Related papers: Distributions that are both log-symmetric and R-sy…
Two-sided statistical tests and p-values are well defined only when the test statistic in question has a symmetric distribution. A new two-sided p-value called conditional p-value $P_C$ is introduced here. It is closely related to the…
The study of sums of possibly associated Bernoulli random variables has been hampered by an asymmetry between positive correlation and negative correlation. The Conway-Maxwell Binomial (COMB) distribution and its multivariate extension, the…
The polygonal distributions are a class of distributions that can be defined via the mixture of triangular distributions over the unit interval. The class includes the uniform and trapezoidal distributions, and is an alternative to the beta…
This paper introduces link functions for transforming one probability distribution to another such that the Kullback-Leibler and R\'enyi divergences between the two distributions are symmetric. Two general classes of link models are…
We introduce families of jointly symmetric, binary distributions that are generated over directed star graphs whose nodes represent variables and whose edges indicate positive dependences. The families are parametrized in terms of a single…
We introduce a class of probability measures whose densities near infinity are mixtures of Pareto distributions. This class can be characterized by the Fourier transform which has a power series expansion including real powers, not only…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
In this paper, an alpha-beta-skew-logistic distribution is proposed following the same methodology as those of alpha-beta-skew-normal of Shafiei et al. (2016) and investigated some of its related distributional properties. Finally, the…
Random operators constitute fundamental building blocks of models of complex systems yet are far from fully understood. Here, we explain an asymmetry emerging upon repeating identical isotropic (uniformly random) operations. Specifically,…
It is known that few characterization results of the logistic distribution were available before, although it is similar in shape to the normal one whose characteristic properties have been well investigated. Fortunately, in the last…
The usual stochastic order and the likelihood ratio order between probability distributions on the real line are reviewed in full generality. In addition, for the distribution of a random pair $(X,Y)$, it is shown that the conditional…
We propose an asymptotic theory for distribution forecasting from the log normal chain-ladder model. The theory overcomes the difficulty of convoluting log normal variables and takes estimation error into account. The results differ from…
We treat all the bivariate lack-of-memory (BLM) distributions in a unified approach and develop some new general properties of the BLM distributions, including joint moment generating function, product moments and dependence structure.…
The object of study is the problem of testing for uniformity of the multinomial distribution. We consider tests based on symmetric statistics, defined as the sum of some function of cell-frequencies. Mainly, attention is focused on the…
We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. Based on these representations,…
We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of $x-y$ dualities in a broader context of log…
We consider products of independent large random rectangular matrices with independent entries. The limit distribution of the expected empirical distribution of singular values of such products is computed. The distribution function is…
We adopt an empirical approach to the characterization of the distribution of twin primes within the set of primes, rather than in the set of all natural numbers. The occurrences of twin primes in any finite sequence of primes are like…
Symmetry is conventionally described in a contrariety manner that the system is either completely symmetric or completely asymmetric. Using group theoretical approach to overcome this dichotomous problem, we introduce the degree of symmetry…
In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate elliptically contoured stable distributions. It is demonstrated that these distributions form a special subclass of…