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Insight into Knapsack Metabolite Ecology Database: A Comprehensive Source of Species: Voc-Biological Activity Relationships
Published in Raquel Cumeras, Xavier Correig, Volatile organic compound analysis in biomedical diagnosis applications, 2018
Azian Azamimi Abdullah, M.D. Altaf-Ul-Amin, Shigehiko Kanaya
Here N is the total number of VOCs; C is the size of a cluster and V and K, respectively, are the number of VOCs of a certain category in the whole data and in the cluster. The hypergeometric distribution is used to calculate the statistical significance of having drawn a specific K successes (out of C total draws) from the whole population. The test is often used to identify which subpopulations are over- or under-represented in a cluster. The calculated p-value implies the probability of getting K or more VOCs of a particular category in a cluster when the cluster is formed by random selection. Lower p-value indicates that the statistical significance is high. Our purpose is to relate a structure group to a biological activity if and only if the structure group is overrepresented by VOCs associated with that biological activity.
Basic Mathematics
Published in M. Modarres, What Every Engineer Should Know About Reliability and Risk Analysis, 2018
The hypergeometric distribution is very useful to certain quality control problems and certain acceptance sampling problems. In the acceptance sampling problems, Np can be replaced by the parameter D (for sampling with replacement) to reflect the number of units with a given characteristic (e.g., defective, high powered, etc.). Therefore, (2.29) can be written as () Pr(x)=(Dx)(N–Dn–x)(Nn),max(0,n+D–N)≤x≤min(D,n),
Quality Control in Manufacturing
Published in Zainul Huda, Manufacturing, 2018
Hypergeometric Distribution: This is the probability distribution of a hypergeometric random variable, k. Let the sample population be N. The hypergeometric distribution is used to model the probability of getting k successes in n draws without replacement. It is given by P(X)=[(Kk)(N−Kn−k)]/(Nn);k=0,1,2,… The mean in hypergeometric distribution, μhgd, is given by μhgd = (n k)/N
Evaluation of GOFP over four forest plots using RAMI and UAV measurements
Published in International Journal of Digital Earth, 2021
Jun Geng, Qian Zhang, Feng Qiu, J. M. Chen, Yongguang Zhang, Weiliang Fan, Lili Tu, Jianwei Huang, Shaoteng Wang, Lichen Xu, Jinchao Li
If n = 1, the hypergeometric distribution is the binomial distribution which is an independent event; if n > 1, it is a conditional probability because every foregoing sampling result could affect the subsequent sampling probability. The essential difference between the Poisson model and the hypergeometric model is that the former uses random sampling with replacement, while the latter uses random sampling without replacement. This characteristic of the hypergeometric model can be used to describe the tree distribution in the forest plantation stands: (1) the characteristic of ‘random sampling’ in the hypergeometric model can be used to express the randomness of the tree distribution in the forest stands; (2) the characteristic of ‘without replacement’ in the model can be used to describe the exclusion effect among trees in the stands. Compared with the Poisson random model and the Neyman model, both the randomness and exclusion effect among trees can be considered in the hypergeometric model. The different descriptions of three distributions with the tree models are shown in Figure 2. The hypergeometric model has an exclusion effect among trees, leading to a minimum degree of overlap among the trees at nadir and the maximum forest coverage in all three forest stands in Figure 2.
Generalized one-tailed hypergeometric test with applications in statistical quality control
Published in Journal of Quality Technology, 2020
Nataliya Chukhrova, Arne Johannssen
As for a statistical decision regarding H0, it is made using random samples of size n (with ) selected without replacement. The n random variables Xi (with ) are Bernoulli distributed with two possible outcomes: fail (0) and success (1). Each Xi follows the zero-one distribution, that is, and , but the random variables are not stochastically independent. The random variable is defined as the number of successes in the sample and follows the hypergeometric distribution.
Optimizing production-inventory replenishment and lead time decisions under a fill rate constraint in a two-echelon sustainable supply chain with quality issues
Published in International Journal of Systems Science: Operations & Logistics, 2023
Davide Castellano, Roberto Gabbrielli, Mosè Gallo, Bibhas C. Giri, Sumon Sarkar
For a given observation of the defective rate ϕ, the number of defective units in the sampled sub-lot, Y, is a random variable with a hypergeometric distribution with parameters Q, f, and ϕ (see, e.g. Wu & Ouyang, 2000). We can thus evaluate and . Using the expressions of and , which can be found in, e.g. Wu and Ouyang (2000), and letting , then Equation (12) becomes