Inverse stereographic hyperbolic secant distribution: a new symmetric circular model by rotated bilinear transformations

Abdullah YILMAZ

doi:https://doi.org/10.31801/cfsuasmas.906339

Makale detayları

Inverse stereographic hyperbolic secant distribution: a new symmetric circular model by rotated bilinear transformations

Yazarlar:

Abdullah YILMAZ

Yayıncı:

Ankara University

Ana Başlıklar:

Olasılıklar ve uygulamalı matematik

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2021 Vol.70 Issue 2, pp.871-887

Belge Tipi:

Makale

Yayın Tarihi:

12/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000908909

Sıklık:

Üç Aylık

eISSN:

2618-6470

pISSN:

1303-5991

DOI:

https://doi.org/10.31801/cfsuasmas.906339

Özet:

 

The inverse stereographic projection (ISP), or equivalently, bilinear transformation, is a method to produce a circular distribution based on an existing linear model. By the genesis of the ISP method, many important circular models have been provided by many researchers. In this study, we propose a new symmetric unimodal/bimodal circular distribution by the rotated ISP method considering the hyperbolic secant distribution as a baseline distribution. Rotation means that fixing the origin and rotating all other points the same amount counterclockwise. Considering the effect of rotation on the circular distribution to be obtained with the bilinear transformation, it is seen that it actually induces a location parameter in the obtained circular probability distribution.  We analyze some of the stochastic properties of the proposed distribution. The methods for the parameter estimation of the new circular model and the simulation-based compare results of these estimators are extensively provided by the paper.  Furthermore, we compare the fitting performance of the new model according to its well-known symmetric alternatives, such as Von-Misses, and wrapped Cauchy distributions, on a real data set. From the information obtained by the analysis on the real data, we say that the fitting performance of the new distribution is better than its alternatives according to the criteria frequently used in the literature.

Makale detayları

Inverse stereographic hyperbolic secant distribution: a new symmetric circular model by rotated bilinear transformations

Yazarlar: Abdullah YILMAZ

Yayıncı: Ankara University

Ana Başlıklar: Olasılıklar ve uygulamalı matematik

Dergi: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2021 Vol.70 Issue 2, pp.871-887

Belge Tipi: Makale

Yayın Tarihi: 12/2021

Belge Dili: İngilizce

Document ID (Org No.): 2000908909

Sıklık: Üç Aylık

eISSN: 2618-6470

pISSN: 1303-5991

DOI: https://doi.org/10.31801/cfsuasmas.906339

Sayı

Yazarlar:

Abdullah YILMAZ

Yayıncı:

Ankara University

Ana Başlıklar:

Olasılıklar ve uygulamalı matematik

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 2021 Vol.70 Issue 2, pp.871-887

Belge Tipi:

Makale

Yayın Tarihi:

12/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000908909

Sıklık:

Üç Aylık

eISSN:

2618-6470

pISSN:

1303-5991

DOI:

https://doi.org/10.31801/cfsuasmas.906339