Main Article Content
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.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- 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.
- 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.
- 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).
- Ahmad, M., Sinclair, C., and Werritty, A. (1988). Log-logistic ﬂood frequency analysis. Journal of Hydrology, 98(3):205 – 224.
- 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.
- 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.
- Cakmakyapan, S. and Ozel, G. (2017). The Lindley family of distributions: Properties and applications. Hacettepe Journal of Mathematics and Statistics, 46:1113–1137.
- Chen, G. and Balakrishnan, N. (1995). A general purpose approximate goodness-of-ﬁt test. Journal of Quality Technology, 27(2):154–161.
- Cordeiro, G. M. and Castro, M. (2011). A new family of generalized distibutions. Journal of Statistical Computation and Simulation, 81(7):883–898.
- 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.
- Drapella, A. (1993). The complementary Weibull distribution: unknown or just forgotten? Quality and Reliability Engineering International, 9(4):383–385.
- Huang, W. and Dong, S. (2019). Probability distribution of wave periods in combined sea states with ﬁnite mixture models. Applied Ocean Research, 92:101938.
- Kleiber, C. and Kotz, S. (2003). Statistical Size Distributions in Economics and Actuarial Sciences. John Wiley & Sons, Inc.
- Lemonte, A. J. (2014). The beta log-logistic distribution. Brazilian Journal of Probability and Statistics, 28(3):313–322.
- 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.
- 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.
- 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.
- R Core Team (2018). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
- 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.