Related papers: A Fresh Look at Bivariate Binomial Distributions
Marshall and Olkin (1997, Biometrika, 84, 641 - 652) introduced a very powerful method to introduce an additional parameter to a class of continuous distribution functions and hence it brings more flexibility to the model. They have…
Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…
Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with…
Bimonotone subdivisions in two dimensions are subdivisions all of whose sides are either vertical or have nonnegative slope. They correspond to statistical estimates of probability distributions of strongly positively dependent random…
Various statistics on wreath products are defined via canonical words, "colored" right to left minima and "colored" descents. It is shown that refined counts with respect to these statistics have nice recurrence formulas of…
A new class of nonparametric prior distributions, termed Beta-Binomial stick-breaking process, is proposed. By allowing the underlying length random variables to be dependent through a Beta marginals Markov chain, an appealing discrete…
Bimodal truncated count distributions are frequently observed in aggregate survey data and in user ratings when respondents are mixed in their opinion. They also arise in censored count data, where the highest category might create an…
Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption…
Randomness is a central concept to statistics and physics. Here, a statistical analysis shows experimental evidence that tossing coins and finding last digits of prime numbers are identical regarding statistics for equally likely outcomes.…
Birnbaum-Saunders models have been widely used to model positively skewed data. In this paper, we introduce a bivariate Birnbaum-Saunders distribution which has the means as parameters. We present some properties of the univariate and…
We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…
In this paper, we systematize the modeling of probabilistic systems for the purpose of analyzing them with model counting techniques. Starting from unbiased coin flips, we show how to model biased coins, correlated coins, and distributions…
Stochastic linear combinations of some random vectors are studied where the distribution of the random vectors and the joint distribution of their coefficients are Dirichlet. A method is provided for calculating the distribution of these…
Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiple random variables. The problem of efficient representation of probability distributions is central in term of…
We describe a novel way to represent the probability distribution of a random binary string as a mixture having a maximally weighted component associated with independent (though not necessarily identically distributed) Bernoulli…
Set-valued quantiles for multivariate distributions with respect to a general convex cone are introduced which are based on a family of (univariate) distribution functions rather than on the joint distribution function. It is shown that…
A simple spin system is constructed to simulate dynamics of asset prices and studied numerically. The outcome for the distribution of prices is shown to depend both on the dimension of the system and the introduction of price into the link…
In this paper, we study a bivariate distributionally robust optimization problem with mean-covariance ambiguity set and half-space support. Under a conventional type of objective function widely adopted in inventory management, option…