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Let A and B_j be sets. Conditional probability requires that P(A intersection B_j)=P(A)P(B_j|A), (1) where intersection denotes intersection ("and"), and also that P(A ...

A confidence interval is an interval in which a measurement or trial falls corresponding to a given probability. Usually, the confidence interval of interest is symmetrically ...

There are at least two distinct notions of an intensity function related to the theory of point processes. In some literature, the intensity lambda of a point process N is ...

The Mills ratio is defined as m(x) = 1/(h(x)) (1) = (S(x))/(P(x)) (2) = (1-D(x))/(P(x)), (3) where h(x) is the hazard function, S(x) is the survival function, P(x) is the ...

A multidimensional point process is a measurable function from a probability space (Omega,A,P) into (X,Sigma) where X is the set of all finite or countable subsets of R^d not ...

A random closed set (RACS) in R^d is a measurable function from a probability space (Omega,A,P) into (F,Sigma) where F is the collection of all closed subsets of R^d and ...

A random variable is a measurable function from a probability space (S,S,P) into a measurable space (S^',S^') known as the state space (Doob 1996). Papoulis (1984, p. 88) ...

Russian roulette is a game of chance in which one or more of the six chambers of a revolver are filled with cartridges, the chamber is rotated at random, and the gun is ...

The score function u(theta) is the partial derivativeof the log-likelihood function F(theta)=lnL(theta), where L(theta) is the standard likelihood function. Defining the ...

A simple point process (or SPP) is an almost surely increasing sequence of strictly positive, possibly infinite random variables which are strictly increasing as long as they ...