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

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.

Anahtar Kelimeler

• Skewed distribution
• Hyperbolic secant distribution
• Bimodality
• Parametric estimation
• Data analysis

Astronomik bir veri kümesi uygulaması ile alfa çarpık hiperbolik sekant dağılımı

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.

Anahtar Kelimeler

• Çarpık dağılım
• Hiperbolik secant dağılımı
• İki modluluk
• Parametrik tahmin
• Veri analizi

Kaynakça

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