On the distribution of the total number of run lengths

Antzoulakos, Demetrios L.; Bersimis, Sotiris; Koutras, Markos V.

doi:10.1007/bf02523398

Cited by 34 publications

(35 citation statements)

References 24 publications

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“…We end this section by noting that the present paper generalizes, unifies, and/or provides alternative formulae for the results of Mood (1940), Philippou et al (1983), Panaretos and Xekalaki (1986), Ling (1988), Godbole (1990), Goldstein (1990), Hirano and Aki (1993), Koutras and Alexandrou (1997), Tripsiannis and Philippou (1997), Sen et al (2002), (2003), Antzoulakos et al (2003aAntzoulakos et al ( ), (2003b, and Makri et al (2007aMakri et al ( ), (2007b.…”

Section: F S Makri Et Almentioning

confidence: 79%

“…Numerical investigations indicate that, for s = 0, this scheme may be more efficient than the corresponding one given by Theorem 3.2 of Antzoulakos et al (2003a).…”

Section: Where P Nwbs (Y) ≡ P N (Y) Is Given By (21)mentioning

confidence: 91%

“…Of statistical importance, among these studies, are the ones which consider the numbers of success runs of length exactly equal to and greater than or equal to a threshold length; see Mood (1940), Fu and Koutras (1994), Muselli (1996), Sen et al (2002), (2003), and Eryilmaz and Demir (2007). Recently Fu et al (2002), Antzoulakos et al (2003a), and Lou (2003) studied a statistic denoting the sum of the lengths of the success runs (i.e. the total number of successes in all the success runs) of length greater than or equal to a prespecified length, and the waiting time for the first time that the abovementioned statistic equals or exceeds a predetermined level (Antzoulakos et al (2003b)).…”

Section: F S Makri Et Almentioning

confidence: 99%

“…The latter distributions defined on linearly and circularly ordered sequences may be used in certain nonparametric tests of randomness. See Koutras and Alexandrou (1997), and Antzoulakos et al (2003a) for a recent use of the linear distributions. Furthermore, in Section 4 we give the distributions of the length of the longest success run and of the waiting time until a specified number of consecutive successes is observed for the first time.…”

Section: F S Makri Et Almentioning

confidence: 99%

“…It follows directly from Proposition 2.1 and Theorem 4.2. Antzoulakos et al (2003a) have also obtained (in their Theorem 4.2) the conditional PDF of S n,k , given S n,1 , and they used it in nonparametric tests of randomness. Their expressions, in comparison to (4.3), involve two additional consecutive summations of binomial coefficients.…”

Section: Success Run Statistics Defined On An Urn Modelmentioning

confidence: 99%

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Success run statistics defined on an urn model

2007

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Statistics denoting the numbers of success runs of length exactly equal and at least equal to a fixed length, as well as the sum of the lengths of success runs of length greater than or equal to a specific length, are considered. They are defined on both linearly and circularly ordered binary sequences, derived according to the Pólya-Eggenberger urn model. A waiting time associated with the sum of lengths statistic in linear sequences is also examined. Exact marginal and joint probability distribution functions are obtained in terms of binomial coefficients by a simple unified combinatorial approach. Mean values are also derived in closed form. Computationally tractable formulae for conditional distributions, given the number of successes in the sequence, useful in nonparametric tests of randomness, are provided. The distribution of the length of the longest success run and the reliability of certain consecutive systems are deduced using specific probabilities of the studied statistics. Numerical examples are given to illustrate the theoretical results.

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Section: F S Makri Et Almentioning

confidence: 79%

“…Numerical investigations indicate that, for s = 0, this scheme may be more efficient than the corresponding one given by Theorem 3.2 of Antzoulakos et al (2003a).…”

Section: Where P Nwbs (Y) ≡ P N (Y) Is Given By (21)mentioning

confidence: 91%

Section: F S Makri Et Almentioning

confidence: 99%

Section: F S Makri Et Almentioning

confidence: 99%

Section: Success Run Statistics Defined On An Urn Modelmentioning

confidence: 99%

See 3 more Smart Citations

Success run statistics defined on an urn model

2007

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A sequential test for assessing observed agreement between raters

2017

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Assessing the agreement between two or more raters is an important topic in medical practice. Existing techniques, which deal with categorical data, are based on contingency tables. This is often an obstacle in practice as we have to wait for a long time to collect the appropriate sample size of subjects to construct the contingency table.In this paper, we introduce a nonparametric sequential test for assessing agreement, which can be applied as data accrues, does not require a contingency table, facilitating a rapid assessment of the agreement. The proposed test is based on the cumulative sum of the number of disagreements between the two raters and a suitable statistic representing the waiting time until the cumulative sum exceeds a predefined threshold. We treat the cases of testing two raters' agreement with respect to one or more characteristics and using two or more classification categories, the case where the two raters extremely disagree, and finally the case of testing more than two raters' agreement. The numerical investigation shows that the proposed test has excellent performance. Compared to the existing methods, the proposed method appears to require significantly smaller sample size with equivalent power. Moreover, the proposed method is easily generalizable and brings the problem of assessing the agreement between two or more raters and one or more characteristics under a unified framework, thus providing an easy to use tool to medical practitioners.

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