In certain applications it is useful to fit multinomial distributions to observed data with a penalty term that encourages sparsity. For example, in probabilistic latent audio source decomposition one may wish to encode the assumption that only a few latent sources are active at any given time. The standard heuristic of applying an L1 penalty is not an option when fitting the parameters to a mu...

We extend recent advances in computing variance-covariance matrices from genetic distances to a sequence method of phylogenetic analysis. These matrices, together with other statistical properties of corrected sequence spectra, are studied as a foundation for more powerful and testable methods in phylogenetics. We start with 8, a vector of the proportion of sites in a sequence of length c showi...

Consider a sequence of multinomial random vectors with increasing number of equiprobable cells. We show that if the number of trials increases fast enough, the sequence of maxima of the cells after a suitable centering and scaling converges to the Gumbel distribution. While results are available for maxima of triangular arrays of independent random variables with certain types of distribution, ...

Generative Adversarial Networks (GAN) have limitations when the goal is to generate sequences of discrete elements. The reason for this is that samples from a distribution on discrete objects such as the multinomial are not differentiable with respect to the distribution parameters. This problem can be avoided by using the Gumbel-softmax distribution, which is a continuous approximation to a mu...

In this article, exact properties of the chi-square test, likelihood ratio test (LRT), Hoel’s test (1938), Nass’ test (1959), and an exact test, for testing the multinomial proportions, are investigated numerically. Numerical studies show that the size behavior of the chi-square test for the multinomial distribution with three or more cells is erratic only when the probabilities are at the boun...

This paper studies a Stated Preference (SP) experiment on the choice of type of (Rail) season card, conducted among current Dutch Railways season cardholders. They were asked to choose from the following three alternatives: (1) an unrestricted season card, (2) a cheaper season card with peak travel and travel frequency restrictions, and (3) not buying a season card. Multinomial logit (MNL), nes...

Fisher’s exact test, named for Sir Ronald Aylmer Fisher, tests contingency tables for homogeneity of proportion. This paper discusses a generalization of Fisher’s exact test for the case where some of the table entries are constrained to be zero. The resulting test is useful for assessing cases where the null hypothesis of conditional multinomial distribution is suspected to be false. The test ...

It is a common finding in empirical discrete choice studies that the estimated mean relative values of the coefficients (i.e. WTP’s) from multinomial logit (MNL) estimations differ from those calculated using mixed logit estimations, where the mixed logit has the better statistical fit. However, it is less clear under exactly what circumstances such differences arise, whether they are important...

Extensions of binomial and multinomial formulae due to Abel, Cayley and Hurwitz are related to the probability distributions of various random subsets, trees, forests, and mappings. For instance, an extension of Hurwitz's binomial formula is associated with the probability distribution of the random set of vertices of a fringe subtree in a random forest whose distribution is de ned by terms of ...