TY - JOUR
T1 - On the modified skew-normal-Cauchy distribution
T2 - properties, inference and applications
AU - Contreras-Reyes, Javier E.
AU - Kahrari, Fereshte
AU - Cortés, Daniel Devia
N1 - Publisher Copyright:
© 2020 Taylor & Francis Group, LLC.
PY - 2021
Y1 - 2021
N2 - In this paper, we study further properties of the modified skew-normal-Cauchy (MSNC) distribution. MSNC distribution corresponds to a reformulation of skew-normal-Cauchy distribution that allows to obtain a nonsingular Fisher Information Matrix at skewness parameter equal zero. We suggest a hierarchical representation which allows alternative derivations for moments generating function, moments, and skewness and kurtosis coefficients. As an application, we develop hypothesis testing for normality considering the Kullback–Leibler divergence between MSNC distribution and the normal one. Finally, we apply this result to condition factor time series of shortfin mako sharks off northern Chile.
AB - In this paper, we study further properties of the modified skew-normal-Cauchy (MSNC) distribution. MSNC distribution corresponds to a reformulation of skew-normal-Cauchy distribution that allows to obtain a nonsingular Fisher Information Matrix at skewness parameter equal zero. We suggest a hierarchical representation which allows alternative derivations for moments generating function, moments, and skewness and kurtosis coefficients. As an application, we develop hypothesis testing for normality considering the Kullback–Leibler divergence between MSNC distribution and the normal one. Finally, we apply this result to condition factor time series of shortfin mako sharks off northern Chile.
KW - condition factor time series
KW - Kullback–Leibler divergence
KW - maximum likelihood
KW - Modified skew-normal-Cauchy
KW - skew-normal
UR - http://www.scopus.com/inward/record.url?scp=85077877124&partnerID=8YFLogxK
U2 - 10.1080/03610926.2019.1708942
DO - 10.1080/03610926.2019.1708942
M3 - Article
AN - SCOPUS:85077877124
SN - 0361-0926
VL - 50
SP - 3615
EP - 3631
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
IS - 15
ER -