Main Article Content

Abstract

This paper proposes a new probability distribution, which belongs a member of the exponential family, defined on (0,1) unit interval. The new unit model has been defined by relation of a random variable defined on unbounded interval with respect to standard logistic function. Some basic statistical properties of newly defined distribution are derived and studied. The different estimation methods and some inferences for the model parameters have been derived. We assess the performance of the estimators of these estimation methods based on the three different simulation scenarios. The analysis of three real data examples which one is related to the coronavirus data, show better fit of proposed distribution than many known distributions on the unit interval under some comparing criteria.

Keywords

Unit distribution Johnson's distributions estimation beta distribution exponential family coronavirus data COVID-19 recovery rate burr modeling

Article Details

How to Cite
Gündüz, S., & Korkmaz, M. Ç. (2020). A New Unit Distribution Based On The Unbounded Johnson Distribution Rule: The Unit Johnson SU Distribution. Pakistan Journal of Statistics and Operation Research, 16(3), 471-490. https://doi.org/10.18187/pjsor.v16i3.3421

References

  1. Altun, E. (2020). The log-weighted exponential regression model: alternative to the beta regression model. Communications in Statistics-Theory and Methods, DOI:10.1080/03610926.2019.1664586.
  2. Altun, E. and Cordeiro, G. M. (2020). The unit-improved second-degree lindley distribution: inference and regression modeling. Computational Statistics, 35(1):259–279.
  3. Altun, E. and Hamedani, G. (2018). The log-xgamma distribution with inference and application. Journal de la Soci´et´e Franc¸aise de Statistique, 159(3):40–55.
  4. Anderson, T. W. and Darling, D. A. (1952). Asymptotic theory of certain” goodness of fit” criteria based on stochastic processes. The annals of mathematical statistics, pages 193–212.
  5. Arnold, B. C. and Groeneveld, R. A. (1980). Some properties of the arcsine distribution. Journal of the American Statistical Association, 75(369):173–175.
  6. Barndorff-Nielsen, O. E. and Jørgensen, B. (1991). Some parametric models on the simplex. Journal of multivariate analysis, 39(1):106–116.
  7. Castagliola, P. (1998). Approximation of the normal sample median distribution using symmetrical Johnson su distributions: application to quality control. Communications in Statistics-Simulation and Computation, 27(2):289–301.
  8. Chen, G. and Balakrishnan, N. (1995). A general purpose approximate goodness-of-fit test. Journal of Quality Technology, 27(2):154–161.
  9. Chen, H. and Kamburowska, G. (2001). Fitting data to the Johnson system. Journal of Statistical Computation and Simulation, 70(1):21–32.
  10. Cheng, R. and Amin, N. (1979). Maximum product of spacings estimation with application to the lognormal distribution (mathematical report 79-1). Cardiff: University of Wales IST.
  11. Consul, P. C. and Jain, G. C. (1971). On the log-gamma distribution and its properties. Statistische Hefte, 12(2):100–106.
  12. Cordeiro, G. M. and Lemonte, A. J. (2014). The mcdonald arcsine distribution: A new model to proportional data. Statistics, 48(1):182–199.
  13. Dasgupta, R. (2011). On the distribution of burr with applications. Sankhya B, 73(1):1–19.
  14. Dey, S., Mazucheli, J., and Anis, M. (2017). Estimation of reliability of multicomponent stress–strength for a kumaraswamy distribution. Communications in Statistics-Theory and Methods, 46(4):1560–1572.
  15. Dey, S., Mazucheli, J., and Nadarajah, S. (2018). Kumaraswamy distribution: different methods of estimation. Computational and Applied Mathematics, 37(2):2094–2111.
  16. Dudewicz, E. J., Zhang, C. X., and Karian, Z. A. (2004). The completeness and uniqueness of Johnson’s system in skewness–kurtosis space. Communications in Statistics-Theory and Methods, 33(9):2097–2116.
  17. George, F. and Ramachandran, K. (2011). Estimation of parameters of Johnson’s system of distributions. Journal of Modern Applied Statistical Methods, 10(2):9.
  18. Ghitany, M., Mazucheli, J., Menezes, A., and Alqallaf, F. (2019). The unit-inverse gaussian distribution: A new alternative to two-parameter distributions on the unit interval. Communications in Statistics-Theory and Methods, 48(14):3423–3438.
  19. Gomez-Déniz, E., Sordo, M. A., and Calder´ın-Ojeda, E. (2014). The log–lindley distribution as an alternative to the beta regression model with applications in insurance. Insurance: Mathematics and Economics, 54:49–57.
  20. Hill, I., Hill, R., and Holder, R. (1976). Algorithm as 99: Fitting Johnson curves by moments. Journal of the royal statistical society. Series C (Applied statistics), 25(2):180–189.
  21. Johnson, N. (1955). Systems of frequency curves derived from the first law of laplace. Trabajos de estad´ıstica, 5(3):283–291.
  22. Johnson, N. L. (1949). Systems of frequency curves generated by methods of translation. Biometrika, 36(1/2):149–176.
  23. Korkmaz, M. Ç . (2020a). A new heavy-tailed distribution defined on the bounded interval: the logit slash distribution and its application. Journal of Applied Statistics, DOI:10.1080/02664763.2019.1704701.
  24. Korkmaz, M. Ç. (2020b). The unit generalized half normal distribution: A new bounded distribution with inference and application. Unıversıty Polıtehnıca of Bucharest Scıentıfıc Bulletın-Serıes A-Applıed Mathematıcs And Physıcs, 82(2):133–140.
  25. Korkmaz, M. Ç. and Erişoğlu, M. (2014). The Burr XII-geometric distribution. Journal of Selçuk University Natural and Applied Science, 3(4):75–87.
  26. Korkmaz, M. Ǹ . and Genc¸, A. İ. (2017). A new generalized two-sided class of distributions with an emphasis on two-sided generalized normal distribution. Communications in Statistics-Simulation and Computation, 46(2):1441–1460.
  27. Kullback, S. (1997). Information theory and statistics. Courier Corporation.
  28. Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of hydrology, 46(1-2):79–88.
  29. Mazucheli, J., Menezes, A. F., and Dey, S. (2018). The unit-birnbaum-saunders distribution with applications. Chilean Journal of Statistics, 9(1):47–57.
  30. Mazucheli, J., Menezes, A. F., and Dey, S. (2019a). Unit-Gompertz distribution with applications. Statistica, 79(1):25–43.
  31. Mazucheli, J., Menezes, A. F. B., and Chakraborty, S. (2019b). On the one parameter unit-lindley distribution and its associated regression model for proportion data. Journal of Applied Statistics, 46(4):700–714.
  32. McDonald, J. B. (1984). Some generalized functions for the size distribution of income. Econometrika, 52(3):647–663.
  33. Ranneby, B. (1984). The maximum spacing method. an estimation method related to the maximum likelihood method. Scandinavian Journal of Statistics, pages 93–112.
  34. Shaked, M. and Shanthikumar, J. G. (2007). Stochastic orders. Springer Science & Business Media.
  35. Slifker, J. F. and Shapiro, S. S. (1980). The Johnson system: selection and parameter estimation. Technometrics, 22(2):239–246.
  36. Tadikamalla, P. R. and Johnson, N. L. (1982). Systems of frequency curves generated by transformations of logistic variables. Biometrika, 69(2):461–465.
  37. Topp, C. W. and Leone, F. C. (1955). A family of J-shaped frequency functions. Journal of the American Statistical Association, 50(269):209–219.
  38. Tuenter, H. J. (2001). An algorithm to determine the parameters of SU-curves in the Johnson system of probabillity distributions by moment matching. Journal of Statistical Computation and Simulation, 70(4):325–347.
  39. van Dorp, J. R. and Jones, M. (2020). The Johnson system of frequency curvesˆahistorical, graphical, and limiting perspectives. The American Statistician, 74(1):37–52.
  40. van Dorp, J. R. and Kotz, S. (2002). The standard two-sided power distribution and its properties: with applications in financial engineering. The American Statistician, 56(2):90–99.
  41. Venkataraman, S. V. and Rao, S. N. (2016). Estimation of dynamic var using JSU and PIV distributions. Risk Management, 18(2-3):111–134.
  42. Wheeler, R. E. (1980). Quantile estimators of Johnson curve parameters. Biometrika, pages 725–728.
  43. ZeinEldin, R. A., Chesneau, C., Jamal, F., and Elgarhy, M. (2019). Different estimation methods for type I half-logistic Topp–Leone distribution. Mathematics, 7(10):985.