SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2022 / Cilt: 51 - Sayı: 3

Testing distributional assumption of unit-Lindley regression model

Deniz ÖZONUR
Pages
882–899
Publication Date
2022-06-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Model selection criteria and residual analysis prove that the unit-Lindley regression model provides a better fit than the Beta and simplex regression models for the real data set.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper proposes smooth goodness of fit test statistic and its components to test the distributional assumption of the unit-Lindley regression model, which is useful for describing data measured between zero and one.
📊
Key Findings & Data:Empirical findings demonstrate that the first smooth component, deviance, and chi-square tests have undesirable behavior for the unit-Lindley regression model.
💡
Conclusion & Impact:Model selection criteria and residual analysis prove that the unit-Lindley regression model provides a better fit than the Beta and simplex regression models for the real data set.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Chi-square test · deviance test · power of test

Abstract

This paper proposes smooth goodness of fit test statistic and its components to test the distributional assumption of the unit-Lindley regression model, which is useful for describing data measured between zero and one. Orthonormal polynomials on the unit-Lindley distribution, score functions and Fisher's information matrix are provided for the smooth test. Deviance and Pearson's chi-square tests are also adapted to the unit-Lindley regression model. A parametric bootstrap simulation study is conducted to compare type I errors and powers of the tests under different scenarios. Empirical findings demonstrate that the first smooth component, deviance, and chi-square tests have undesirable behavior for the unit-Lindley regression model. A real data set is analyzed by using the developed tests to show the adequacy of the unit-Lindley regression model. Model selection criteria and residual analysis prove that the unit-Lindley regression model provides a better fit than the Beta and simplex regression models for the real data set.

🔖

Cite This Article

ÖZONUR, D. (2022). Testing distributional assumption of unit-Lindley regression model. Hacettepe Journal of Mathematics and Statistics, Cilt: 51 - Sayı: 3, 882–899. https://ajindex.com/articles/669207

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (17)

  1. H. Akaike, A new look at the statistical model identification, IEEE Trans. Automat. Contr. 19 (6), 716-723, 1974
  2. E. Altun, The log-weighted exponential regression model: alternative to the beta regression model, Comm. Statist. Theory Methods 50 (10), 2306-2321, 2021
  3. E. Altun and G.M. Cordeiro, The unit-improved second-degree Lindley distribution: inference and regression modeling, Comput. Statist. 35 (1), 259-279, 2020
  4. E. Altun, M. El-Morshedy and M.S. Eliwa, A new regression model for bounded response variable: an alternative to the beta and unit-Lindley regression models, PloS one 16 (1), e0245627, 2021
  5. H.S. Bakouch, B.M. Al-Zahrani, A.A. Al-Shomrani, V.A. Marchi and F. Louzada, An extended Lindley distribution, J. Korean Statist. Soc. 41 (1), 75-85, 2012
  6. W. Barreto-Souza and H.S. Bakouch, A new lifetime model with decreasing failure rate, Stats. 47 (2), 465-476, 2013
  7. D.J. Best and J.C.W. Rayner, Smooth tests of fit for the Lindley distribution, Stats 1 (1), 92-97, 2018
  8. J.M. Carrasco and N. Reid, Simplex regression models with measurement error, Comm. Statist. Simulation Comput. 50 (11), 3420-3435, 2021
  9. D.R. Cox and E.J. Snell, A general definition of residuals, J. R. Stat. Soc. Ser. B. Stat. Methodol. 30 (2), 248-275, 1968
  10. B. De Boeck, O. Thas, J.C.W. Rayner and D.J. Best, Smooth tests for the gamma distribution, J. Stat. Comput. Simul. 81 (7), 843-855, 2011
  11. R.S. Defries, M.C. Hansen, J.R. Townshend, A.C. Janetos and T.R. Loveland, A new global 1km dataset of percentage tree cover derived from remote sensing, Glob. Change Biol. 6 (2), 247-254, 2000
  12. A.J. Dobson and A.G. Barnett, An Introduction to Generalized Linear Models, Chapman and Hall/CRC, 2008
  13. P.K. Dunn and G.K. Smyth, Randomized quantile residuals, J. Comput. Graph. Statist. 5 (3), 236-244, 1996
  14. S. Ferrari and F. Cribari-Neto, Beta regression for modelling rates and proportions, J. Appl. Stat. 31 (7), 799-815, 2004
  15. M.E. Ghitany, D.K. Al-Mutairi, N. Balakrishnan and L.J. Al-Enezi, Power Lindley distribution and associated inference, Comput. Statist. Data Anal. 64, 20-33, 2013
  16. M.E. Ghitany, J. Mazucheli, A.F.B. Menezes and F. Alqallaf, The unit-inverse Gaussian distribution: a new alternative to two-parameter distributions on the unit interval, Comm. Statist. Theory Methods 48 (14), 3423-3438, 2019
  17. E.J. Hannan and B.G. Quinn, The determination of the order of an autoregression, J. R. Stat. Soc. Ser. B. Stat.