Main Article Content
In this paper, a new form of log-alpha-skew distribution is proposed by the same methodology of Venegas et al. (2016) and investigated some of its related distributions. The moments and distributional properties of the proposed distribution are also discussed. Also, the appropriateness of this distribution are checked by performing the data fitting experiment and comparing the values of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) with the values of some other known distributions. Likelihood ratio test is used for discriminating between normal and the proposed distributions.
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).
- Ahrens, L. (1953). A fundamental law of geochemistry. Nature. 172(4390), 1148.
- Ahrens, L. (1954a). The lognormal distribution of the elements.Geochimica et Cosmochimica acta 5, 49-73.
- Ahrens, L. (1954b). The lognormal distribution of the elements. Geochimica et Cosmochimica acta 6, 121-131.
- Arnold, B. C., and Beaver, R. J. (2002). Skewed multivariate models related to hidden truncation and/or selective reporting. Test, 11(1), 7-54.
- Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics,12: 171-178.
- Azzalini, A, Dal Cappello T, and Kotz S. (2003). Log-skew-normal and log-skew-t distributions as models for family income data. Journal of Income Distribution, 11(3-4), 12-20.
- Balakrishnan, N. (2002). Discussion on “Skew multivariate models related to hidden truncation and/or selective reporting” by B. C. Arnold and R. J. Beaver. Test,11:37-39
- Elal-Olivero, D. (2010). Alpha-skew-normal distribution. Proyecciones (Antofagasta), 29(3), 224-240.
- Hazarika, P. J., Shah, S., and Chakraborty, S. (2019). Balakrishnan Alpha Skew Normal Distribution: Properties and Applications. arXiv:1906.07424 [math.ST].
- Huang, W. J., and Chen, Y. H. (2007). Generalized skew-Cauchy distribution. Statistics and Probability Letters, 77(11), 1137-1147.
- Mateu-Figueras, G., Pawlosky-Glanh, and Barcelo-Vidal, C. (2004). The natural law in geochemistry: Lognormal or log skew-normal?, “32th International Geological Congress”, International Union of Soil Sciences, Florence, Italy, 1849-1858.
- Venegas, O., Bolfarine, H., Gallardo, D. I., Vergara-Fernández, A., and Gómez, H. W. (2016). A Note on the Log-Alpha-Skew-Normal Model with Geochemical Applications. Appl. Math, 10(5), 1697-1703.
- Vistelius, A. B. (1960). The skew frequency distributions and the fundamental law of the geochemical processes. The Journalof Geology, 68 (1), 1-22.