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Spherical logistic distribution. (English) Zbl 1442.62115
The authors define a spherical logistic distribution on the unit sphere \(\mathbb{S}^{d-1}\) in \(d\)-dimensional Euclidean space, with density function \[ f(y)=C_d(b,\kappa)\frac{e^{\kappa y^T\mu}}{(b-1+e^{\kappa y^T\mu})^2}\,, \] for \(y\in\mathbb{S}^{d-1}\), where \(\mu\in\mathbb{S}^{d-1}\), \(b\geq1\) and \(\kappa>0\) are parameters, and \(C_d(b,\kappa)\) is a normalizing constant. They consider method-of-moments and maximum likelihood estimation of these parameters, illustrating their results with simulations, with special attention given to the case \(d=3\). The paper concludes with an application of this spherical logistic distribution to a real data set.
MSC:
62H11 Directional data; spatial statistics
62J12 Generalized linear models (logistic models)
62F10 Point estimation
62H12 Estimation in multivariate analysis
62R30 Statistics on manifolds
60E10 Characteristic functions; other transforms
62E15 Exact distribution theory in statistics
62H10 Multivariate distribution of statistics
60E05 Probability distributions: general theory
62P20 Applications of statistics to economics
Software:
HSAUR; HSAUR2; movMF; SPLIDA
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References:
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