Von Mises Distribution - Limiting Behavior

Limiting Behavior

In the limit of large κ the distribution becomes a normal distribution

\lim_{\kappa\rightarrow\infty} f(x|\mu,\kappa)=\frac{\exp\left}{\sigma\sqrt{2\pi}}

where σ2 = 1/κ. In the limit of small κ it becomes a uniform distribution:

where the interval for the uniform distribution U(x) is the chosen interval of length 2π.

Read more about this topic:  Von Mises Distribution

Famous quotes containing the words limiting and/or behavior:

    “There could be no fairer destiny for any physical theory than that it should point the way to a more comprehensive theory in which it lives on as a limiting case.”
    —Albert Einstein (1879–1955)

    “Growing up human is uniquely a matter of social relations rather than biology. What we learn from connections within the family takes the place of instincts that program the behavior of animals; which raises the question, how good are these connections?”
    —Elizabeth Janeway (b. 1913)