Abstract
This work demonstrates the attractivity of the alpha-skew hyperbolic secant distribution, a new skewed distribution based on the alpha-skew technique and the hyperbolic secant distribution. In the first part, we determine its main features, including its cumulative distribution function, modality, non-central moments, skewness, kurtosis, moment generating function and characteristic function. The remaining part is devoted to the model applicability in a statistical context. As a first step, the parameters are estimated by maximum likelihood estimates. Then, we perform a data fitting experiment and compare the values of the Akaike and Bayesian information criteriawith those of some other similar distributions. By considering an astronomical dataset and valuable competitors also based on the alpha-skew technique, the alpha-skew hyperbolic secant distribution turns out to be the best.
Keywords
Skewed distribution Hyperbolic secant distribution Bimodality Parametric estimation Data analysis
References
- Asgharzadeh, A., Esmaeili, L. and Nadarajah, S. (2016), Balakrishnan skew logistic distribution, Communication in Statistics- Theory and Methods, 45(2), 444-464.
- Azzalini, A. A. (1985), Class of distributions which includes the normal ones, Scandinavian Journal of Statistics, 12, 171-178.
- Azzalini, A. and Capitanio, A. (2014), The Skew-Normal and related families, IMS monographs, Cambridge University Press, Cambridge, UK.
- Bakouch, H. S., Salinas, H. S., Mamode Khan, N. and Chesneau, C. (2021), A new family of skewed distributions with application to some daily closing prices, Computational and Mathematical Methods, 3(4), e1154.
- Baten, W.D. (1934), The probability law for the sum of n independent variables, each subject to the law, Bulletin of the American MathematicalSociety, 40, 284-290.
- Casella, G. and Berger, R. L. (1990), Statistical inference, Brooks/Cole Publishing Company, California.
- Chesneau, C., Okorie, I. E. and Bakouch, H. S. (2020), A skewed Nadarajah-Haghighi distribution with some applications, Journal of the Indian Society for Probability and Statistics, 21, 225-245.
- Elal-Olivero, D. (2010), Alpha-skew-normal distribution, Proyecciones (Antofagasta), 29 224-240.
- Fischer, M. J. (2013), Generalized Hyperbolic Secant distributions: With applications to Finance, Springer, Berlin, Germany.
- Gómez, H. S., Salinas, H. S. and Bolfarine, H. (2006), Generalized skew-normal models: properties and inference, Statistics, 40(6), 495-505.
- Harandi, S. S. and Alamatsaz, M. H. (2013), Alpha-skew-Laplace distribution, Statistics and Probability Letters, 83(3), 774-782.
- Hazarika, P. and Chakraborty, S. (2014), Alpha-skew-logistic distribution, IOSR Journal of Mathematics, 10(4), 36-46.
- Kim, H.-J. (2005), On a class of two-piece skew-normal distributions, Statistics, 39(6), 537-553.
- R Core Team (2005), R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria.
- Roeder, K. (1990), Density estimation with confidence sets exemplified by superclusters and voids in galaxies, Journal of the American Statistical Association, 85, 617-624.
- Talacko, J. (1956), Perks' distributions and their role in the theory of Wiener's stochastic variables, Trabajos de Estadistica, 7, 159-174.
Abstract
Bu çalışma, alfa-çarpık tekniğine ve hiperbolik sekant dağılımına dayanan yeni bir çarpık dağılım olan alfa-çarpık hiperbolik sekant dağılımının çekiciliğini göstermektedir. Birinci bölümde, kümülatif dağılım fonksiyonu, modalite, merkezi olmayan momentler, çarpıklık, basıklık, moment üreten fonksiyon ve karakteristik fonksiyon dahil olmak üzere ana özellikleri belirlenmiştir. Kalan kısım, istatistiksel bağlamda modelin uygulanabilirliğine ayrılmıştır. İlk adım olarak, parametreler en çok olabilirlik tahminleriyle tahmin edilmiştir. Daha sonra, bir veri uygulaması gerçekleştirilmiş ve Akaike ve Bayesian bilgi kriterlerinin değerlerini diğer bazı benzer dağılımların değerleriyle karşılaştırılmıştır. Alfa-çarpık tekniğine dayanan astronomik bir veri seti ve rakipler göz önüne alındığında, alfa-çarpık hiperbolik sekant dağılımının en iyisi olduğu ortaya çıkmıştır.
References
- Asgharzadeh, A., Esmaeili, L. and Nadarajah, S. (2016), Balakrishnan skew logistic distribution, Communication in Statistics- Theory and Methods, 45(2), 444-464.
- Azzalini, A. A. (1985), Class of distributions which includes the normal ones, Scandinavian Journal of Statistics, 12, 171-178.
- Azzalini, A. and Capitanio, A. (2014), The Skew-Normal and related families, IMS monographs, Cambridge University Press, Cambridge, UK.
- Bakouch, H. S., Salinas, H. S., Mamode Khan, N. and Chesneau, C. (2021), A new family of skewed distributions with application to some daily closing prices, Computational and Mathematical Methods, 3(4), e1154.
- Baten, W.D. (1934), The probability law for the sum of n independent variables, each subject to the law, Bulletin of the American MathematicalSociety, 40, 284-290.
- Casella, G. and Berger, R. L. (1990), Statistical inference, Brooks/Cole Publishing Company, California.
- Chesneau, C., Okorie, I. E. and Bakouch, H. S. (2020), A skewed Nadarajah-Haghighi distribution with some applications, Journal of the Indian Society for Probability and Statistics, 21, 225-245.
- Elal-Olivero, D. (2010), Alpha-skew-normal distribution, Proyecciones (Antofagasta), 29 224-240.
- Fischer, M. J. (2013), Generalized Hyperbolic Secant distributions: With applications to Finance, Springer, Berlin, Germany.
- Gómez, H. S., Salinas, H. S. and Bolfarine, H. (2006), Generalized skew-normal models: properties and inference, Statistics, 40(6), 495-505.
- Harandi, S. S. and Alamatsaz, M. H. (2013), Alpha-skew-Laplace distribution, Statistics and Probability Letters, 83(3), 774-782.
- Hazarika, P. and Chakraborty, S. (2014), Alpha-skew-logistic distribution, IOSR Journal of Mathematics, 10(4), 36-46.
- Kim, H.-J. (2005), On a class of two-piece skew-normal distributions, Statistics, 39(6), 537-553.
- R Core Team (2005), R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria.
- Roeder, K. (1990), Density estimation with confidence sets exemplified by superclusters and voids in galaxies, Journal of the American Statistical Association, 85, 617-624.
- Talacko, J. (1956), Perks' distributions and their role in the theory of Wiener's stochastic variables, Trabajos de Estadistica, 7, 159-174.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Articles |
| Authors | |
| Publication Date | June 30, 2022 |
| Published in Issue | Year 2022 Volume: 4 Issue: 1 |
