Main Article Content

Abstract

This paper introduces a novel class of probability distributions called normal-tangent-G, whose submodels are parsi- monious and bring no additional parameters besides the baseline’s. We demonstrate that these submodels are iden- tifiable as long as the baseline is. We present some properties of the class, including the series representation of its probability density function (pdf) and two special cases. Monte Carlo simulations are carried out to study the behav- ior of the maximum likelihood estimates (MLEs) of the parameters for a particular submodel. We also perform an application of it to a real dataset to exemplify the modelling benefits of the class.

Keywords

Class of probabilistic distributions Identifiable Maximum likelihood Modelling Normal distribution

Article Details

How to Cite
Silveira, F., Gomes-Silva, F., Brito, C., Cunha-Filho, M., Jale, J., Gusmão, F., & Xavier-Júnior, S. (2020). The normal-tangent-G class of probabilistic distributions: properties and real data modelling. Pakistan Journal of Statistics and Operation Research, 16(4), 827-838. https://doi.org/10.18187/pjsor.v16i4.3443

References

  1. Ahmad, M., Sinclair, C., and Werritty, A. (1988). Log-logistic flood frequency analysis. Journal of Hydrology, 98(3):205 – 224.
  2. Alizadeh, M., Cordeiro, G. M., Pinho, L. G. B., and Ghosh, I. (2017). The Gompertz-G family of distributions. Journal of Statistical Theory and Practice, 11(1):179–207.
  3. Brito, C. R., Rego, L. C., Oliveira, W. R., and Gomes-Silva, F. (2019). Method for generating distributions and classes of probability distributions: the univariate case. Hacettepe Journal of Mathematics and Statistics, 48(3):897–930.
  4. Cakmakyapan, S. and Ozel, G. (2017). The Lindley family of distributions: Properties and applications. Hacettepe Journal of Mathematics and Statistics, 46:1113–1137.
  5. Chen, G. and Balakrishnan, N. (1995). A general purpose approximate goodness-of-fit test. Journal of Quality Technology, 27(2):154–161.
  6. Cordeiro, G. M. and Castro, M. (2011). A new family of generalized distibutions. Journal of Statistical Computation and Simulation, 81(7):883–898.
  7. De Gusmao, F. R. S., Ortega, E. M. M., and Cordeiro, G. M. (2011). The generalized inverse Weibull distribution Statistical Papers, 52(3):591–619.
  8. Drapella, A. (1993). The complementary Weibull distribution: unknown or just forgotten? Quality and Reliability Engineering International, 9(4):383–385.
  9. Huang, W. and Dong, S. (2019). Probability distribution of wave periods in combined sea states with finite mixture models. Applied Ocean Research, 92:101938.
  10. Kleiber, C. and Kotz, S. (2003). Statistical Size Distributions in Economics and Actuarial Sciences. John Wiley & Sons, Inc.
  11. Lemonte, A. J. (2014). The beta log-logistic distribution. Brazilian Journal of Probability and Statistics, 28(3):313–322.
  12. Marinho, P. R. D., Cordeiro, G. M., Ramirez, F. P., Alizadeh, M., and Bourguignon, M. (2018). The exponen- tiated logarithmic generated family of distributions and the evaluation of the confidence intervals by percentile bootstrap. Brazilian Journal of Probability and Statistics, 32(2):281–308.
  13. Mudholkar, G. S. and Srivastava, D. K. (1993). Exponentiated Weibull family for analyzing bathtub failure- rate data. IEEE transactions on reliability, 42(2):299–302.
  14. Patrıcio, M., Pereira, J., Crisostomo, J., Matafome, P., Gomes, M., Seic¸a, R., and Caramelo, F. (2018). Using resistin, glucose, age and BMI to predict the presence of breast cancer. BMC cancer, 18(1):29.
  15. R Core Team (2018). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
  16. 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(1):65–82.