In this paper, we provide a new family of trivariate proper quasi-copulas. As an application, we show that – the best-possible lower bound for the set of trivariate quasi-copulas (and copulas) – is the limit member of this family, showing how the mass of is distributed on the plane of in an easy manner, and providing the generalization of this result to dimensions.
A new weighted version of the Gompertz distribution is introduced. It is noted that the model represents a mixture of classical Gompertz and second upper record value of Gompertz densities, and using a certain transformation it gives a new version of the two-parameter Lindley distribution. The model can be also regarded as a dual member of the log-Lindley- family. Various properties of the model are obtained, including hazard rate function, moments, moment generating function, quantile function,...
It is a well-known fact that the Dempster combination rule for combination of uncertainty degrees coming from two or more sources is legitimate only if the combined empirical data, charged with uncertainty and taken as random variables, are statistically (stochastically) independent. We shall prove, however, that for a particular but large enough class of probability measures, an analogy of Dempster combination rule, preserving its extensional character but using some nonstandard and boolean-like...
We present an analogue of the Harer–Zagier recursion formula for the moments of the gaussian Orthogonal Ensemble in the form of a five term recurrence equation. The proof is based on simple gaussian integration by parts and differential equations on Laplace transforms. A similar recursion formula holds for the gaussian Symplectic Ensemble. As in the complex case, the result is interpreted as a recursion formula for the number of 1-vertex maps in locally orientable surfaces with a given number of...
A method for producing associative copulas from a binary operation and a convex function on an interval is described.
We derive a necessary condition for stochastic dominance of any order based on the Laplace transform of probability measures on [0,∞) for which it follows easily Fishburn's theorem on the lexicographic order of the moments.
Given any finite or countable collection of real numbers Tj, j∈J, we find all solutions Fto the stochastic fixed point equation whereW and the Wj, j∈J, are independent real-valued random variables with distribution Fand means equality in distribution. The bulk of the necessary analysis is spent on the case when |J|≥2 and all Tj are (strictly) positive. Nontrivial solutions are then concentrated on either the positive or negative half line. In the most interesting (and difficult) situation T...
In this paper it is taken up a revision and characterization of the class of absolutely continuous elliptical distributions upon a parameterization based on the density function. Their properties (probabilistic characteristics, affine transformations, marginal and conditional distributions and regression) are shown in a practical and easy to interpret way. Two examples are fully undertaken: the multivariate double exponential distribution and the multivariate uniform distribution.
Weighted Gamma (WG), a weighted version of Gamma distribution, is introduced. The hazard function is increasing or upside-down bathtub depending upon the values of the parameters. This distribution can be obtained as a hidden upper truncation model. The expressions for the moment generating function and the moments are given. The non-linear equations for finding maximum likelihood estimators (MLEs) of parameters are provided and MLEs have been computed through simulations and also for a real data...
We prove an extension of a result by Peres and Solomyak on almost sure absolute continuity in a class of symmetric Bernoulli convolutions.