Journal ArticleDOI
Runs and Scans With Applications
TLDR
This text is a revision of the book by Arnold, Costillo, and Sarabia (1992), but with much more depth than the original, and comprises a lively overview of conditionally speci ed models of the conditional distribution.Abstract:
of the conditional distribution speci cations. Chapters 8 and 10 extend these methods from two to more dimensions. Chapter 9 investigates estimation in conditionally speci ed models. Chapter 11 considers models speci ed by conditioning on events speci ed by one variable exceeding a value rather than equaling a value, and Chapter 12 considers models for extreme-value data. Chapter 13 extends conditional speci cation to Bayesian analysis. Chapter 14 describes the related simultaneous-equation models, and Chapter 15 ties in some additional topics. An appendix describes methods of simulation from conditionally speci ed models. Chapters 1–4, plus Chapters 9 and 13, comprise a lively overview of conditionally speci ed models. The remainder of the text constitutes a detailed catalog of results speci c to different conditional distributions. Although this catalog is certainly of value, the reader desiring a briefer and less detailed introduction to the subject might skip the remainder at rst reading. This text is a revision of the book by Arnold, Costillo, and Sarabia (1992). The current version is of similar breadth, but with much more depth than the original. The text is clearly written and accessible with relatively few mathematical prerequisites. I found surprisingly few typographical errors; the authors are to be congratulated for this. In a few cases, regularity conditions for results are not given in full. Generally, this causes little confusion, although something does appear to be missing in the statement of Aczél’s key theorem (Theorem 1.3). Fortunately, most of the results in the sequel are derived from corollaries to this theorem, and the corollaries are stated more precisely. I noted few gaps in the material covered. The only area that I thought was insuf ciently represented was application to Markov chain Monte Carlo. Conditional speci cation is particularly important in Gibbs sampling. I believe that many practitioners would bene t from a discussion of the issues involved in these sampling schemes. Each chapter contains numerous exercises. These exercises appear to be at an appropriate level for a graduate course in statistics, and appear to provide appropriate reinforcement for the material in the preceding chapters.read more
Citations
More filters
Journal ArticleDOI
A martingale approach to scan statistics
TL;DR: A new martingale method is proposed which allows one to approximate the distribution for a wide variety of scan statistics, including some for which analytical results are computationally infeasible.
Journal ArticleDOI
A General Model for Start-Up Demonstration Tests
TL;DR: This work provides interval confidence bounds for the estimation of the reliability for the start-up demonstration test, which is based on maximum likelihood estimators and determines the minimum sample size needed in a demonstration test to achieve a certain precision of this reliability at a specified confidence level.
Journal ArticleDOI
The distributions of sum, minima and maxima of generalized geometric random variables
Fatih Tank,Serkan Eryilmaz +1 more
TL;DR: In this paper, a discrete phase-type distribution was proposed to represent the generalized geometric distribution of Bernoulli trials with success probability of ≥ 0.5 in the case of two independent random variables having geometric distributions of order.
Journal ArticleDOI
Generalized binomial and negative binomial distributions of orderk by thel-overlapping enumeration scheme
Kiyoshi Inoue,Sigeo Aki +1 more
TL;DR: In this article, the exact distribution of the waiting time for ther-th loverlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials is investigated.
Journal ArticleDOI
Run statistics in a sequence of arbitrarily dependent binary trials
Sevcan Demir,Serkan Eryilmaz +1 more
TL;DR: In this paper, the exact distribution of runs for binary trials arising in urn models is derived based on the joint distribution of success and failure run lengths and unifies the results on distribution of run.
References
More filters
Journal ArticleDOI
Nonparametric intensity bounds for the delineation of spatial clusters
Fernando Luiz Pereira de Oliveira,Luiz Henrique Duczmal,André Luiz Fernandes Cançado,Ricardo Tavares +3 more
TL;DR: A method to measure the plausibility of each area being part of a possible localized anomaly in the map of rates and find intensity bounds for the delineation of spatial clusters in maps of areas with known populations and observed number of cases is proposed.
Journal ArticleDOI
Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition
Gesine Reinert,Adrian Röllin +1 more
TL;DR: In this paper, a multivariate exchangeable pairs approach was proposed to assess distributional distances to potentially singular multivariate normal distributions, which allows for a normal approximation even when the corresponding statistics of interest do not lend themselves easily to Stein's exchangeable pair approach.
Journal ArticleDOI
Statistical Process Control using Shewhart Control Charts with Supplementary Runs Rules
TL;DR: In this paper, the authors present the basic principles and recent advances in the area of statistical process control charting with the aid of runs rules, and briefly discuss the Markov chain approach which is the most popular technique for studying the run length distribution of run based control charts.
Journal ArticleDOI
A Nonparametric Shewhart-Type Signed-Rank Control Chart Based on Runs
TL;DR: Shewhart-type distribution-free control charts are considered for the known in-control median of a continuous process distribution based on the Wilcoxon signed-rank statistic and some runs type rules and can have better out-of-control performance than the Shewhart X-bar chart and the basicsigned-rank chart for the normal distribution and for some heavy-tailed distributions.
Journal ArticleDOI
Sensitivity analysis and efficient method for identifying optimal spaced seeds
Kwok Pui Choi,Louxin Zhang +1 more
TL;DR: The computational aspects of calculating the hitting probability of spaced seeds are studied; and an efficient algorithm for identifying optimal spaced seeds is proposed.