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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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