What does pseudo-random number mean?

Pseudo-random numbers are random number sequences calculated from the "[0,1]" uniform distribution using a deterministic algorithm. Pseudo-random numbers are not truly random numbers, but have statistical characteristics similar to random numbers, such as uniformity, independence, etc. Methods for generating pseudo-random numbers include: 1. Direct method, which is generated based on the physical meaning of the distribution function; 2. Reversal method; 3. Acceptance-rejection method.

The operating environment of this tutorial: Windows 7 system, Dell G3 computer.

Pseudo-random number

Pseudo-random number is a random number sequence calculated from the uniform distribution of [0,1] using a deterministic algorithm , is not truly random, but has statistical characteristics similar to random numbers, such as uniformity, independence, etc.

When calculating pseudo-random numbers, if the initial value (seed) used remains unchanged, then the number sequence of the pseudo-random numbers will also remain unchanged. Pseudo-random numbers can be generated in large quantities by computers. In order to improve simulation efficiency in simulation research, pseudo-random numbers are generally used instead of real random numbers. Generally used in simulations are pseudo-random numbers with extremely long cycle periods that can pass the random number test to ensure the randomness of the calculation results.

Generation method:

Generally, there are three main methods of generating pseudo-random numbers:

(1) Direct Method, based on the distribution function Physical meaning generation. The disadvantage is that it is only applicable to certain random numbers with special distributions, such as binomial distribution and Poisson distribution.

(2) Inversion Method, assuming that U obeys the uniform distribution in the interval [0, 1], let X=F-1(U), then the cumulative distribution function (CDF) of X is F. This method has simple principle, convenient programming and wide applicability.

(3) Acceptance-Rejection Method: Assume that the probability density function (PDF) of the random number you want to generate is f, then first find a random number generator with a PDF of g and a constant c , making f(x)≤cg(x), and then solve it according to the acceptance-rejection algorithm. Since the algorithm operates c times on average to obtain a random number that you want to generate, the value of c must be as small as possible. Obviously, the disadvantage of this algorithm is that it is difficult to determine g and c.

Therefore, pseudo-random number generators (PRNG) generally use the reversal method, which is based on uniform distribution. The quality of uniformly distributed PRNG determines the quality of the entire random number system.

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