Startseite Mathematik Novel weighted distribution: Properties, applications and web-tool
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Novel weighted distribution: Properties, applications and web-tool

  • Emrah Altun EMAIL logo und Christophe Chesneau
Veröffentlicht/Copyright: 12. Dezember 2025
Veröffentlichen auch Sie bei De Gruyter Brill
Informationen für Autor*innen Erkunden Sie dieses Fachgebiet
Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 75 Heft 6

Abstract

Weighted distributions play an important role in reliability and engineering. This research contributes to the topic by presenting a novel flexible two-parameter weighted distribution characterized by extensive statistical properties. Various parameter estimation methods are also thoroughly investigated. Their effectiveness is validated by complete simulation studies. Within the framework of generalized linear models, a regression model is established for positively defined response variables. Two data sets are examined to emphasize the importance of the proposed model. In addition, the WBreg tool is presented to facilitate its use by researchers. WBreg is available “free of charge” at https://beststat.shinyapps.io/WB2reg.

Keywords: Weighted distributions; different estimation methods; simulation; regression; software
MSC 2010: Primary 62E15

  1. (Communicated by Gejza Wimmer)

References

[1] Abd-Elrahman, A. M.: Utilizing ordered statistics in lifetime distributions production: a new lifetime distribution and applications, J. Probab. Stat. Sci. 11 (2013), 153–164.Suche in Google Scholar

[2] Abd-Elrahman, A. M.: A new two-parameter lifetime distribution with decreasing, increasing or upside-down bathtub-shaped failure rate, Comm. Statist. Theory Methods 46 (2017), 8865–8880.10.1080/03610926.2016.1193198Suche in Google Scholar

[3] Ahmad, A.—Ahmad, S. P.—Ahmed, A.: Length-biased weighted Lomax distribution: statistical properties and application, Pak. J. Stat. Oper. Res. XII (2016), 245–255.10.18187/pjsor.v12i2.1178Suche in Google Scholar

[4] Aldeni, M.—Lee, C.—Famoye, F.: Families of distributions arising from the quantile of generalized lambda distribution, J. Stat. Distrib. Appl. 4 (2017), 1–18.10.1186/s40488-017-0081-4Suche in Google Scholar

[5] Al-Omari, A. I.—Alsultan, R.—Alomani, G.: Asymmetric right-skewed size-biased Bilal distribution with mathematical properties, reliability analysis, inference and applications, Symmetry 15 (2023), Art. No. 1578.10.3390/sym15081578Suche in Google Scholar

[6] Altun, E.: A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models, Math. Slovaca 70 (2020), 979–994.10.1515/ms-2017-0407Suche in Google Scholar

[7] Altun, E.—El-Morshedy, M.—Eliwa, M. S.: A new regression model for bounded response variable: An alternative to the beta and unit-Lindley regression models, Plos One 16 (2021), 1–15.10.1371/journal.pone.0245627Suche in Google Scholar PubMed PubMed Central

[8] Altun, E.—El-Morshedy, M.—Eliwa, M. S.: A study on discrete Bilal distribution with properties and applications on integer valued autoregressive process, REVSTAT 20 (2022), 501–528.Suche in Google Scholar

[9] Canty, A.—Ripley, B.: boot: Bootstrap R (S-Plus) Functions. R package version 1.3-31, https://CRAN.R-project.org/package=boot 2024.Suche in Google Scholar

[10] Chang, W.—Ribeiro, B. B.: shinydashboard: Create Dashboards with ’Shiny’. R package version 0.7.2, https://CRAN.R-project.org/package=shinydashboard 2021.Suche in Google Scholar

[11] Cox, D. R.—Snell, E. J.: A general definition of residuals, J. R. Stat. Soc. Ser. B. Stat. Methodol. Series B (Methodological) (1968), 248–275.10.1111/j.2517-6161.1968.tb00724.xSuche in Google Scholar

[12] Dey, S.—Dey, T.—Anis, M. Z.: Weighted Weibull distribution: properties and estimation, J. Stat. Theory Pract. 9 (2015), 250–265.10.1080/15598608.2013.875966Suche in Google Scholar

[13] Dunn, P. K.—Smyth, G. K.: Randomized quantile residuals, J. Comput. Graph. Statist. 5 (1996), 236–244.10.1080/10618600.1996.10474708Suche in Google Scholar

[14] Evert, S.—Baroni, M.: zipfR: Word frequency distributions in R. In: Proceedings of the 45th Annual Meeting of the Association for Computational Linguistics, Posters and Demonstrations Sessions, 2007, 29–32, Prague, Czech Republic.10.3115/1557769.1557780Suche in Google Scholar

[15] Ghitany, M. E.—Alqallaf, F.—Al-Mutairi, D. K.—Husain, H. A.: A two-parameter weighted Lindley distribution and its applications to survival data, Math. Comput. Simul. 81 (2011), 1190–1201.10.1016/j.matcom.2010.11.005Suche in Google Scholar

[16] Gupta, R. D.—Kundu, D.: Theory & methods: Generalized exponential distributions, Aust. N. Z. J. Stat. 41 (1999), 173–188.10.1111/1467-842X.00072Suche in Google Scholar

[17] Gupta, R. C.—Kirmani, S. N. U. A..: The role of weighted distributions in stochastic modeling, Comm. Statist. Theory Methods 19 (1990), 3147–3162.10.1080/03610929008830371Suche in Google Scholar

[18] Jain, K.—Singla, N.—Gupta, R.: A weighted version of gamma distribution, Discuss. Math. Probab. Stat. 34 (2014), 89–111.10.7151/dmps.1166Suche in Google Scholar

[19] Lele, S. R.—Keim, J. L.: Weighted distributions and estimation of resource selection probability functions, Ecology 87 (2006), 3021–3028.10.1890/0012-9658(2006)87[3021:WDAEOR]2.0.CO;2Suche in Google Scholar

[20] Patil, G. P.—Rao, C. R.: Weighted distributions and size-biased sampling with applications to wildlife populations and human families, Biometrics (1978), 179–189.10.2307/2530008Suche in Google Scholar

[21] R Core Team: R: A Language and Environment for Statistical Computing, Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.Suche in Google Scholar

[22] Riad, F. H.—Alruwaili, B.—Gemeay, A. M.—Hussam, E.: Statistical modeling for COVID-19 virus spread in Kingdom of Saudi Arabia and Netherlands, Alex. Eng. J. 61 (2022), 9849–9866.10.1016/j.aej.2022.03.015Suche in Google Scholar

[23] Sen, S.—Chandra, N.—Maiti, S. S.: The weighted xgamma distribution: properties and application, J. Reliab. Stat. Stud. 10 (2017), 43–58.Suche in Google Scholar

[24] Wickham, H.—Bryan, J.: readxl: Read Excel Files. R package version 1.4.3, https://CRAN.R-project.org/package=readxl.Suche in Google Scholar

[25] Xie, Y.—Cheng, J.—Tan, X.: DT: A Wrapper of the JavaScript Library ’DataTables’. R package version 0.33; https://CRAN.R-project.org/package=DT.Suche in Google Scholar

Appendix

Proof of Proposition 1. Based on the mixture representation in (2.8), we have

EXr=∫0∞xr6αθ−αxα−1exp−2xθ3α−2αΓα−6αθ−αxα−1exp−3xθ3α−2αΓαdx=∫0∞xr6αθ−αxα−1exp−2xθ3α−2αΓαdx−∫0∞xr6αθ−αxα−1exp−3xθ3α−2αΓαdx=6αθ−α3α−2αΓα∫0∞xr+α−1exp−2xθdx−6αθ−α3α−2αΓα∫0∞xr+α−1exp−3xθdx=6αθ−α3α−2αΓαΓα+rθ2α+r−6αθ−α3α−2αΓαΓα+rθ3α+r=θrΓα+r2α+r−3α+r6rΓα2α−3α.

This concludes the proof. □

Proof of Proposition 2. The moment generating function of the WB distribution is defined by M (t) = E (exp (tX)), where X is a random variable with the WB distribution. Based on this classical definition, we have

Mt=∫0∞exptx6αθ−αxα−1exp−2xθ3α−2αΓα−6αθ−αxα−1exp−3xθ3α−2αΓαdx=∫0∞exptx6αθ−αxα−1exp−2xθ3α−2αΓαdx−∫0∞exptx6αθ−αxα−1exp−3xθ3α−2αΓαdx=6αθ−α3α−2αΓα∫0∞xα−1exptx−2xθdx−6αθ−α3α−2αΓα∫0∞xα−1exptx−3xθdx=6αθ−α3α−2αΓαθαΓα2−tθα−6αθ−α3α−2αΓαθαΓα3−tθα=6α3α−2α12−tθα−6α3α−2α12−tθα=6α3α−2α121−tθ2α−6α3α−2α131−tθ2α=3α3α−2α11−tθ2α−2α3α−2α11−tθ3α=3α3α−2α1−tθ2−α−2α3α−2α1−tθ3−α.

This end the proof. □

Proof of Proposition 3. Using the following expression: φ (t) = M (it) and Proposition 2, we conclude directly. □

Proof of Proposition 4. The proof can be easily done using the mixture representation of the WB distribution. □
Received: 2025-01-27
Accepted: 2025-08-14
Published Online: 2025-12-12
Published in Print: 2025-12-17

© 2025 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  1. A new categorical equivalence for stone algebras
  2. On special classes of prime filters in BL-algebras
  3. A note on characterized and statistically characterized subgroups of 𝕋 = ℝ/ℤ
  4. New Young-type integral inequalities using composition schemes
  5. The structure of pseudo-n-uninorms with continuous underlying functions
  6. Jensen-type inequalities for a second-order differential inequality condition
  7. A direct proof of the characterization of the convexity of the discrete Choquet integral
  8. Envelope of plurifinely plurisubharmonic functions and complex Monge-Ampère type equation
  9. Fekete-Szegö inequalities for Φ-parametric and β-spirllike mappings of complex order in ℂn
  10. Entire function sharing two values partially with its derivative and a conjecture of Li and Yang
  11. Oscillatory properties of third-order semi-canonical dynamic equations on time scales via canonical transformation
  12. Weighted B-summability and positive linear operators
  13. Some properties and applications of convolution algebras
  14. On measures of σ-noncompactess in F-spaces
  15. On the kolmogorov–feller–gut weak law of large numbers for triangular arrays of rowwise and pairwise negatively dependent random variables
  16. Intermediately trimmed sums of oppenheim expansions: A strong law
  17. Novel weighted distribution: Properties, applications and web-tool
  18. On the q-Gamma distribution: Properties and inference
  19. Finiteorthoatomistic effect algebras and regular algebraic E-test spaces
  20. Prof. RNDr. Anatolij Dvurečenskij, DrSc. 75th anniversary
https://doi.org/10.1515/ms-2025-0110
Schlagwörter für diesen Artikel
Weighted distributions; different estimation methods; simulation; regression; software

Artikel in diesem Heft

  1. A new categorical equivalence for stone algebras
  2. On special classes of prime filters in BL-algebras
  3. A note on characterized and statistically characterized subgroups of 𝕋 = ℝ/ℤ
  4. New Young-type integral inequalities using composition schemes
  5. The structure of pseudo-n-uninorms with continuous underlying functions
  6. Jensen-type inequalities for a second-order differential inequality condition
  7. A direct proof of the characterization of the convexity of the discrete Choquet integral
  8. Envelope of plurifinely plurisubharmonic functions and complex Monge-Ampère type equation
  9. Fekete-Szegö inequalities for Φ-parametric and β-spirllike mappings of complex order in ℂn
  10. Entire function sharing two values partially with its derivative and a conjecture of Li and Yang
  11. Oscillatory properties of third-order semi-canonical dynamic equations on time scales via canonical transformation
  12. Weighted B-summability and positive linear operators
  13. Some properties and applications of convolution algebras
  14. On measures of σ-noncompactess in F-spaces
  15. On the kolmogorov–feller–gut weak law of large numbers for triangular arrays of rowwise and pairwise negatively dependent random variables
  16. Intermediately trimmed sums of oppenheim expansions: A strong law
  17. Novel weighted distribution: Properties, applications and web-tool
  18. On the q-Gamma distribution: Properties and inference
  19. Finiteorthoatomistic effect algebras and regular algebraic E-test spaces
  20. Prof. RNDr. Anatolij Dvurečenskij, DrSc. 75th anniversary
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2025 De Gruyter Brill
Heruntergeladen am 16.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2025-0110/pdf?lang=de
Button zum nach oben scrollen