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The Birnbaum–Saunders distribution, also known as the fatigue life distribution, is a probability distribution used extensively in reliability applications to model failure times. The chi distribution. The noncentral chi distribution; The chi-squared distribution, which is the sum of the squares of n independent Gaussian random variables.
The quantile function, Q, of a probability distribution is the inverse of its cumulative distribution function F. The derivative of the quantile function, namely the quantile density function, is yet another way of prescribing a probability distribution. It is the reciprocal of the pdf composed with the quantile function.
The Tukey lambda distribution has a simple, closed form for the CDF and / or PDF only for a few exceptional values of the shape parameter, for example: λ ∈ {2, 1, 1 / 2 , 0 } (see uniform distribution [ cases λ = 1 and λ = 2 ] and the logistic distribution [ case λ = 0 ].
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.
A discrete probability distribution is applicable to the scenarios where the set of possible outcomes is discrete (e.g. a coin toss, a roll of a die) and the probabilities are encoded by a discrete list of the probabilities of the outcomes; in this case the discrete probability distribution is known as probability mass function.
The distribution is called "folded" because probability mass to the left of x = 0 is folded over by taking the absolute value. In the physics of heat conduction, the folded normal distribution is a fundamental solution of the heat equation on the half space; it corresponds to having a perfect insulator on a hyperplane through the origin.
Sturges's rule [1] is a method to choose the number of bins for a histogram.Given observations, Sturges's rule suggests using ^ = + bins in the histogram. This rule is widely employed in data analysis software including Python [2] and R, where it is the default bin selection method.
The bimodality of the resulting distribution has been attributed to the presence of both first-time and second-time spawners in the river, the latter of which tend to weigh more. [28] Hydrology. A 10-term semi-bounded metalog was used to model the probability distribution of annual river gauge heights. [29] Oil field production. Semi-bounded ...