Araştırma Makalesi
BibTex RIS Kaynak Göster

The Alpha-Skew Hyperbolic Secant Distribution with Applications to an Astronomical Dataset

Yıl 2022, Cilt: 4 Sayı: 1, 70 - 84, 30.06.2022
https://doi.org/10.51541/nicel.1021116

Öz

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.

Kaynakça

  • 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.

Astronomik bir veri kümesi uygulaması ile alfa çarpık hiperbolik sekant dağılımı

Yıl 2022, Cilt: 4 Sayı: 1, 70 - 84, 30.06.2022
https://doi.org/10.51541/nicel.1021116

Öz

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.

Kaynakça

  • 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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm Makaleler
Yazarlar

Mustafa Çağatay Korkmaz 0000-0003-3302-0705

El-fahad Toibourani Bu kişi benim 0000-0001-5289-6441

Jean Yves Togo Kioye Bu kişi benim 0000-0003-0678-2851

Christophe Chesneau 0000-0002-1522-9292

Yayımlanma Tarihi 30 Haziran 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 4 Sayı: 1

Kaynak Göster

APA Korkmaz, M. Ç., Toibourani, E.-f., Togo Kioye, J. Y., Chesneau, C. (2022). The Alpha-Skew Hyperbolic Secant Distribution with Applications to an Astronomical Dataset. Nicel Bilimler Dergisi, 4(1), 70-84. https://doi.org/10.51541/nicel.1021116