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)

    “To be told that our child’s behavior is “normal” offers little solace when our feelings are badly hurt, or when we worry that his actions are harmful at the moment or may be injurious to his future. It does not help me as a parent nor lessen my worries when my child drives carelessly, even dangerously, if I am told that this is “normal” behavior for children of his age. I’d much prefer him to deviate from the norm and be a cautious driver!”
    —Bruno Bettelheim (20th century)