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  2. 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 ...

  3. 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 ...

  4. 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

  5. Truncated normal distribution - Wikipedia

    en.wikipedia.org/wiki/Truncated_normal_distribution

    In probability and statistics, the truncated normal distribution is the probability distribution derived from that of a normally distributed random variable by bounding the random variable from either below or above (or both). The truncated normal distribution has wide applications in statistics and econometrics.

  6. Shapiro–Wilk test - Wikipedia

    en.wikipedia.org/wiki/Shapiro–Wilk_test

    The Shapiro–Wilk test tests the null hypothesis that a sample x 1, ..., x n came from a normally distributed population. The test statistic is = (= ()) = (¯), where with parentheses enclosing the subscript index i is the ith order statistic, i.e., the ith-smallest number in the sample (not to be confused with ).

  7. Empirical distribution function - Wikipedia

    en.wikipedia.org/wiki/Empirical_distribution...

    A non-exhaustive list of software implementations of Empirical Distribution function includes: In R software, we compute an empirical cumulative distribution function, with several methods for plotting, printing and computing with such an “ecdf” object. In MATLAB we can use Empirical cumulative distribution function (cdf) plot

  8. 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.

  9. Sum of normally distributed random variables - Wikipedia

    en.wikipedia.org/wiki/Sum_of_normally...

    It is possible to have variables X and Y which are individually normally distributed, but have a more complicated joint distribution. In that instance, X + Y may of course have a complicated, non-normal distribution. In some cases, this situation can be treated using copulas.