Skip to main content
SpringerLink
Log in

The Log-Logistic Regression Model Under Censoring Scheme

  • Published:
Methodology and Computing in Applied Probability Aims and scope Submit manuscript

Abstract

A regression model, based on the well-known log-logistic distribution is proposed. This model is parameterized in terms of the median of the distribution, through a link function. The regression model assumes the censored data structure. The unknown parameters are estimated by maximum likelihood. Monte Carlo simulations with censoring and application to real censored data show the good quality of the proposed regression 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

Similar content being viewed by others

Availability of Data and Material

The data used in the application can be found at Lawless (2003).

References

  • Alizadeh M, MirMostafee SMTK, Ortega EMM, Ramires TG, Cordeiro GM (2017) The odd log-logistic logarithmic generated family of distributions with applications in different areas. Journal of Statistical Distributions and Applications 4(1):1–25

    Article  MATH  Google Scholar 

  • Atkinson AC (1981) Two graphical displays for outlying and influential observations in regression. Biometrika 68(1):13–20

    Article  MathSciNet  MATH  Google Scholar 

  • Cordeiro GM, Alizadeh M, Ozel G, Hosseini B, Ortega EMM, Altun E (2017) The generalized odd log-logistic family of distributions: properties, regression models and applications. J Stat Comput Simul 87(5):908–932

    Article  MathSciNet  MATH  Google Scholar 

  • de Santana TVF, Ortega EMM, Cordeiro GM, Silva GO (2012) The Kumaraswamy-log-logistic distribution. Journal of Statistical Theory and Applications 11(3):265–291

    Google Scholar 

  • Doornik JA (2018) Ox: an object-oriented matrix programming language. Timberlake Consultants and Oxford, London, United Kingdown. https://www.doornik.com/

  • Gleaton JU, Lynch JD (2006) Properties of generalized log-logistic families of lifetime distributions. J Probab Stat Sci 4(1):51–64

    MathSciNet  Google Scholar 

  • Gleaton JU, Lynch JD (2010) Extended generalized log-logistic families of lifetime distributions with an application. J Probab Stat Sci 8(1):1–17

    MathSciNet  Google Scholar 

  • Gui W (2013) Marshall-Olkin extended log-logistic distribution and its application in minification processes. Appl Math Sci 7(80):3947–3961

    MathSciNet  Google Scholar 

  • Korkmaz MÇ, Cordeiro GM, Yousof HM, Pescim RR, Afify AZ, Nadarajah S (2019) The Weibull Marshall-Olkin family: regression model and application to censored data. Commun Stat Theory Methods 48(16):4171–4194

    Article  MathSciNet  MATH  Google Scholar 

  • Lawless JF (2003) Statistical models and methods for lifetime data. Wiley, New Jersey

    MATH  Google Scholar 

  • Lemonte AJ (2014) The beta log-logistic distribution. Braz J Probab Stat 28(3):313–332

    Article  MathSciNet  MATH  Google Scholar 

  • Lima SR, Cordeiro GM (2017) The extended log-logistic distribution: Properties and application. An Acad Bras Ciênc 89(1):3–17

    Article  MathSciNet  MATH  Google Scholar 

  • Peña-Ramírez FA, Guerra RR, Canterle DR, Cordeiro GM (2020) The logistic Nadarajah-Haghighi distribution and its associated regression model for reliability applications. Reliability Engineering & System Safety 204:1–13

    Article  Google Scholar 

  • Prataviera F, Ortega EMM, Cordeiro GM, Pescim RR, Verssani BAW (2018) A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems. Reliab Eng Syst Saf 176:13–26

    Article  Google Scholar 

  • R Core Team (2020) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/

  • Ramos MWA, Cordeiro GM, Marinho PRD, Dias CRB, Hamedani GG (2013) The Zografos-Balakrishnan log-logistic distribution: properties and applications. Journal of Statistical Theory and Applications

  • Reath J, Dong J, Wang M (2018) Improved parameter estimation of the log-logistic distribution with applications. Comput Statistics 33(1):339–356

    Article  MathSciNet  MATH  Google Scholar 

  • Ribeiro-Reis LD (2021) Unit log-logistic distribution and unit log-logistic regression model. J Indian Soc Probab Stat 22(2):375–388

    Article  Google Scholar 

  • Vuong QH (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica Journal of the Econometric Society 57:307–333

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Estatística, Universidade Federal de Pernambuco, Recife, PE, Brazil

    Lucas David Ribeiro-Reis

Authors
  1. Lucas David Ribeiro-Reis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lucas David Ribeiro-Reis.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ribeiro-Reis, L.D. The Log-Logistic Regression Model Under Censoring Scheme. Methodol Comput Appl Probab 25, 55 (2023). https://doi.org/10.1007/s11009-023-10039-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11009-023-10039-w

Keywords

Mathematics Subject Classification

Search

Navigation