Generalized Odd Power Cauchy Family and Its Associated Heteroscedastic Regression Model

  • Emrah Altun EA Bartin University
  • Morad Alizadeh Persian Gulf university
  • Thiago Ramires Federal University of Technology
  • Edwin Ortega University of São Paulo
DOI: https://doi.org/10.19139/soic-2310-5070-765
Keywords: Generated family; Heteroscedastic regression model; Maximum likelihood; Moment; Power Cauchy.

Abstract

This study introduces a generalization of the odd power Cauchy family by adding one more shape parameter togain more flexibility modeling the complex data structures. The linear representations for the density, moments, quantile,and generating functions are derived. The model parameters are estimated employing the maximum likelihood estimationmethod. The Monte Carlo simulations are performed under different parameter settings and sample sizes for the proposedmodels. In addition, we introduce a new heteroscedastic regression model based on the special member of the proposedfamily. Three data sets are analyzed with competitive and proposed models.

References

Alizadeh, M., Altun, E., Cordeiro, G. M. and Rasekhi, M. (2018). The odd power cauchy family of distributions: properties, regression models and applications. Journal of statistical computation and simulation, 88, 785-807.

Bowley, A. L. (1901). Elements of Statistics, P.S. King & Son, Laondon.

Chen, G. and Balakrishnan, N. (1995). A general purpose approximate goodness-of-fit test. Journal of Quality Technology, 27, 154-161.

Cordeiro, G. M., Alizadeh, M. and Ortega, E. M. (2014). The exponentiated half-logistic family of distributions: Properties and applications. Journal of Probability and Statistics, 2014, 1-21.

Cordeiro, G. M., Ortega, E. M. and da Cunha, D. C. (2013). The exponentiated generalized class of distributions. Journal of Data Science, 11, 1-27.

Cordeiro, G. M., Alizadeh, M., Ramires, T. G. and Ortega, E. M. (2017a). The Generalized Odd Half-Cauchy Family of Distributions: Properties and Applications. Communications in Statistics-Theory and Methods, 46, 5685-5705.

Cordeiro, G. M., Ramires, T. G., Ortega, E. M. and Alizadeh, M. (2017b). The new family of distributions and applications in heteroscedastic regression analysis. Journal of Statistical Theory and Applications, 16, 401-418.

Cordeiro, G. M. and Nadarajah, S. (2011). Closed-form expressions for moments of a class of beta generalized distributions. Brazilian Journal of Probability and Statistics, 25, 14-33.

Dunn P.K and Smyth G.K. (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics, 5, 236–244.

Eugene, N., Lee, C. and Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics-Theory and Methods, 31, 497-512.

Gleaton, J.U. and Lynch, J.D. (2006) Properties of generalized log-logistic families of lifetime distributions, Journal of Probability and Statistical Science, 4, 51–64.

Lawless, J. F. (2003). Statistical models and methods for lifetime data (Vol. 362). John Wiley and Sons

Liu, X. (2014). Survival models on unobserved heterogeneity and their applications in analyzing large-scale survey data. Journal of Biometrics and Biostatistics, 5, 1-23.

Moors, J. J. A. (1986). The meaning of kurtosis: Darlington reexamined. The American Statistician, 40, 283-284.

Mudholkar, G.S., Srivastava, D.K. and Freimer, M. (1995). The exponentiated Weibull family: a reanalysis of the bus-motor-failure data. Technometrics, 37, 436–445.

Nadarajah, S. (2008). A truncated inverted beta distribution with application to air pollution data. Stochastic Environmental Research and Risk Assessment, 22, 285-289.

Nadarajah, S. and Kotz, S. (2006). The exponentiated type distributions. Acta Applicandae Mathematicae, 92, 97–111.

Ortega, E.M.M., Lemonte, A.J., Cordeiro, G.M., Cancho, and Mialhe, F.L. (2017). Heteroscedastic log-exponentiated Weibull regression model. Journal of Applied Statistics, 45, 384–408.

Rooks, B., Schumacher, A. and Cooray, K. (2010). The power Cauchy distribution: derivation, description, and composite models, NSF-REU Program Reports. Available from http://www.cst.cmich.edumathematics/research/REU_and_LURE. shtml

Published
2021-07-10
How to Cite
EA, E. A., Alizadeh, M., Ramires, T., & Ortega, E. (2021). Generalized Odd Power Cauchy Family and Its Associated Heteroscedastic Regression Model. Statistics, Optimization & Information Computing, 9(3), 516-528. https://doi.org/10.19139/soic-2310-5070-765
Issue
Vol 9 No 3 (2021)
Section
Research Articles
Authors who publish with this journal agree to the following terms:

    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
    2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
    3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).