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Distributions Related to Weak Runs With a Minimum and a Maximum Number of Successes: A Unified Approach
In the present paper we extend the definition of r-weak runs in sequences of binary trials so that such a run contains both a minimum and a maximum...
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Weak runs in sequences of binary trials
In the present paper the metric of distance is adapted to a sequence of binary trials and the concept of r -weak runs is introduced and defined. The...
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On the Distribution of the Number of Success Runs in a Continuous Time Markov Chain
We propose a continuous-time adaptation of the well-known concept of success runs by considering a marked point process with two types of marks...
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Generalizations of Runs and Patterns Distributions for Sequences of Binary Trials
In the present paper we study the distributions of families of patterns which generalize runs and patterns distributions extensively examined in the...
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On the Individuals Chart with Supplementary Runs Rules under Serial Dependence
To improve the sensitivity of a Shewhart control chart, it is common among practitioners to use supplementary runs rules. The performance of such...
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An Asymptotic Conditional Test of Independence in Bernoulli Sequences Using the Number of Runs Given the Number of Successes
In this paper, we prove the asymptotic normality of the conditional distribution of the number of runs given the number of successes for a sequence...
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Binomial Distribution of Order k in a Modified Binary Sequence
Let us consider a sequence of n binary trials (signals). A counter registers successes, but once a success is registered the mechanism is locked for...
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Research on Probability Models for Cluster of Points Before the Year 1960
Scan statistics describe large number of events or objects clustered close in time or space. A few special cases of scan statistics – long success...
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Decoupling Combinatorial Complexity: a Two-Step Approach to Distributions of Runs
Runs statistics have found many applications in various fields and have attracted attentions of many researchers. Traditional methods used to...
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Voting Rights, Markov Chains, and Optimization by Short Bursts
Finding outlying elementsin probability distributions can be a hard problem. Taking a real example from Voting Rights Act enforcement, we consider...
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Generating Function Methods for Run and Scan Statistics
Runs and pattern statistics have found successful applications in various fields. Many classical results of distributions of runs were obtained by...
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Conditional waiting time distributions of runs and patterns and their applications
In this paper, a simple and general method based on the finite Markov chain imbedding technique is proposed to determine the exact conditional...
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The Bayesian Group-Sequential Predictive Evidence Value Design for Phase II Clinical Trials with Binary Endpoints
In clinical research, the initial efficacy of a new agent is typically assessed in a phase IIA study. Bayesian group-sequential designs are often...
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Stochastic Ordering Among Success Runs Statistics in a Sequence of Exchangeable Binary Trials
A new scheme-distribution-based representation is presented for the cumulative distribution function of the number of success runs of length k in a...
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Integration of model-based recursive partitioning with bias reduction estimation: a case study assessing the impact of Oliver’s four factors on the probability of winning a basketball game
In this contribution, we investigate the importance of Oliver’s Four Factors, proposed in the literature to identify a basketball team’s strengths...
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Quarterback evaluation in the national football league using tracking data
This paper evaluates quarterback performance in the National Football League. With the availability of player tracking data, there exists the...
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The Tilted Beta-Binomial Distribution in Overdispersed Data: Maximum Likelihood and Bayesian Estimation
Binary success/failure data is an important type of data which occurs in a wide range of fields and application domains. We examine a new...
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Markov-switching decision trees
Decision trees constitute a simple yet powerful and interpretable machine learning tool. While tree-based methods are designed only for...
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Correlation
Moneyball is a 2011 movie about baseball and statistics. A movie about statistics that received six Academy Award nominations: best picture, best...