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  2. Normal distribution - Wikipedia

    en.wikipedia.org/wiki/Normal_distribution

    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 ...

  3. Truncated normal distribution - Wikipedia

    en.wikipedia.org/wiki/Truncated_normal_distribution

    One such truncated normal generator (implemented in Matlab and in R (programming language) as trandn.R) is based on an acceptance rejection idea due to Marsaglia. [10] Despite the slightly suboptimal acceptance rate of Marsaglia (1964) in comparison with Robert (1995) , Marsaglia's method is typically faster, [ 9 ] because it does not require ...

  4. Normality test - Wikipedia

    en.wikipedia.org/wiki/Normality_test

    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 ...

  5. List of probability distributions - Wikipedia

    en.wikipedia.org/wiki/List_of_probability...

    The normal-exponential-gamma distribution; The normal-inverse Gaussian distribution; The Pearson Type IV distribution (see Pearson distributions) The Quantile-parameterized distributions, which are highly shape-flexible and can be parameterized with data using linear least squares. The skew normal distribution

  6. Marsaglia polar method - Wikipedia

    en.wikipedia.org/wiki/Marsaglia_polar_method

    The Marsaglia polar method [1] is a pseudo-random number sampling method for generating a pair of independent standard normal random variables. [2]Standard normal random variables are frequently used in computer science, computational statistics, and in particular, in applications of the Monte Carlo method.

  7. Multivariate normal distribution - Wikipedia

    en.wikipedia.org/wiki/Multivariate_normal...

    The fact that two random variables and both have a normal distribution does not imply that the pair (,) has a joint normal distribution. A simple example is one in which X has a normal distribution with expected value 0 and variance 1, and = if | | > and = if | | <, where >. There are similar counterexamples for more than two random variables.

  8. Norm-referenced test - Wikipedia

    en.wikipedia.org/wiki/Norm-referenced_test

    Consistent with the example illustrated above, a grading curve allows academic institutions to ensure the distribution of students across certain grade point average (GPA) thresholds. As many professors establish the curve to target a course average of a C, [ clarification needed ] the corresponding grade point average equivalent would be a 2.0 ...

  9. Standard normal table - Wikipedia

    en.wikipedia.org/wiki/Standard_normal_table

    Normal distributions are symmetrical, bell-shaped distributions that are useful in describing real-world data. The standard normal distribution, represented by Z, is the normal distribution having a mean of 0 and a standard deviation of 1.