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  2. Non-uniform random variate generation - Wikipedia

    en.wikipedia.org/wiki/Non-uniform_random_variate...

    Non-uniform random variate generation or pseudo-random number sampling is the numerical practice of generating pseudo-random numbers (PRN) that follow a given probability distribution. Methods are typically based on the availability of a uniformly distributed PRN generator .

  3. Inverse transform sampling - Wikipedia

    en.wikipedia.org/wiki/Inverse_transform_sampling

    Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, or the Smirnov transform) is a basic method for pseudo-random number sampling, i.e., for generating sample numbers at random from any probability distribution given its cumulative distribution function.

  4. Random number generation - Wikipedia

    en.wikipedia.org/wiki/Random_number_generation

    Dice are an example of a mechanical hardware random number generator. When a cubical die is rolled, a random number from 1 to 6 is obtained. Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols is generated that cannot be reasonably predicted better than by random chance.

  5. Simple random sample - Wikipedia

    en.wikipedia.org/wiki/Simple_random_sample

    If a systematic pattern is introduced into random sampling, it is referred to as "systematic (random) sampling". An example would be if the students in the school had numbers attached to their names ranging from 0001 to 1000, and we chose a random starting point, e.g. 0533, and then picked every 10th name thereafter to give us our sample of 100 ...

  6. Monte Carlo method - Wikipedia

    en.wikipedia.org/wiki/Monte_Carlo_method

    the (pseudo-random) number generator has certain characteristics (e.g. a long "period" before the sequence repeats) the (pseudo-random) number generator produces values that pass tests for randomness; there are enough samples to ensure accurate results; the proper sampling technique is used; the algorithm used is valid for what is being modeled

  7. Independent and identically distributed random variables

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

    A random sample can be thought of as a set of objects that are chosen randomly. More formally, it is "a sequence of independent, identically distributed (IID) random data points." In other words, the terms random sample and IID are synonymous. In statistics, "random sample" is the typical terminology, but in probability, it is more common to ...

  8. Pseudorandom number generator - Wikipedia

    en.wikipedia.org/wiki/Pseudorandom_number_generator

    It can be shown that if is a pseudo-random number generator for the uniform distribution on (,) and if is the CDF of some given probability distribution , then is a pseudo-random number generator for , where : (,) is the percentile of , i.e. ():= {: ()}. Intuitively, an arbitrary distribution can be simulated from a simulation of the standard ...

  9. Pseudorandomness - Wikipedia

    en.wikipedia.org/wiki/Pseudorandomness

    The generation of random numbers has many uses, such as for random sampling, Monte Carlo methods, board games, or gambling.In physics, however, most processes, such as gravitational acceleration, are deterministic, meaning that they always produce the same outcome from the same starting point.