Joint distributions of numbers of success runs of specified lengths in linear and circular sequences

2005 ◽  
Vol 57 (2) ◽  
pp. 353-368 ◽  
Author(s):  
Kiyoshi Inoue ◽  
Sigeo Aki
Keyword(s):  
Success Runs ◽  
Joint Distributions

Lengths of runs and waiting time distributions by using Pólya-Eggenberger sampling scheme

2002 ◽  
Vol 39 (3-4) ◽  
pp. 309-332 ◽  
Author(s):  
K. Sen ◽  
Manju L. Agarwal ◽  
S. Chakraborty
Keyword(s):  
Waiting Time ◽  
Lattice Path ◽  
Sampling Scheme ◽  
Bernoulli Trials ◽  
Success Runs ◽  
Waiting Time Distributions ◽  
Joint Distributions ◽  
First Occurrence

In this paper, joint distributions of number of success runs of length k and number of failure runs of length k' are obtained by using combinatorial techniques including lattice path approach under Pólya-Eggenberger model. Some of its particular cases, for different values of the parameters, are derived. Sooner and later waiting time problems and joint distributions of number of success runs of various types until first occurrence of consecutive success runs of specified length under the model are obtained. The sooner and later waiting time problems for Bernoulli trials (see Ebneshahrashoob and Sobel [3]) and joint distributions of the type discussed by Uchiada and Aki [11] are shown as particular cases. Assuming Ln and Sn to be the lengths of longest and smallest success runs, respectively, in a sample of size n drawn by Pólya-Eggenberger sampling scheme, the joint distributions of Ln and  Sn as well as distribution of M=max(Ln,Fn)n, where Fn is the length of longest failure run, are also  obtained.

Assessing joint distributions with isoprobability contours

2009 ◽  
Author(s):  
David V. Budescu ◽  
Ali E. Abbas ◽  
Yuhong Gu
Keyword(s):  
Joint Distributions

scholarly journals Copula-based software metrics aggregation

2021 ◽  
Author(s):  
Maria Ulan ◽  
Welf Löwe ◽  
Morgan Ericsson ◽  
Anna Wingkvist
Keyword(s):  
Open Source Software ◽  
Software Metrics ◽  
Information Quality ◽  
Empirical Studies ◽  
Probabilistic Approach ◽  
Software Systems ◽  
Quality Model ◽  
Quality Models ◽  
Joint Distributions ◽  
Abstract Notion

AbstractA quality model is a conceptual decomposition of an abstract notion of quality into relevant, possibly conflicting characteristics and further into measurable metrics. For quality assessment and decision making, metrics values are aggregated to characteristics and ultimately to quality scores. Aggregation has often been problematic as quality models do not provide the semantics of aggregation. This makes it hard to formally reason about metrics, characteristics, and quality. We argue that aggregation needs to be interpretable and mathematically well defined in order to assess, to compare, and to improve quality. To address this challenge, we propose a probabilistic approach to aggregation and define quality scores based on joint distributions of absolute metrics values. To evaluate the proposed approach and its implementation under realistic conditions, we conduct empirical studies on bug prediction of ca. 5000 software classes, maintainability of ca. 15000 open-source software systems, and on the information quality of ca. 100000 real-world technical documents. We found that our approach is feasible, accurate, and scalable in performance.

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