Estimation of <i>P</i>(<i>X</i> ≤ <i>Y</i>) for discrete distributions with non-identical support

Bayesian entropy estimation for countable discrete distributions

We consider the problem of estimating Shannon’s entropy H from discrete data, in cases where the number of possible symbols is unknown or even countably infinite. The Pitman-Yor process, a generalization of Dirichlet process, provides a tractable prior distribution over the space of countably infinite discrete distributions, and has found major applications in Bayesian non-parametric statistics...

Online Learning with Samples Drawn from Non-identical Distributions

Learning algorithms are based on samples which are often drawn independently from an identical distribution (i.i.d.). In this paper we consider a different setting with samples drawn according to a non-identical sequence of probability distributions. Each time a sample is drawn from a different distribution. In this setting we investigate a fully online learning algorithm associated with a gene...

Efficient MCMC estimation of discrete distributions

In this paper we propose an efficient Markov chain Monte Carlo (MCMC) method for estimation of discrete distributions by solving an appropriate system of linear equations. We call the estimator the equation-solving estimator. Our numerical results show that the new estimator makes significant improvements over the conventional frequencyMCMCestimator in terms of accuracy of the estimates. The ne...

S –convex Extremal Distributions with Arbitrary Discrete Support

This paper considers the class of s -convex stochastic orderings for random variables valued in an arbitrary discrete subset of the half-positive real line. After having established a sufficient condition of crossing-type for these orderings, explicit expressions are derived for stochastic extrema in moment spaces. Some applications in actuarial science are discussed. Mathematics subject classi...

Discrete triangular distributions and non-parametric estimation for probability mass function