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:10.1090/s0025-5718-1967-0221730-x

Cited by 8 publications

(4 citation statements)

References 11 publications

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“…The OC curve represents the probability of acceptance of the population as a function of . For the binomial distribution (2), the OC curve is given by DiDonato and Jarnagin (1967) and Press et al (1996, Chap. 6) for details on the numerical computation.…”

Section: Lqas Plansmentioning

confidence: 99%

“…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%

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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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Section: Lqas Plansmentioning

confidence: 99%

“…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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“…When λ = 0, (4) reduces to the Pearson type II pdf (2). Further particular cases of (25) can be obtained by applying the properties (5-10) of the incomplete beta function ratio; see DiDonato and Jarnagin [12] and Saunders [13] and the references therein.…”

Section: Skew Pearson Type II Distributionmentioning

confidence: 99%

Skew Models II

Nadarajah

Kotz

2007

Acta Appl Math

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“…The incomplete beta function [41] and relation between beta and gamma functions are given in the following. Definition 4.…”

Section: Introductionmentioning

confidence: 99%

Exploration of Hermite–Hadamard-Type Integral Inequalities for Twice Differentiable h-Convex Functions

et al. 2023

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The significance of fractional calculus cannot be underestimated, as it plays a crucial role in the theory of inequalities. In this paper, we study a new class of mean-type inequalities by incorporating Riemann-type fractional integrals. By doing so, we discover a novel set of such inequalities and analyze them using different mathematical identities. This particular class of inequalities is introduced by employing a generalized convexity concept. To validate our work, we create visual graphs and a table of values using specific functions to represent the inequalities. This approach allows us to demonstrate the validity of our findings and further solidify our conclusions. Moreover, we find that some previously published results emerge as special consequences of our main findings. This research serves as a catalyst for future investigations, encouraging researchers to explore more comprehensive outcomes by using generalized fractional operators and expanding the concept of convexity.

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The efficient calculation of the incomplete beta-function ratio for half-integer values of the parameters 𝑎,𝑏

Cited by 8 publications

References 11 publications

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

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

Skew Models II

Exploration of Hermite–Hadamard-Type Integral Inequalities for Twice Differentiable h-Convex Functions

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