A Method for Computing the Circular Coverage Function

DiDonato, A. R.; Jarnagin, M. P.

doi:10.2307/2004054

Cited by 7 publications

(2 citation statements)

References 4 publications

(16 reference statements)

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“…where r = fjFO, s = f2/JF0, Iv(z) is the modified Bessel function of the first kind of order v and argument z and C(u, v) = pr {X2(2, v2) < u} is popularly known as the circular coverage function; see, for example, Didonato & Jarnagin (1962). The function Sm(fJ,f2; 4t) involves the cumulative sum of binomial probabilities but can be expressed more simply as The restriction to even numbers of variables is of little consequence as our interest is primarily in the behaviour of the various error rates as the number of variables used for discrimination is increased.…”

Section: Evaluation Of the Expectations Of The Error Ratesmentioning

confidence: 99%

On the Expectation of Errors of Allocation Associated with a Linear Discriminant Function

Moran¹

1975

Biometrika

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARY Exact expressions are obtained for the expectations of the actual, apparent and estimated errors of allocation which result when a linear discriminant function is used to allocate individuals to one of two multivariate normal populations with a known common dispersion matrix. Approximations suggested in the literature for the expectation of the actual error of allocation are compared with the exact values.

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Section: Evaluation Of the Expectations Of The Error Ratesmentioning

confidence: 99%

On the Expectation of Errors of Allocation Associated with a Linear Discriminant Function

Moran¹

1975

Biometrika

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“…A recent paper of Gilliland and Hansen [4] reviews prior results and provides an appropriate mixture representation for (1.1) when the mean vector is not zero. Some authors have represented the impact probability as an integral of the modified Bessel function l o ( x ) (see e.g., DiDonato and Jarnagin [2]). For statistical purposes it is more expeditious to treat this probability as a mixture of Poisson probabilities.…”

Section: Introductionmentioning

confidence: 99%

Lower confidence limits for the impact probability within a circle in the normal case

Zacks

Solomon

1975

Naval Research Logistics

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Lower confidence limits are derived for the impact probability within a circle of fixed radius. The bivariate normal distribution with zero means, unequal variances, and zero correlation is the probability model for impacts. A new representation of the impact probability function is offered. This presentation is valid also for the dependent case, where the eigenvalues of the covariance matrix replace the variances. When the ratio of variances is known the lower confidence limits are uniformly most accurate (UMA). A few alternative approaches are compared by simulation when the ratio of variances is unknown.

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Radial Error

Chew¹

2005

Encyclopedia of Statistical Sciences

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A Method for Computing the Circular Coverage Function

Cited by 7 publications

References 4 publications

On the Expectation of Errors of Allocation Associated with a Linear Discriminant Function

On the Expectation of Errors of Allocation Associated with a Linear Discriminant Function

Lower confidence limits for the impact probability within a circle in the normal case

Radial Error

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