Statistical Analysis of Covid-19 Outbreak with Benford’s Law

Öz

The coronavirus disease first identified in mid-December 2019 in Wuhan, China is an ongoing pandemic and the virus has spread around the world. As of 13 March 2020, the number of new cases started to increase significantly in Europe, and Europe was considered as the new center of the Covid-19 pandemic as announced by the WHO. Confirmed case rate (CCR), computed from the numbers of confirmed cases over numbers of tests of the countries can be used to confirm the quality of the numbers, and to detect the manipulation for health surveillance systems of the countries for managing the situation by testing whether or not follow Benford’s Law (BL). The main aim of this study is to test CCRs of the countries in Europe by BL to detect the data qualities and to monitor the manipulations, which can help to take precautions for the health surveillance systems of the countries.

Anahtar Kelimeler

• Outbreak
• Covid-19
• Benford's Law
• Chi-Squared Test
• Kolmogorov-Smirnov Test

Kaynakça

1. Ausloos M, Herteliu C, Ileanu B. Breakdown of Benford’s law for birth data. Physica A. 2015;419:736–745.
2. Balashov VS, Yan Y, Zhu X. Are less developed countries more likely to manipulate data during pandemics? Evidence from Newcomb-Benford law. arXiv:2007.14841. 2020
3. Becker PW. Patterns in listings of failure-rate & MTTF values and listings of other data. IEEE Trans Reliab. 1982;31:132–134
4. Benford F. The Law of Anomalous Numbers. Proceeding of the American Philosophical Society. 1938;78(4):551-573
5. Berger A, Hill TP, Rogers E. Benford online bibliography. http://www.benfordonl ine.net. 2009; Accessed March 25, 2020.
6. Gómez-Camponovo M, Moreno J, Idrovo AJ, Páez M, Achkar M. Monitoring the Paraguayan epidemiological dengue surveillance system (2009-2011) using Benford’s law. Biomédica. 2016; 36:583-92.
7. Hill TP. A statistical derivation of the significant-digit law. Stat Sci. 1995;10(4):354–363
8. Idrovo AJ, Fernández-Nino JA, Bojorquez-Chapela I, Moreno-Montoya J. Performance of public health surveillance systems during the influenza A(H1N1) pandemic in the Americas: testing a new method based on Benford’s Law. Epidemiol. Infect. 2011;139, 1827–1834.

9. Idrovo AJ, Manrique-Hernández EF. Data Quality of Chinese Surveillance of COVID-19: Objective Analysis Based on WHO’s Situation Reports. Asia Pacific Journal of Public Health. 2020;32(4):165–167.
10. Manrique-Hernández EF, Fernández-Nino JA, Idrovo AJ. Global performance of epidemiologic surveillance of Zika virus: rapid assessment of an ongoing epidemic. Public Health. 2017;143:14-16.
11. Marsaglia G, Tsang WW, Wang J. Evaluating Kolmogorov’s distribution. Journal of Statistical Software. 2003;8(18):1-4.
12. Massey Jr FJ. The Kolmogorov-Smirnov test for goodness of fit. Journal of the American statistical Association. 1951;46(253):68-78.
13. Mir TA. The law of the leading digits and the world religions. Physica A. 2012;391:792–798.
14. Mir TA. The Benford law behavior of the religious activity data. Physica A. 2014;408: 1–9.
15. Moosa IA. The effectiveness of social distancing in containing Covid-19. Applied Economics. 2020. DOI: 10.1080/00036846.2020.1789061
16. Nagasaka K. On Benford’s law. Ann Inst Stat Math. 1984;36(Part A):337–352
17. Newcomb S. Note on the frequency of use of the different digits in natural numbers. Am J Math. 1881;4(1):39–40
18. Roser M, Ritchie H, Ortiz-Ospina E, Hasell J. Coronavirus pandemic (COVID-19). Our World in Data. 2020.
19. Shao L, Ma BQ. First digit distribution of hadron full width. Mod. Phys. Lett. 2009;A24: 3275–3282.
20. Tunalioglu N, Erdogan B. Usability of the Benford’s law for the results of least square Estimation. Acta Geodaetica et Geophysica. 2019;54:315–331.
21. Walpole RE, Myers RH, Myers SL. Probability and Statistics for Engineers and Scientists. 1998; sixth edition, Prentice.
22. WHO. 2020. Situation reports. https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports/ Accessed April 30, 2020.
23. Zhang J. Testing case number of coronavirus disease 2019 in China with Newcomb-Benford law. arXiv:2002.05695. 2020.
24. [URL-1] https://covid19.who.int/ (Accessed: 31.10.2020)