A WEB-BASED SOFTWARE FOR THE CALCULATION OF THEORETICAL PROBABILITY DISTRIBUTIONS

Abstract

Abstract— Aim: The aim of this study is to develop a public web-based theoretical probability distributions software (KODY) that can calculate probabilities for discrete and continuous distributions. Materials and Methods: The Discrete Uniform, Bernoulli, Binomial, Multinomial, Poisson, Geometric, Negative Binomial, Hypergeometric and Zeta (Zipf) distributions from the discrete distributions are explained. Among the continuous distributions, The Continuous Uniform, Beta, Normal, Log-Normal, Exponential, Gamma, Weibull, Rayleigh, Logistics, Pareto, Laplace, Cauchy and Erlang distributions are elucidated. Illustrative examples are presented on hypothetical medical data. The software was developed using the MATH and DASH libraries of the Python programming language. Results: When making statistical analysis, the feature of the distribution is essential. Because the descriptive and analytical statistical methods to be applied to data with different distributions are also different. Probability distributions of variables are important in the effectiveness of these methods. For this reason, it is an essential step for researchers to determine the probability distributions of their data before starting their studies. It is thought that the software developed in this study will enable researchers to make the necessary calculations in probabilistic estimates regarding the theoretical probability distributions. The developed software can be accessed at http://biostatapps.inonu.edu.tr/KODY/. Conclusion: The open access web-based software with Turkish/English language options may guide and contribute to researchers in probabilistic estimation processes regarding theoretical distributions. In the later stages of this study, it is foreseen to develop simulation processes based on each probability distribution. Keywords— Discrete Probability Distributions, Continuous Probability Distributions, Web - Based Software, Python.

Keywords

• Discrete Probability Distributions
• Continuous Probability Distributions
• Web - Based Software
• Python

References

1. [1] F. Akdeniz, Olasılık ve istatistik: AÜ FF Döner Sermaye İşletmesi Yayınları, 1995.
2. [2] G. P. Beaumont, "Introductory applied probability," JOHN WILEY & SONS, INC., 605 THIRD AVE., NEW YORK, NY 10158, USA, 1983, 200, 1983.
3. [3] S. Ghahramani, Fundamentals of probability vol. 2: Prentice Hall New Jersey:, 2000.
4. [4] E. Sandhya and C. Prasanth, "Marshall-Olkin discrete uniform distribution," Journal of probability, vol. 2014, 2014.
5. [5] B. Dai, S. Ding, and G. Wahba, "Multivariate bernoulli distribution," Bernoulli, vol. 19, pp. 1465-1483, 2013.
6. [6] P. M. Altham, "Two generalizations of the binomial distribution," Journal of the Royal Statistical Society: Series C (Applied Statistics), vol. 27, pp. 162-167, 1978.
7. [7] J. E. Mosimann, "On the compound multinomial distribution, the multivariate β-distribution, and correlations among proportions," Biometrika, vol. 49, pp. 65-82, 1962.
8. [8] P. C. Consul and G. C. Jain, "A generalization of the Poisson distribution," Technometrics, vol. 15, pp. 791-799, 1973.

9. [9] A. N. Philippou, C. Georghiou, and G. N. Philippou, "A generalized geometric distribution and some of its properties," Statistics & Probability Letters, vol. 1, pp. 171-175, 1983.
10. [10] P. Fisher, "Negative Binomial Distribution," Annals of Eugenics, vol. 11, pp. 182-787, 1941.
11. [11] W. L. Harkness, "Properties of the extended hypergeometric distribution," The Annals of Mathematical Statistics, vol. 36, pp. 938-945, 1965.
12. [12] A. Grami, Probability, random variables, statistics, and random processes: Fundamentals & applications: John Wiley & Sons, 2019.
13. [13] L. Kuipers and H. Niederreiter, Uniform distribution of sequences: Courier Corporation, 2012.
14. [14] A. K. Gupta and S. Nadarajah, Handbook of beta distribution and its applications: CRC press, 2004.
15. [15] M. Ahsanullah, B. G. Kibria, and M. Shakil, "Normal distribution," in Normal and Student´ st Distributions and Their Applications, ed: Springer, 2014, pp. 7-50.
16. [16] R. L. Mitchell, "Permanence of the log-normal distribution," JOSA, vol. 58, pp. 1267-1272, 1968.
17. [17] N. Balakrishnan, "AP Basu: The Exponential Distribution: Theory, Method and Applications," ed: Gordon and Breach Publishers. Langliorne, Pennsylvania, 1995.
18. [18] H. C. Thom, "A note on the gamma distribution," Monthly Weather Review, vol. 86, pp. 117-122, 1958.
19. [19] H. Rinne, The Weibull distribution: a handbook: CRC press, 2008.
20. [20] D. Kundu and M. Z. Raqab, "Generalized Rayleigh distribution: different methods of estimations," Computational statistics & data analysis, vol. 49, pp. 187-200, 2005.
21. [21] N. Balakrishnan, Handbook of the logistic distribution: CRC Press, 1991.
22. [22] B. C. Arnold, "Pareto distribution," Wiley StatsRef: Statistics Reference Online, pp. 1-10, 2014.
23. [23]S. Kotz, T. Kozubowski, and K. Podgorski, The Laplace distribution and generalizations: a revisit with applications to communications, economics, engineering, and finance: Springer Science & Business Media, 2012.
24. [24]B. C. Arnold and R. J. Beaver, "The skew-Cauchy distribution," Statistics & probability letters, vol. 49, pp. 285-290, 2000.
25. [25]O. Ibe, Markov processes for stochastic modeling: Newnes, 2013.
26. [26]M. F. Sanner, "Python: a programming language for software integration and development," J Mol Graph Model, vol. 17, pp. 57-61, 1999.
27. [27] G. S. GRIMMETT, Probability and random processes: Oxford university press, 2020.
28. [28]D. E. Morris, J. E. Oakley, and J. A. Crowe, "A web-based tool for eliciting probability distributions from experts," Environmental Modelling & Software, vol. 52, pp. 1-4, 2014.
29. [29]D. Fylstra, L. Lasdon, J. Watson, and A. Waren, "Design and use of the Microsoft Excel Solver," Interfaces, vol. 28, pp. 29-55, 1998.
30. [30]N. H. Nie, D. H. Bent, and C. H. Hull, SPSS: Statistical package for the social sciences vol. 227: McGraw-Hill New York, 1975.
31. [31] F. Schoonjans, A. Zalata, C. Depuydt, and F. Comhaire, "MedCalc: a new computer program for medical statistics," Computer methods and programs in biomedicine, vol. 48, pp. 257-262, 1995.
32. [32]I. StatSoft, "STATISTICA (data analysis software system), version 6," Tulsa, USA, vol. 150, pp. 91-94, 2001.