TARU PUBLICATIONS
Journal of Statistics and Management Systems cover

Journal of Statistics and Management Systems

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0014·ISSN (Print): 0972-0510

Indexed in ABDC Australia

Powered by:Powered by

Monthly Journal: Publishes peer-reviewed aticles on theoretical and applied statistics and management systems, expoloring industrial statistics, actuarial and decision sciences.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Taru Online First Current IssueSpecial IssuesBrowse all Issues
Journal of Statistics and Management Systems
Open Access Research Article

Large deviations : Estimating the number of positive individuals in a Bernoulli sample through sample pooling

, *

* Corresponding author · click or hover a name for details

pp. 959–969Vol. 27Issue 5July 2024DOI: 10.47974/JSMS-1220XML
Received:
10 Aug 2020
Published Online:
05 Aug 2024
Article type:
Research Article
Language:
EN
Article no.:
JSMS-1220
Pages:
959–969

Abstract

We define the empirical positives measure as a stochastic measure that quantifies the number of infections in a Bernoulli sample. Similarly, we define the empirical pool measure as a stochastic measure that enumerates the number of infected pool samples. A joint large deviation principle (LDP) is established for both empirical measures derived from the Bernoulli samples. Using this joint LDP, we establish a correlation between the asymptotic ratio of infected individuals to the sample size and the asymptotic ratio of infected pool samples to the total number of pool samples.

Keywords

Large deviationsInfected pool sampleEmpirical pool measureEmpirical positives measureInteger partitionEntropyRelative entropy

Subject Classifications

60F1011B6811P8468Q25

References

[1] Biggins, J. D. Large deviations for mixtures In Electron. Comm. Probab.9 60-71 (2004). 
[2] Bhatnagar, V., Poonia, R. C., Nagar, P., Kumar, S. ,Singh, V. , Raja, L. and Dass, P. Descriptive analysis of COVID-19 patients in the context of India. Journal of Interdisciplinary Mathematics (2020), DOI: 10.1080/09720502.2020.1761635. 
[3] Doku-Amponsah, K. Large Deviations and Basic Information Theory for Hierarchical and Networked Data Structures Ph.D Thesis, Bath (2006). 
[4] Doku-Amponsah, K. (2006). Large deviations, asymptotic bounds on the number of positive individuals in a Bernoulli sample via the number of positive pool samples drawn on the bernoulli sample https://doi.org/10.48550/arXiv.2008.02151. 
[5] Doku-Amponsah, K. and Moeters. P. Large deviation principle for empirical measures of coloured random graphs. Ann. Appl. Prob. 20(6), 1089-2021 (2010).
[6] Dembo, A. and Zeitouni, O. Large deviations Techniques and Applications. Springer (1998). 
[7] Sakyi-Yeboah, E., Asiedu, L. and Doku-Amponsah, K. Local large deviation principle, large deviation principle and information theory for the signal-to-interference-plus-noise ratio graph models. Journal of Information and Optimization Science, 42(1), 249-273 (2020). 
[8] Singh, V., Poonia, R. C., Kumar, S., Dass, P., Agarwal, P., Bhatnagar, V. and Raja, L. Prediction of COVID-19 corona virus pandemic based on time series data using support vector machine. Journal of Discrete Mathematical Sciences and Cryptography (2020), DOI: 10.1080/09720529.2020.1784535.

Views: 118Downloads: 54Citations: 0