Search results
Results from the WOW.Com Content Network
In statistics, the Q-function is the tail distribution function of the standard normal distribution. [ 1 ] [ 2 ] In other words, Q ( x ) {\displaystyle Q(x)} is the probability that a normal (Gaussian) random variable will obtain a value larger than x {\displaystyle x} standard deviations.
In mathematical physics and probability and statistics, the Gaussian q-distribution is a family of probability distributions that includes, as limiting cases, the uniform distribution and the normal (Gaussian) distribution. It was introduced by Diaz and Teruel.
The q-Gaussian distribution is also obtained as the asymptotic probability density function of the position of the unidimensional motion of a mass subject to two forces: a deterministic force of the type () = / (determining an infinite potential well) and a stochastic white noise force () = (), where () is a white noise.
Toggle the table of contents. List of q-analogs. ... Gaussian q-distribution; ... q-theta function; See also
The Dirac comb of period 2 π, although not strictly a function, is a limiting form of many directional distributions. It is essentially a wrapped Dirac delta function. It represents a discrete probability distribution concentrated at 2 π n — a degenerate distribution — but the notation treats it as if it were a continuous distribution.
Example: To find 0.69, one would look down the rows to find 0.6 and then across the columns to 0.09 which would yield a probability of 0.25490 for a cumulative from mean table or 0.75490 from a cumulative table. To find a negative value such as -0.83, one could use a cumulative table for negative z-values [3] which yield a probability of 0.20327.
Mathematically, the derivatives of the Gaussian function can be represented using Hermite functions. For unit variance, the n-th derivative of the Gaussian is the Gaussian function itself multiplied by the n-th Hermite polynomial, up to scale. Consequently, Gaussian functions are also associated with the vacuum state in quantum field theory.
In mathematics and statistics, Q-distribution or q-distribution may refer to: Q-function, the tail distribution function of the standard normal distribution; The studentized range distribution, which is the distribution followed by the q-statistic (lowercase Q; the Q-statistic with uppercase Q, from the Box-Pierce test or Ljung-Box test, follows the chi-squared distribution)