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v. t. e. A normal distribution or Gaussian distribution (also known as the "bell-shaped curve") is a concept used in probability theory and statistics. [2] The normal distribution concept is applied in numerous disciplines, including education, psychology, economics, business, the sciences and nursing.
Diagram showing the cumulative distribution function for the normal distribution with mean (μ) 0 and variance (σ 2) 1. These numerical values "68%, 95%, 99.7%" come from the cumulative distribution function of the normal distribution. The prediction interval for any standard score z corresponds numerically to (1 − (1 − Φ μ,σ 2 (z)) · 2).
The multivariate normal distribution is said to be "non-degenerate" when the symmetric covariance matrix is positive definite. In this case the distribution has density [5] where is a real k -dimensional column vector and is the determinant of , also known as the generalized variance.
Properties. The truncated normal is one of two possible maximum entropy probability distributions for a fixed mean and variance constrained to the interval [a,b], the other being the truncated U. [2] Truncated normals with fixed support form an exponential family.
Standard normal table. 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. It is used to find the probability that a statistic is observed below, above, or between values on the standard normal ...
S. Skew normal distribution. Skewed generalized t distribution. Slash distribution. Split normal distribution. Standard normal deviate. Standard normal table. Student's t-distribution. Sum of normally distributed random variables.
The characteristic function. of the sum of two independent random variables X and Y is just the product of the two separate characteristic functions: of X and Y. The characteristic function of the normal distribution with expected value μ and variance σ 2 is. {\displaystyle \varphi (t)=\exp \left (it\mu - {\sigma ^ {2}t^ {2} \over 2}\right).} So.
Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".