM-Poisson distribution can deal with under-,…
The advent of data science has spurred interest in estimating properties of distributions over large alphabets. Fundamental symmetric properties such as support size, support coverage, entropy, and proximity to uniformity, received most…
We develop a framework for the operationalization of models and parameters by combining de Finetti's representation theorem with a conditional form of Sanov's theorem. This synthesis, the tilted de Finetti theorem, shows that conditioning…
In this article, we propose a new three parameter distribution by compounding negative binomial with reciprocal inverse Gaussian model called negative binomial-reciprocal inverse Gaussian distribution. This model is tractable with some…
This work deals with the estimation of parameters of Mittag-Leffler (ML($\alpha, \sigma$)) distribution. We estimate the parameters of ML($\alpha, \sigma$) using empirical Laplace transform method. The simulation study indicates that the…
In this paper we consider a semiparametric regression model involving a $d$-dimensional quantitative explanatory variable $X$ and including a dimension reduction of $X$ via an index $\beta'X$. In this model, the main goal is to estimate the…
The beta distribution is the best-known distribution for modelling doubly-bounded data, \eg percentage data or probabilities. A new generalization of the beta distribution is proposed, which uses a cubic transformation of the beta random…
The length-biased Birnbaum-Saunders distribution is both useful and practical for environmental sciences. In this paper, we initially derive some new properties for the length-biased Birnbaum-Saunders distribution, showing that one of its…
Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions…
Density regression characterizes the conditional density of the response variable given the covariates, and provides much more information than the commonly used conditional mean or quantile regression. However, it is often computationally…
In a regression analysis, suppose we suspect that there are several heterogeneous groups in the population that a sample represents. Mixture regression models have been applied to address such problems. By modeling the conditional…
For one-parameter continuous exponential families, we identify an unbiased estimator of the inverse of the natural parameter $\theta$ for cases where $\theta > 0$, extending an earlier result of \cite{voinov1985unbiased} applicable to a…
This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of…
Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…
A transformation group approach to the prior for the parameters of the beta distribution is suggested which accounts for finite sets of data by imposing a limit to the range of parameter values under consideration. The relationship between…
Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…
Beta regression models are employed to model continuous response variables in the unit interval, like rates, percentages, or proportions. Their applications rise in several areas, such as medicine, environment research, finance, and natural…
Some special functions are particularly relevant in applied probability and statistics. For example, the incomplete beta function is the cumulative central beta distribution. In this paper, we consider the inversion of the central…
In this paper we consider an extension of the beta regression model proposed by Ferrari and Cribari-Neto (2004). We extend their model in two different ways, first, we let the regression structure be nonlinear, second, we allow a regression…
We introduce the bivariate unit-log-symmetric model based on the bivariate log-symmetric distribution (BLS) defined in [Vila et al., 2022, Bivariate Log-symmetric Models: Theoretical Properties and Parameter Estimation. Avaliable at…