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  2. 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.

  3. List of random number generators - Wikipedia

    en.wikipedia.org/wiki/List_of_random_number...

    Widely used in many programs, e.g. it is used in Excel 2003 and later versions for the Excel function RAND [8] and it was the default generator in the language Python up to version 2.2. [9] Rule 30: 1983 S. Wolfram [10] Based on cellular automata. Inversive congruential generator (ICG) 1986 J. Eichenauer and J. Lehn [11] Blum Blum Shub: 1986

  4. Independent and identically distributed random variables

    en.wikipedia.org/wiki/Independent_and...

    The i.i.d. assumption is also used in the central limit theorem, which states that the probability distribution of the sum (or average) of i.i.d. variables with finite variance approaches a normal distribution. [4] The i.i.d. assumption frequently arises in the context of sequences of random variables. Then, "independent and identically ...

  5. Box–Muller transform - Wikipedia

    en.wikipedia.org/wiki/Box–Muller_transform

    Suppose U 1 and U 2 are independent samples chosen from the uniform distribution on the unit interval (0, 1).Let = ⁡ = ⁡ ⁡ and = ⁡ = ⁡ ⁡ (). Then Z 0 and Z 1 are independent random variables with a standard normal distribution.

  6. 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.

  7. Robust measures of scale - Wikipedia

    en.wikipedia.org/wiki/Robust_measures_of_scale

    The theoretical analysis of such an experiment is complicated, but it is easy to set up a spreadsheet which draws random numbers from a normal distribution with standard deviation σ to simulate the situation; this can be done in Microsoft Excel using =NORMINV(RAND(),0,σ)), as discussed in [4] and the same techniques can be used in other ...

  8. 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 ...

  9. List of probability distributions - Wikipedia

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

    The skew normal distribution; Student's t-distribution, useful for estimating unknown means of Gaussian populations. The noncentral t-distribution; The skew t distribution; The Champernowne distribution; The type-1 Gumbel distribution; The Tracy–Widom distribution; The Voigt distribution, or Voigt profile, is the convolution of a normal ...