The Efficient Calculation of the Incomplete Beta-Function Ratio for Half- Integer Values of the Parameters a, b

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

doi:10.2307/2005009

Cited by 2 publications

(2 citation statements)

References 4 publications

(6 reference statements)

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“…(6c) replacing f(x) by f a (x) = (1 -x/δ) n we have to demonstrate how the space-fractional RL derivative works with f a (x). Following the rule of RL derivative of a binomial function (C -cx) p we have [40]: Beta function can be expressed in terms of elementary functions when the sum a + b is a negative integer [43][44][45]. In the case of eq.…”

Section: Assumed Profile and The Space-fractional Derivative Of It: Pmentioning

confidence: 99%

An approximate solution to the transient space-fractional diffusion equation: Integral-balance approach, optimization problems and analyzes

Hristov

2017

THERM SCI

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This paper presents approximate analytical solutions of an initial-boundary value problem of fractional partial differential diffusion equation with spatial Riemann-Liouville fractional derivative. The proposed approximate solutions are based on the concept of a finite penetration depth with the integral-balance method and series expansions of the assumed parabolic profile with undefined exponent. Optimization problems referring to optimal exponents of the assumed parabolic have been developed.

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Section: Assumed Profile and The Space-fractional Derivative Of It: Pmentioning

confidence: 99%

An approximate solution to the transient space-fractional diffusion equation: Integral-balance approach, optimization problems and analyzes

Hristov

2017

THERM SCI

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“…The OC curve represents the probability of acceptance of the population as a function of p . For the binomial distribution , the OC curve is given by

F false(p false| n, r false) = \sum_{x = r}^{n} ℙ false(x false) = \sum_{x = r}^{n} ((), \begin{matrix} center n \\ center x \end{matrix}) p^{x} {false(1 - p false)}^{n - x} = I false(p, n - r + 1, r false),

where

I false(p, n - r + 1, r false) = \int_{0}^{p} z^{n - r} {false(1 - z false)}^{r - 1} normald z / \int_{0}^{1} z^{n - r} {false(1 - z false)}^{r - 1} normald z

is the cumulative regularized Beta function, see DiDonato and Jarnagin () and Press et al (, Chap. 6) for details on the numerical computation.…”

Section: Introductionmentioning

confidence: 99%

Optimal Design of Multiple-Objective Lot Quality Assurance Sampling (LQAS) Plans

Duarte

Wong

2018

Biometrics

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Lot Quality Assurance Sampling (LQAS) plans are widely used for health monitoring purposes. We propose a systematic approach to design multiple‐objective LQAS plans that meet user‐specified type 1 and 2 error rates and targets for selected diagnostic accuracy metrics. These metrics may include sensitivity, specificity, positive predictive value, and negative predictive value in high or low anticipated prevalence rate populations. We use Mixed Integer Nonlinear Programming (MINLP) tools to implement our design methodology. Our approach is flexible in that it can directly generate classic LQAS plans that control error rates only and find optimal LQAS plans that meet multiple objectives in terms of diagnostic metrics. We give examples, compare results with the classic LQAS and provide an application using a malaria outcome indicator survey in Mozambique.

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The Efficient Calculation of the Incomplete Beta-Function Ratio for Half- Integer Values of the Parameters a, b

Cited by 2 publications

References 4 publications

An approximate solution to the transient space-fractional diffusion equation: Integral-balance approach, optimization problems and analyzes

An approximate solution to the transient space-fractional diffusion equation: Integral-balance approach, optimization problems and analyzes

Optimal Design of Multiple-Objective Lot Quality Assurance Sampling (LQAS) Plans

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