In certain statistical process control applications, quality of a process or product can be characterized by a function commonly referred to as profile. Some of the potential applications of profile monitoring are cases where quality characteristic of interest is modelled using binary,multinomial or ordinal variables. In this paper, profiles with multinomial response are studied. For this purpo...

This paper presents a strong true-score model for tests that consist of polytomously-scored items. Errors conditional on true score are assumed to be distributed as multinomial, true category-proportion scores are assumed to follow a Dirichlet distribution, and the marginal category scores are the Dirichletmultinomial distribution. The model is illustrated using real data sets in the following ...

The Pearson’s chi-squared statistic (X2) does not in general follow a chi-square distribution when it is used for goodness-of-fit testing for a multinomial distribution based on sparse contingency table data. We explore properties of Zelterman’s (1987) D2 statistic and compare them with those of X2 and we also compare these two statistics and the statistic (Lr) which is proposed by Maydeu-Oliva...

Algorithms for computing exact distribution values of statistics-linear combination of some multinomial variables called, 3-nomial variables, are derived. In the general case, there are not explicit formulae of the cumulative distribution function of these statistics that allow the direct computation of p-values. The exact distribution in the independent case and in some dependent ones is studi...

Modeling fault behaviors such as fault occurrences and active/benign durations is an essential step to the design and evaluation of fault-tolerant controller computers. We use a beta-binomial distribution to model fault occurrences both in the presence and in the absence of environmentally-induced (thus common-cause) faults. A multinomial distribution is used to model fault active durations. Th...

Distance sampling is a wildlife sampling technique used to estimate population size or density. Describing how density varies spatially is often of equal interest; however, conventional methods of analysis do not allow for explicit modeling of both density and detection probability. The function distsamp implements the multinomial-Poisson mixture model of Royle et al. (2004), which was develope...

This article provides a contemporary exposition at a moderately quantitative level of the distribution theory associated with sequences and patterns in iid multinomial trials, the birthday problem, and the matching problem. The section on patterns includes the classic distribution theory for waiting time for runs and more general patterns, and their means and moments. It also includes the centr...

We consider the problem of testing for differences among a number of discrete distributions. Our approach is based on viewing the different samples as drawn from a mixture distribution where each mixture component represents a different group or cluster. We adapt the methodology of Dasgupta and Raftery (1998) to this problem, giving explicit details in the case of multinomial and first-order Ma...

With the development of next generation sequencing technology, researchers have now been able to study the microbiome composition using direct sequencing, whose output are bacterial taxa counts for each microbiome sample. One goal of microbiome study is to associate the microbiome composition with environmental covariates. We propose to model the taxa counts using a Dirichlet-multinomial (DM) r...

We propose two Markov chains for sampling (m + 1)-dimensional contingency tables indexed by {1, 2}m × {1, 2, . . . , n}. Stationary distributions of our chains are the uniform distribution and a conditional multinomial distribution (which is equivalent to the hypergeometric distribution ifm=1). Mixing times of our chains are bounded by ( 1 2 )n(n− 1) ln(N/(2m ))= ( 1 2 )n(n− 1) ln(dn/ ), where ...