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Evans et al. (2000, p. 6) use the unfortunate term "probability domain" to refer to the range of the distribution function of a probability density function. For a continuous ...

The distribution with probability density function and distribution function P(x) = (ab^a)/(x^(a+1)) (1) D(x) = 1-(b/x)^a (2) defined over the interval x>=b. It is ...

A standard normal distribution is a normal distribution with zero mean (mu=0) and unit variance (sigma^2=1), given by the probability density function and distribution ...

When a measure lambda is absolutely continuous with respect to a positive measure mu, then it can be written as lambda(E)=int_Efdmu. By analogy with the first fundamental ...

Let T be an ergodic endomorphism of the probability space X and let f:X->R be a real-valued measurable function. Then for almost every x in X, we have 1/nsum_(j=1)^nf ...

The expectation value of a function f(x) in a variable x is denoted <f(x)> or E{f(x)}. For a single discrete variable, it is defined by <f(x)>=sum_(x)f(x)P(x), (1) where P(x) ...

A continuous transformation from one function to another. A homotopy between two functions f and g from a space X to a space Y is a continuous map G from X×[0,1]|->Y such ...

The ratio X/Y of independent normally distributed variates with zero mean is distributed with a Cauchy distribution. This can be seen as follows. Let X and Y both have mean 0 ...

The S distribution is defined in terms of its distribution function F(x) as the solution to the initial value problem (dF)/(dx)=alpha(F^g-F^h), where F(x_0)=F_0 (Savageau ...

Many authors (e.g., Mendelson 1963; Pervin 1964) use the term arcwise-connected as a synonym for pathwise-connected. Other authors (e.g., Armstrong 1983; Cullen 1968; and ...