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Random Number Generator | Various Distributions

Online generator for random numbers. Supports various probability distributions: uniform, left-skewed, right-skewed, and normal (bell-shaped) distributions.
Generate random numbers with defined properties. With uniform distribution and bell-shaped distrubution, negative random numbers can be generated as well, minimum and maximum are at will. At left- and right-skewed distribution, the minimum has to be 0. The factor defines the shape of the skewness or bell. The calculation for the left-skewed distribution is (Random number to the power of Factor) / (Maximum to the power of Factor-1), for the right-skewed distribution it is (Maximum to the power of Factor - Random number to the power of Factor) / (Maximum to the power of Factor-1). For the bell-shaped distribution it is (Random number 1 + Random number 2 + ... + Random number Factor) / Factor. The algorithm used for the random numbers is Mersenne Twister.

Uniform distribution means that all values ​​are expected to occur equally often, not that they occur exactly the same. This is the case, for example, with dice, where every value from one to six has the same probability. Random values ​​are very often normally distributed, i.e. they follow a bell curve. In this case, the middle values ​​occur more frequently, the more extreme values ​​less frequently. This can be achieved with the sum of two dice, where seven is the most frequently expected value and two and twelve should occur least frequently. The distribution generated here did not follow the Gaussian bell curve.
Distributions that are steep to the left are often those where there is a real lower limit (for example 0 for lengths) but no or a very high upper limit. An example of this is the distribution of stars in the universe according to mass, where most are small, so-called red dwarfs. Right-stepping distributions, on the other hand, are less common. The length of nightly sleep is distributed steep to the right if one can normally sleep in and has a healthy sleeping pattern. A good left- or right-skewed distribution requires a larger range of values ​​than the other two distributions.

Last updated on 04/20/2026. Author: Jürgen Kummer

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