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  "body": "\n## Summary\n\nThe von Mises–Fisher distribution is a probability distribution on the unit [[sphere|T62369RFH6]] that is concentrated around a mean direction.\nIts density is proportional to $\\exp(\\kappa \\mu^T x)$, where $\\mu$ is the mean direction and $\\kappa \\ge 0$ controls the concentration.\nIt plays the role of the normal distribution in [[directional statistics|8GZJQBPBY0]].\nOn the circle it is the von Mises distribution, and on the ordinary sphere it is the Fisher distribution.\n\n## Explanations\n\n### L1 human\n\nImagine arrows that mostly point north but wobble a little around it.\nThe von Mises–Fisher distribution is the standard model for such arrows in any dimension.\nThe number $\\kappa$ says how tightly the arrows cluster: $\\kappa = 0$ means no preferred direction at all, and large $\\kappa$ means a tight bundle around $\\mu$.\nFor large $\\kappa$, the arrows near $\\mu$ look like a normal distribution on the tangent plane.\n",
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