Skip to main content
SpringerLink
Log in

Unit Modified Burr-III Distribution: Estimation, Characterizations and Validation Test

  • Published:
Annals of Data Science Aims and scope Submit manuscript

Abstract

In this paper, a new three-parameter unit probability distribution is proposed. The new model is a generalization of Burr III distribution, and it is more flexible than some existing well-known distribution due to its different shapes of the hazard function and probability density functions. The mathematical properties of this distribution are presented, including moments, reliability measures, mean residual life, and characterizations, and we also propose a modified Chi squared goodness-of-fit test based on Nikulin–Rao–Robson statistic Y2 in the presence of complete and censored data. The parameters related to the proposed distribution are estimated using well-known estimation methods. A numerical simulations study is conducted for reinforcement of the results. In the end, we considered two real datasets to illustrate the applicability of the proposed model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Ali A, Ahmad M (2015) The transmuted modified Burr III distribution. J ISOSS 1(2):119–130

    Google Scholar 

  2. Ali A, Hasnain SA, Ahmad M (2015) Modified Burr III distribution, properties and applications. Pak J Stat 31(6):697–708

    Google Scholar 

  3. Bagdonavičius V, Nikulin M (2011) Chi squared goodness-of-fit test for right-censored data. Int J Appl Math Stat 24:30–50

    Google Scholar 

  4. Bagdonavičius V, Levuliene RJ, Nikulin M (2013) Chi squared goodness-of-fit tests for parametric accelerated failure time models. Commun Stat Theory Methods 42(15):2768–2785

    Article  Google Scholar 

  5. Bhatt FA, Hamedani GG, Ali A, Ahmad M (2018) Some characterizations of transmuted modified Burr III distribution. Asian J Proba Stat 1(1):1–9

    Google Scholar 

  6. Chakraborty S, Handique L, Usman RM (2020) A simple extension of Burr-III distribution and its advantages over existing ones in modelling failure time data. Ann Data Sci 7(1):17–31

    Article  Google Scholar 

  7. Cheng RCH, Amin NAK (1983) Estimating parameters in continuous univariate distributions with a shifted origin. J R Stat Soc Ser B: Methodol 45(3):394–403

    Google Scholar 

  8. Cordeiro GM, dos Santos Brito R (2012) The beta power distribution. Braz J Probab Stat 26(1):88–112

    Google Scholar 

  9. Ghitany ME, Mazucheli J, Menezes AFB, Alqallaf F (2019) The unit-inverse Gaussian distribution: a new alternative to two-parameter distributions on the unit interval. Commun Stat Theory Methods 48(14):3423–3438

    Article  Google Scholar 

  10. Glanzel WA (1987) Characterization theorem based on truncated moments and its application to some distribution families. Springer, Dordrecht

    Book  Google Scholar 

  11. Glänzel WA (1990) Some consequences of a characterization theorem based on truncated moments. Statistics 21:613–618

    Article  Google Scholar 

  12. Glanzel W, Hamedani GG (2001) Characterizations of univariate continuous distributions. Stud Sci Math Hung 37:11883

    Google Scholar 

  13. Gupta AK, Nadarajah S (2004) Handbook of beta distribution and its applications. CRC Press, Boca Raton

    Book  Google Scholar 

  14. Hamedani GG (1993) Characterizations of cauchy, normal and uniform distributions. Stud Sci Math Hung 28(3):243–248

    Google Scholar 

  15. Hamedani GG (2002) Characterizations of univariate continuous distributions. II. Stud Sci Math Hung 39:407–424

    Google Scholar 

  16. Haq MAU, Elgarhy M, Hashmi S (2019) The generalized odd Burr III family of distributions: properties, applications and characterizations. J Taibah Univ Sci 13(1):961–971

    Article  Google Scholar 

  17. Johnson NL (1949) Bivariate distributions based on simple translation systems. Biometrika 36(3/4):297–304

    Article  Google Scholar 

  18. Kao JHK (1959) A graphical estimation of mixed Weibull parameters in life-testing of electron tubes. Technometrics 1(4):389–407

    Article  Google Scholar 

  19. Klein JP, Moeschberger ML (2006) Survival analysis: techniques for censored and truncated data. Springer, Berlin

    Google Scholar 

  20. Kumaraswamy P (1980) A generalized probability density function for double bounded random processes. J Hydrol 46:79–88

    Article  Google Scholar 

  21. Louzada F, Luiz Ramos P, Henrique Ferreira P (2020) Exponential-Poisson distribution: estimation and applications to rainfall and aircraft data with zero occurrence. Commun Stat Simul Comput 49(4):1024–1043

    Article  Google Scholar 

  22. Mazucheli J, Menezes AF, Dey S (2018) The unit-Birnbaum–Saunders distribution with applications. Chil J Stat 9(1):47–57

    Google Scholar 

  23. Mazucheli J, Menezes AFB, Ghitany ME (2018) The unit-Weibull distribution and associated inference. J Appl Probab Stat 13:1–22

    Google Scholar 

  24. Mazucheli J, Menezes AF, Dey S (2019) Unit-Gompertz distribution with applications. Statistica 79(1):25–43

    Google Scholar 

  25. Menezes AFB, Mazucheli J, Dey S (2018) The unit-logistic distribution: different methods of estimation. Pesqui Oper 38(3):555–578

    Article  Google Scholar 

  26. Mukhtar S, Ali A, Alya AM (2019) Mc-Donald modified Burr-III distribution: properties and applications. J Taibah Univ Sci 13(1):184–192

    Article  Google Scholar 

  27. Nahman NS, Middendorf DF, Bay WH, McElligott R, Powell S, Anderson J (1992) Modification of the percutaneous approach to peritoneal dialysis catheter placement under peritoneoscopic visualization: clinical results in 78 patients. J Am Soc Nephrol 3(1):103–107

    Article  Google Scholar 

  28. Olson DL, Shi Y, Shi Y (2007) Introduction to business data mining, vol 10. McGraw-Hill, Englewood Cliffs, pp 2250–2254

    Google Scholar 

  29. Pedro L. Ramos acknowledges support from the São Paulo State Research Foundation (FAPESP Proc. 2017/25971-0)

  30. Ramos PL, Louzada F, Ramos E, Dey S (2019) The Fréchet distribution: estimation and application—an overview. J Stat Manag Syst 1–30

  31. Ravi V, Gilbert PD (2009) BB: An R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function. J Stat Softw 32(4):1–26

    Google Scholar 

  32. Shi Y (2014) Big data: history, current status, and challenges going forward. Bridge US Natl Acad Eng 44(4):6–11

    Google Scholar 

  33. Shi Y, Tian Y, Kou G, Peng Y, Li J (2011) Optimization based data mining: theory and applications. Springer, Berlin

    Book  Google Scholar 

  34. Topp CW, Leone FC (1955) A family of J-shaped frequency functions. J Am Stat Assoc 50(269):209–219

    Article  Google Scholar 

  35. Usman RM, Haq MA (2019) Some remarks on odd Burr III Weibull distribution. Ann Data Sci 6(1):21–38

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Statistical and Actuarial Sciences, University of the Punjab, Lahore, Pakistan

    Muhammad Ahsan ul Haq & Sharqa Hashmi

  2. Quality Enhancement Cell, National College of Arts, Lahore, Pakistan

    Muhammad Ahsan ul Haq

  3. Lahore College for Women University (LCWU), Lahore, Pakistan

    Sharqa Hashmi

  4. Laboratory of Probability and Statistics LaPS, University Badji Mokhtar, Annaba, Algeria

    Khaoula Aidi

  5. Institute of Mathematical Science and Computing, University of São Paulo, São Carlos, SP, Brazil

    Pedro Luiz Ramos & Francisco Louzada

Authors
  1. Muhammad Ahsan ul Haq
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sharqa Hashmi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Khaoula Aidi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pedro Luiz Ramos
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Francisco Louzada
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Ahsan ul Haq.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Haq, M.A., Hashmi, S., Aidi, K. et al. Unit Modified Burr-III Distribution: Estimation, Characterizations and Validation Test. Ann. Data. Sci. 10, 415–440 (2023). https://doi.org/10.1007/s40745-020-00298-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40745-020-00298-6

Keywords

Search

Navigation