Науковий вісник НГУ

Cumulative triangle for visual analysis of empirical data

• 
• 

User Rating:  / 0

PoorBest 

Details

Category: Content №4 2024

Last Updated on 28 August 2024

Published on 30 November -0001

Hits: 1974

Authors:

Yu.Golovko, orcid.org/0000-0001-6081-8072, Dnipro University of Technology, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

O.Sdvyzhkova*, orcid.org/0000-0001-6322-7526, Dnipro University of Technology, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

* Corresponding author e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

повний текст / full article

Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2024, (4): 114 - 120

https://doi.org/10.33271/nvngu/2024-4/114

Abstract:

Purpose. The development of a graphical object for visual analysis that allows for simultaneous evaluation of both general characteristics and details of the empirical data distribution.

Methodology. Justification of the feasibility and sequence of creating the cumulative triangle, as well as proving its properties, was carried out using geometric constructions, generalization, and lattice functions. The construction of the cumulative triangle was implemented in the “Matlab” software. Samples of random variables with known distribution laws were obtained using a pseudo-random number generator. Previously calculated dependencies of the spectral power density of seismic-acoustic noise-like signals were used as empirical data.

Findings. A folded cumulative function of the n-th order was introduced as a generalization of the known folded cumulative function. Using the folded cumulative functions, a geometric object that is the cumulative triangle, was designed to visualize the empirical distribution function. Lines dividing the triangle into flat curvilinear quadrilaterals are plotted on each triangle. It is shown that the face area can be used as a characteristic of the random variable concentration near the abscissa of the face upper node, and the difference in the areas of the face left and right parts provides for assessing the asymmetry of the distribution over the interval covering the face.

Originality. A new graphical object for visual analysis of empirical data distribution is proposed. It is shown how, relying on its appearance, conclusions can be drawn both regarding the characteristics of the entire sample and individual intervals of the distribution function.

Practical value. The cumulative triangle can be a useful addition to graphical visualization tools. Its use allows for simultaneous detailing and generalization of the properties of experimentally obtained data at different scale levels, which is particularly valuable when data have complicated and variable distributions.

Keywords: visualization, empirical data, distribution function, folded cumulative function, power spectrum

References.

1. Wilke, C. O. (2019). Fundamentals of Data Visualization. O’Reilly Media. Retrieved from https://data.vk.edu.ee/powerbi/opikud/Fundamentals_of_Data_Visualization.pdf.

2. Scott, D. W. (2010). Scott’s rule. Wiley Interdisciplinary Reviews: Computational Statistics, 2. https://doi.org/10.1002/wics.103.

3. Chen, Y. C. (2017). A tutorial on kernel density estimation and recent advances. Biostat. Epidemiol, 1, 161–187. Retrieved from https://arxiv.org/pdf/1704.03924.pdf.

4. Weglarczyk, S. (2018). Kernel density estimation and its application. In ITM Web of Conferences; EDP Sciences: Les Ulis, France, 23, 00037. https://doi.org/10.1051/itmconf/20182300037.

5. Scott, D. W. (2018). Kernel density estimation. Wiley StatsRef: Statistics Reference Online, 1-7. https://doi.org/10.1002/9781118445112.stat07186.pub2.

6. Koutsoyiannis, D. (2022). Replacing Histogram with Smooth Empirical Probability Density Function Estimated by K-Moments. Sci, 4, 50. https://doi.org/10.3390/sci4040050.

7. Karczewski, M., & Michalski, A. (2022). A data-driven kernel estimator of the density function. Journal of Statistical Computation and Simulation, 92(17), 3529-3541. https://doi.org/10.1080/00949655.2022.2072503.

8. Park, K. I. (2018). Basic Mathematical Preliminaries. In Fundamentals of Probability and Stochastic Processes with Applications to Communications. Springer. Cham. https://doi.org/10.1007/978-3-319-68075-0_2.

9. Weaver, K. F., Morales, V. C., Dunn, S. L., Godde, K., & Weaver, P. F. (2017). An Introduction to Statistical Analysis in Research: With Applications in the Biological and Life Sciences. Germany: Wiley.

10. Marmolejo-Ramos, F., & Tian, S. (2010). The shifting boxplot. A boxplot based on essential summary statistics around the mean. International Journal of Psychological Research, 3(1), 37-45. https://doi.org/10.21500/20112084.823.

11. Wickham, H., & Stryjewski, L. (2011). 40 years of boxplots. Retrieved from https://vita.had.co.nz/papers/boxplots.pdf.

12. Xue, J.-H., & Titterington, D. M. (2011). The p-folded cumulative distribution function and the mean absolute deviation from the p-quantile. Statistics and Probability Letters, 81, 1179-1182. https://doi.org/10.1016/j.spl.2011.03.014.

13. Olshaker, H., Buhbut, O., Achiron, А., & Dotan, G. (2021). Comparison of keratometry data using handheld and table-mounted instruments in healthy adults. International Ophthalmology, 41(1). https://doi.org/10.1007/s10792-021-01909-8.

14. Stokar, J., Leibowitz, D., Durst, R., Shaham, D., & Zwas, D. (2019). Echocardiography overestimates LV mass in the elderly as compared to cardiac CT. PLoS ONE, 14(10), e0224104. https://doi.org/10.1371/journal.pone.0224104.

15. Weisstein, E. W. (2024, April 25). Pearson’s Skewness Coefficients. From MathWorld--A Wolfram Web Resource. Retrieved from https://mathworld.wolfram.com/PearsonsSkewnessCoefficients.html.

16. Sdvyzhkova, O., Golovko, Yu., Dubytska, M., & Klymenko, D. (2016). Studying a crack initiation in terms of elastic oscillations in stress strain rock mass. Mining of Mineral Deposits. Dnepr: National Mining University (Dnepr, Ukraine), 10(2), 72-77. https://doi.org/10.15407/mining10.02.072.

17. Golovko, Yu. (2017). Estimation of seismoacoustic signal spectral parameters under the current prediction of gasodynamic phenomena in mines. Heotekhnichna mekhanika, 134, 141-154.

18. Golovko, Yu. М. (2023). Spectral estimation of a broadband time-limited noise signal. Matematychne modeliuvannia, 2(49), 86-97. https://doi.org/10.31319/2519-8106.2(49)2023.292638.

• < Prev
• Next >