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The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when μ = 0 {\textstyle \mu =0} and σ 2 = 1 {\textstyle \sigma ^{2}=1} , and it is described by this probability density function (or density): φ ( z ) = e − z 2 2 2 π . {\displaystyle \varphi (z ...
Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.
The logit-normal distribution on (0,1). The Dirac delta function , although not strictly a probability distribution, is a limiting form of many continuous probability functions. It represents a discrete probability distribution concentrated at 0 — a degenerate distribution — it is a Distribution (mathematics) in the generalized function ...
A graphical tool for assessing normality is the normal probability plot, a quantile-quantile plot (QQ plot) of the standardized data against the standard normal distribution. Here the correlation between the sample data and normal quantiles (a measure of the goodness of fit) measures how well the data are modeled by a normal distribution. For ...
Many central limit theorems provide conditions such that S n / √ Var(S n) converges in distribution to N(0,1) (the normal distribution with mean 0, variance 1) as n → ∞. In some cases, it is possible to find a constant σ 2 and function f(n) such that S n /(σ √ n⋅f (n)) converges in distribution to N(0,1) as n → ∞.
The folded normal distribution is a probability distribution related to the normal distribution. Given a normally distributed random variable X with mean μ and variance σ 2, the random variable Y = |X| has a folded normal distribution. Such a case may be encountered if only the magnitude of some variable is recorded, but not its sign.
In probability theory, regular conditional probability is a concept that formalizes the notion of conditioning on the outcome of a random variable. The resulting conditional probability distribution is a parametrized family of probability measures called a Markov kernel .
In statistics, a standard normal table, also called the unit normal table or Z table, [1] is a mathematical table for the values of Φ, the cumulative distribution function of the normal distribution.