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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 ...
The normal distribution is the basis for the charts and requires the following assumptions: The quality characteristic to be monitored is adequately modeled by a normally distributed random variable; The parameters μ and σ for the random variable are the same for each unit and each unit is independent of its predecessors or successors
Normal probability plots are made of raw data, residuals from model fits, and estimated parameters. A normal probability plot. In a normal probability plot (also called a "normal plot"), the sorted data are plotted vs. values selected to make the resulting image look close to a straight line if the data are approximately normally distributed.
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.
The Bates distribution is the distribution of the mean of n independent random variables, each of which having the uniform distribution on [0,1]. 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.
Cumulative probability of a normal distribution with expected value 0 and standard deviation 1 In statistics , the standard deviation is a measure of the amount of variation of the values of a variable about its mean . [ 1 ]
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Other non-dimensional normalizations that can be used with no assumptions on the distribution include: Assignment of percentiles. This is common on standardized tests. See also quantile normalization. Normalization by adding and/or multiplying by constants so values fall between 0 and 1.