Random crossings of cumulative distribution functions

On the Number of Crossings of Empirical Distribution Functions

Let F and G be two continuous distribution functions that cross at a finite number of points − ∞ ≤ t1 < ⋯ < tk ≤ ∞. We study the limiting behavior of the number of times the empirical distribution function Gn crosses F and the number of times Gn crosses Fn. It is shown that these variables can be represented, as n → ∞, as the sum of k independent geometric random variables whose distributions d...

Random Distribution Functions

Cumulative distribution networks: Inference, estimation and applications of graphical models for cumulative distribution functions

Cumulative distribution networks: Inference, estimation and applications of graphical models for cumulative distribution functions Jim C. Huang Doctor of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto 2009 This thesis presents a class of graphical models for directly representing the joint cumulative distribution function (CDF) of many random variabl...

Random walks on networks: cumulative distribution of cover time.

We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a complete graph, a cycle graph, and a path graph. An accurate approximation for the cover time distribution, with computational complexity of O(2n) , is also present...

Maximum-likelihood learning of cumulative distribution functions on graphs

For many applications, a probability model can be more easily expressed as a cumulative distribution functions (CDF) as compared to the use of probability density or mass functions (PDF/PMFs). One advantage of CDF models is the simplicity of representing multivariate heavy-tailed distributions. Examples of fields that can benefit from the use of graphical models for CDFs include climatology and...