[Home ] [Archive]   [ فارسی ]  
:: Main :: About :: Current Issue :: Archive :: Search :: Submit :: Contact ::
Main Menu
Home::
Journal Information::
Articles archive::
For Authors::
For Reviewers::
Registration::
Ethics Considerations::
Contact us::
Site Facilities::
::
Search in website

Advanced Search
..
Receive site information
Enter your Email in the following box to receive the site news and information.
..
Indexing and Abstracting



 
..
Social Media

..
Licenses
Creative Commons License
This Journal is licensed under a Creative Commons Attribution NonCommercial 4.0
International License
(CC BY-NC 4.0).
 
..
Similarity Check Systems


..
:: ::
Back to the articles list Back to browse issues page
On Properties of a New Generalization of the Log-Logistic Distribution and Its Application
Mohammad Shafaei Noughabi * , Mohammad Khorashadizade
Abstract:   (471 Views)
This article introduces a new extension of the log-logistic distribution, and its properties and parameter estimation are studied and analyzed. It is shown that adding a parameter to this distribution makes its shape more symmetric and less skewed as the parameter increases. Unlike the original distribution, the moments of the new distribution and its quantile function always exist. Furthermore, it is demonstrated that the reliability measures, such as the hazard rate function, the mean residual life function, and stochastic orderings, are more flexible in the new distribution. Additionally, the parameters of the distribution are estimated using the LLP and ML methods, and the efficiency and consistency of the estimators are evaluated through simulation studies. Finally, the practical applicability of the model is demonstrated by applying the new model to real-world data from airborne equipment and lung cancer patients.
Keywords: Reliability engineering, Log-logistic model, Log-logistic plot, Lifetime data.
Full-Text [PDF 1379 kb]   (246 Downloads)    
Type of Study: Research | Subject: General
Received: 2024/12/16 | Accepted: 2024/08/31
References
1. ‎Ahmad‎, ‎M.I.‎, ‎Sinclair‎, ‎C.D‎. ‎and Werritty‎, ‎A‎. ‎(1988)‎, ‎Log-Logistic ‎F‎lood Frequency Analysis‎, ‎Journal of Hydrology‎, ‎98‎, ‎205-224‎. [DOI:10.1016/0022-1694(88)90015-7]
2. ‎Alfaer N.M.‎, ‎Gemeay‎, ‎A.M.‎, ‎Aljohani‎, ‎H.M. ‎and‎ ‎Afify‎, ‎A.Z‎. ‎(2021)‎, ‎The Extended Log-Logistic Distribution‎: ‎Inference and Actuarial Applications‎, ‎Mathematics‎, ‎9‎, ‎1-22‎. [DOI:10.3390/math9121386]
3. ‎Alven‎, ‎W.H.‎, ‎(1964)‎, ‎Reliability Engineering‎, ‎ARINC‎. ‎Prentice-hall‎, ‎New Jersey‎.
4. ‎Arber‎, ‎Q‎. ‎and Muça‎, ‎M‎. ‎(2018)‎, ‎A New Modified Generalized Odd Log-Logistic Distribution with Three Parameters‎, ‎Mathematical Theory and Modeling‎, ‎ 8‎, ‎49-60‎.
5. ‎Bennett‎, ‎S‎. ‎(1983)‎, ‎Log-Logistic Regression Models for Survival Data‎, ‎Journal of the Royal Statistical Society‎, ‎Series C‎, ‎32 (2)‎, ‎165-171‎. [DOI:10.2307/2347295]
6. ‎‎Burr‎, ‎I‎. ‎W‎. ‎(1942)‎, ‎Cumulative Frequency Functions‎, ‎Annals of Mathematical Statistics‎, ‎13‎, ‎215-232‎. ‎ [DOI:10.1214/aoms/1177731607]
7. ‎Cordeiro‎, ‎G.M.‎, ‎Alizadeh‎, ‎M.‎, ‎Ozel‎, ‎G.‎, ‎Hosseini‎, ‎B.‎, ‎Ortega‎, ‎E.M.M‎. ‎and Altun‎, ‎E‎. ‎(2017)‎, ‎The Generalized Odd Log-Logistic Family of Distributions‎: ‎Properties‎, ‎Regression Models and Applications‎, ‎Journal of Statistical Computation and Simulation‎, ‎87‎, ‎908-932‎. [DOI:10.1080/00949655.2016.1238088]
8. ‎Esfahani M.‎, ‎Amini M‎. and ‎Mohtashami Borzadaran G.R‎. ‎(2021)‎, ‎On the Applications of Total Time on Test Transform in Reliability‎, ‎ Journal of Statistical Sciences‎, ‎15 (1)‎, ‎1-22‎.
9. ‎Fisk‎, ‎P.R‎. ‎(1961)‎, ‎The Graduation of Income Distributions‎, ‎ Econometrica‎, ‎29‎, ‎171-185‎. [DOI:10.2307/1909287]
10. ‎Gago-Benítez‎, ‎A.‎, ‎Fernández-Madrigal‎, ‎J.A. ‎and‎ ‎Cruz-Martín‎, ‎A‎. ‎(2013)‎, ‎Log-logistic Modeling of Sensory Flow Delays in Networked Telerobots‎,‎IEEE Sensors Journal‎, ‎IEEE Sensors, 13‎, ‎2944-2953‎. [DOI:10.1109/JSEN.2013.2263381]
11. ‎Gupta‎, ‎R‎. ‎C.‎, ‎Akman‎, ‎H‎. ‎O and Lvin‎, ‎S‎. ‎(1999)‎, ‎A Study of Log-Logistic Model in Survival Analysis‎, ‎ Biometrical Journal‎, ‎41(4)‎, ‎431-443‎. https://doi.org/10.1002/(SICI)1521-4036(199907)41:4<431::AID-BIMJ431>3.0.CO;2-U [DOI:10.1002/(SICI)1521-4036(199907)41:43.0.CO;2-U]
12. ‎Haghbin‎, ‎H.‎, ‎Ozel‎, ‎G.‎, ‎Alizadeh‎, ‎M‎. ‎and Hamedani‎, ‎G.G‎. ‎(2017)‎, ‎A New Generalized Odd Log-Logistic Family of Distributions‎, ‎Communications in Statistics‎ - ‎Theory and Methods‎, ‎46‎, ‎9897-9920‎. [DOI:10.1080/03610926.2016.1222428]
13. ‎Kayid‎, ‎M‎. ‎(2022)‎, ‎Applications of Bladder Cancer Data Using a Modified Log-Logistic Model‎. ‎ Applied Bionics and Biomechanics‎, ‎‎ ‎2022‎, ‎Article ID 6600278‎, ‎12‎. [DOI:10.1155/2022/6600278] [PMID] []
14. ‎Khan‎, ‎S‎. ‎and Khosa‎, ‎S‎. ‎(2016)‎. ‎Generalized Log-Logistic Proportional Hazard Model with Applications in Survival Analysis‎, ‎Journal of Statistical Distributions and Applications‎, ‎3‎, ‎1-18‎. ‎ [DOI:10.1186/s40488-016-0054-z]
15. ‎Lima‎, ‎S.R‎. ‎and Cordeiro‎, ‎G.M‎. ‎(2017)‎, ‎The Extended Log-Logistic Distribution‎: ‎Properties and Application‎, ‎Anais da Academia Brasileira de Ciências‎, ‎89‎, ‎3-17‎. [DOI:10.1590/0001-3765201720150579] [PMID]
16. ‎Malik‎, ‎A.S‎. ‎and Ahmad‎, ‎S‎. ‎(2020)‎, ‎An Extension of Log-Logistic Distribution for Analyzing Survival Data‎, ‎Pakistan Journal of Statistics and Operation Research‎, ‎16‎, ‎789-801‎. [DOI:10.18187/pjsor.v16i4.2961]
17. ‎Marshall‎, ‎A‎. ‎W.‎, ‎and Olkin‎, ‎I‎. ‎(1997)‎, ‎A New Method for Adding a Parameter to a Family of Distributions with Application to the Exponential and Weibull Families‎, ‎Biometrika‎, ‎84‎, ‎3‎, ‎641-52‎. [DOI:10.1093/biomet/84.3.641]
18. ‎Mead‎, ‎M.‎, ‎Nassar‎, ‎M‎. ‎M.‎, ‎and Dey‎, ‎S‎. ‎(2018‎), ‎A Generalization of Generalized Gamma Distributions‎, ‎Pakistan Journal of Statistics and Operation Research‎, ‎14‎, ‎121-138‎. [DOI:10.18187/pjsor.v14i1.1692]
19. ‎Mielke‎, ‎P‎. ‎W.‎, ‎and Johnson‎, ‎E‎. ‎S‎. ‎(1973)‎, ‎Three-Parameter Kappa Distribution Maximum Likelihood Estimates and Likelihood Ratio Tests‎, ‎Monthly Weather Review‎, ‎101(9)‎, ‎701-707‎. https://doi.org/10.1175/1520-0493(1973)101<0701:TKDMLE>2.3.CO;2 [DOI:10.1175/1520-0493(1973)1012.3.CO;2]
20. ‎Muse‎, ‎A.H.‎, ‎Mwalili‎, ‎S.M. ‎and ‎‎Ngesa‎, ‎O‎. ‎(2021)‎, ‎On the Log-Logistic Distribution and Its Generalizations‎: ‎A Survey‎, ‎International Journal of Statistics and Probability‎, ‎10‎, ‎93-125‎. [DOI:10.5539/ijsp.v10n3p93]
21. ‎Ojo‎, ‎M.O‎. ‎and Olapade‎, ‎A.K‎. ‎(2003)‎, ‎On the Generalized Logistic and Log-Logistic Distributions‎, ‎Kragujevac Journal of Mathematics‎, ‎25‎, ‎65-73‎.
22. ‎Prentice‎, ‎R‎. ‎L‎. ‎(1973)‎, ‎Exponential Survivals with Censoring and Explanatory Variables‎, ‎Biometrika‎, ‎60‎, ‎279-288‎. [DOI:10.1093/biomet/60.2.279]
23. ‎Schmittlein D.C‎. ‎and Morrison‎, ‎D.G‎. ‎(1981)‎, ‎The Median Residual Lifetime‎: ‎A Characterization Theorem and an Application‎, ‎ Operations Research‎, ‎ 29‎, ‎392-399‎. [DOI:10.1287/opre.29.2.392]
24. ‎Shakhatreh‎, ‎M.K‎. ‎(2018)‎, ‎A New Three-Parameter Extension of the Log-Logistic Distribution with Applications to Survival Data‎, ‎ Communications in Statistics‎ - ‎Theory and Methods‎, ‎47‎, ‎5205-5226‎. [DOI:10.1080/03610926.2017.1388399]
25. ‎Singh‎, ‎K.P.‎, ‎Lee‎, ‎C.M.-S‎. ‎and George‎, ‎E.O‎. ‎(1988)‎, ‎On Generalized Log-Logistic Model for Censored Survival Data‎, ‎Biometrical Journal‎, ‎30‎, ‎843-850‎. [DOI:10.1002/bimj.4710300714]
26. ‎Tahir‎, ‎M.H.‎, ‎Mansoor‎, ‎M.‎, ‎Zubair‎, ‎M‎. ‎and Hamedani‎, ‎G.G‎. ‎(2014)‎, ‎McDonald Log-Logistic Distribution with an Application to Breast Cancer Data‎, ‎Journal of Statistical Theory and Applications‎, ‎13‎, ‎65-82‎. [DOI:10.2991/jsta.2014.13.1.6]
Send email to the article author

Add your comments about this article
Your username or Email:

CAPTCHA



XML   Persian Abstract   Print



Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Back to the articles list Back to browse issues page
مجله علوم آماری – نشریه علمی پژوهشی انجمن آمار ایران Journal of Statistical Sciences

Persian site map - English site map - Created in 0.06 seconds with 45 queries by YEKTAWEB 4710