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Marked Point Processes

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  • A set A of a space X is a collection of elements or points of X. When x is an element of the set A,
  • From the mathematical point of view, the paradigm distribution function for lifetimes is the exponential function, which has a constant hazard independent of age: for x > 0,
  • For our present purposes, we shall understand by a point process some method of randomly allocating points to intervals of the real line or (occasionally)to rectangles or hyper-rectangles in a d-dimensional Euclidean space .
  • the distributions are stationary: they depend only on the lengths Failed to parse (syntax error): {\displaystyle b_i−a_i} of the intervals.

Added to Poisson process:

Useful Mathematical Signs (just copy and past) ≥ ≤