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In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…
Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…
Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…
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…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
We consider high-dimensional generalized linear models when the covariates are contaminated by measurement error. Estimates from errors-in-variables regression models are well-known to be biased in traditional low-dimensional settings if…
We investigate the asymptotic behavior of posterior distributions of regression coefficients in high-dimensional linear models as the number of dimensions grows with the number of observations. We show that the posterior distribution…
Regression models that ignore measurement error in predictors may produce highly biased estimates leading to erroneous inferences. It is well known that it is extremely difficult to take measurement error into account in Gaussian…
The generalized linear model (GLM) plays a key role in regression analyses. In high-dimensional data, the sparse GLM has been used but it is not robust against outliers. Recently, the robust methods have been proposed for the specific…
Mean density of lower dimensional random closed sets, as well as the mean boundary density of full dimensional random sets, and their estimation are of great interest in many real applications. Only partial results are available so far in…
This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution…
Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…
Let $X$ have a Generalized Poisson distribution with mean $kb$, where $b$ is a known constant in the unit interval and $k$ is a discrete, non-negative parameter. We show that if an uninformative uniform prior for $k$ is assumed, then the…
The generalised random graph contains $n$ vertices with positive i.i.d. weights. The probability of adding an edge between two vertices is increasing in their weights. We require the weight distribution to have finite second moments and…
To obtain a probabilistic model for a dependent variable based on some set of explanatory variables, a distributional approach is often adopted where the parameters of the distribution are linked to regressors. In many classical models this…
The paper deals with planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. These distributions generally do not coincide…
This paper introduces a class of generalised linear models (GLMs) driven by latent processes for modelling count, real-valued, binary, and positive continuous time series. Extending earlier latent-process regression frameworks based on…
In this paper, we consider the problem of estimating the marginal density in some nonlinear autoregressive time series models for which the conditional mean and variance have a parametric specification. Under some regularity conditions, we…
In this paper we propose an objective Bayesian estimation approach for the parameters of the generalized gamma distribution. Various reference priors are obtained, but showing that they lead to improper posterior distributions. We overcome…
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…