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A general class of means introduced by Italian mathematician Oscar Chisini (pronounced keeseenee) in 1929. Given a function of n variables f(x_1,...,x_n), the Chisini mean of ...

A statistical distribution whose variables can take on only discrete values. Abramowitz and Stegun (1972, p. 929) give a table of the parameters of most common discrete ...

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 probability Q_delta that a random sample from an infinite normally distributed universe will have a mean m within a distance |delta| of the mean mu of the universe 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 ...

The probability density function for Student's z-distribution is given by f_n(z)=(Gamma(n/2))/(sqrt(pi)Gamma((n-1)/2))(1+z^2)^(-n/2). (1) Now define ...

F_k[P_N(k)](x)=F_k[exp(-N|k|^beta)](x), where F is the Fourier transform of the probability P_N(k) for N-step addition of random variables. Lévy showed that beta in (0,2) for ...

A generalization of Student's t-distribution known as the noncentral Student's t-distribution is given by (1) where Gamma(z) is the gamma function and _1F_1(a;b;z) is a ...

The ratio X_1/X_2 of uniform variates X_1 and X_2 on the interval [0,1] can be found directly as P_(X_1/X_2)(u) = int_0^1int_0^1delta((x_1)/(x_2)-u)dx_1dx_2 (1) = ...

Given the closed interval [0,x] with x>1, let one-dimensional "cars" of unit length be parked randomly on the interval. The mean number M(x) of cars which can fit (without ...