Online Pseudo Random Number Generator

This online tool generates pseudo random numbers based on the selected algorithm. A random number generator (RNG) is a computational or physical device designed to generate a sequence of numbers or symbols that lack any pattern, i.e. appear random. A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG) is an algorithm for generating a sequence of numbers that approximates the properties of true random numbers. The online pseudo random number generator supports:

Generators	Distributions
Mersenne Twister WELL (Well Equidistributed Long-period Linear) CryptMT PRBS BlumBlumShub	Uniform Gaussian (Standard Normal Distribution) Poisson Gamma and more...

Enjoy generating pseudo random numbers!

This tool is not qualified for cryptographic uses and is not cryptographically secure. You should not rely on it in security-sensitive situations.

• It is not how wide the random number is, how fast (often) the random number generator samples (generates) a random number that makes it more random.
• There is no such thing as true random, it is just we don't know the algorithm yet!
• Casio Calculator
• NIST Probability Distributions
• Crest Factor

Generators:

Algorithm to be used to generate the pseudorandom numbers

• Mersenne Twister is based on a matrix linear recurrence over a finite binary field F₂.
• WELL (Well Equidistributed Long-period Linear) is based on linear recurrences modulo 2 over a finite binary field F₂.
• CryptMT computes the accumulative product of the output of MT, and use the most significant 8 bits as a secure random numbers. Range fields are ignored. Output is always 8 bits.
• PRBS is introduced by L’Ecuyer99 combined LFSR Tausworthe generators LFSR113.
• Blum Blum Shub is a product of distinct primes, each congruent to 3 mod 4, and x_0 is a quadratic residue. Blum Blum Shub and Wichmann-Hill are Complementary-multiply-with-carry Inversive congruential generators.

Distribution:

Algorithm to be used to distribute number randoms

• Gaussian Standard normal distributed random numbers are generated using Inverse Cumulative Normal Distribution, Box-Muller, Ziggurat, or Central limit theorem methods.
  μ=0,σ=1: Standard Normal Distribution,
  μ=0,σ=0: Dirac Delta function.
  
  For mean μ and standard deviation σ the probability distribution for Gaussian random variates is,
  
  for x in the range -∞ to +∞. Use the transformation z = μ + x on the numbers returned by gsl_ran_gaussian to obtain a Gaussian distribution with mean μ. This function uses the Box-Mueller algorithm which requires two calls the random number generator r.
• Gamma:
  
  where α is the shape parameter, μ is the location parameter, β is the scale parameter The case where μ = 0 and β = 1 is called the standard gamma distribution.
• The Rayleigh distribution is a continuous distribution with the probability density function:
  f(x, σ) = x * exp(-x2/2 σ2) / σ2 for sigma parameter σ > 0, and x > 0.
  The Rayleigh distribution is often used where two orthogonal components have an absolute value, for example, wind velocity and direction may be combined to yield a wind speed, or real and imaginary components may have absolute values that are Rayleigh distributed. The absolute value of two independent normal distributions X and Y, √ (X2 + Y2) is a Rayleigh distribution.
• The Chi, Rice and Weibull distributions are generalizations of the Rayleigh distribution.

The following table denotes the acceptable strings for name, as well as the parameters for that distribution:
name	Distribution	Input Parameters
'beta' or 'Beta'	Beta Distribution	a b
'bino' or 'Binomial'	Binomial Distribution	n: number of trials p: probability of success for each trial
'birnbaumsaunders'	Birnbaum-Saunders Distribution	β γ
'burr' or 'Burr'	Burr Type XII Distribution	α: scale parameter c: shape parameter k: shape parameter
'chi2' or 'Chisquare'	Chi-Square Distribution	ν: degrees of freedom
'exp' or 'Exponential'	Exponential Distribution	μ: mean
'ev' or 'Extreme Value'	Extreme Value Distribution	μ: location parameter σ: scale parameter
'f' or 'F'	F Distribution	ν1: numerator degrees of freedom ν2: denominator degrees of freedom
'gam' or 'Gamma'	Gamma Distribution	a: shape parameter b: scale parameter
'gev' or 'Generalized Extreme Value'	Generalized Extreme Value Distribution	k: shape parameter σ: scale parameter μ: location parameter
'gp' or 'Generalized Pareto'	Generalized Pareto Distribution	k: tail index (shape) parameter σ: scale parameter μ: threshold (location) parameter
'geo' or 'Geometric'	Geometric Distribution	p: probability parameter
'hyge' or 'Hypergeometric'	Hypergeometric Distribution	M: size of the population K: number of items with the desired characteristic in the population n: number of samples drawn
'inversegaussian'	Inverse Gaussian Distribution	μ λ
'logistic'	Logistic Distribution	μ σ
'loglogistic'	Loglogistic Distribution	μ σ
'logn' or 'Lognormal'	Lognormal Distribution	μ σ
'nakagami'	Nakagami Distribution	μ ω
'nbin' or 'Negative Binomial'	Negative Binomial Distribution	r: number of successes p: probability of success in a single trial
'ncf' or 'Noncentral F'	Noncentral F Distribution	ν1: numerator degrees of freedom ν2: denominator degrees of freedom δ: noncentrality parameter
'nct' or 'Noncentral t'	Noncentral t Distribution	ν: degrees of freedom δ: noncentrality parameter
'ncx2' or 'Noncentral Chi-square'	Noncentral Chi-Square Distribution	ν: degrees of freedom δ: noncentrality parameter
'norm' or 'Normal'	Normal Distribution	μ: mean σ: standard deviation
'poiss' or 'Poisson'	Poisson Distribution	λ: mean
'rayl' or 'Rayleigh'	Rayleigh Distribution	σ: scale parameter
'rician'	Rician Distribution	s: noncentrality parameter σ: scale parameter
't' or 'T'	Student's t Distribution	ν: degrees of freedom
'tlocationscale'	t Location-Scale Distribution	μ: location parameter σ: scale parameter ν: shape parameter
'unif' or 'Uniform'	Uniform Distribution (Continuous)	a: lower endpoint (minimum) b: upper endpoint (maximum)
'unid' or 'Discrete Uniform'	Uniform Distribution (Discrete)	N: maximum observable value
'wbl' or 'Weibull'	Weibull Distribution	λ: scale parameter k: shape parameter

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The following algorithms are pseudorandom number generators:

ISAAC (cipher) with substantial Lagged Fibonacci generator forms Linear congruential generator.

- The most common type in computer programming languages for Linear feedback shift register, Maximal periodic reciprocals, and Mersenne twister contains Multiply-with-carry. However Naor-Reingold Pseudorandom Function complies with Park–Miller random number generator under RC4 PRGA rules.

Well Equidistributed Long-period Linear uses Xorshift in Hardware (True) Random Number Generators (TRNGs).

Test speed of Box-Muller method vs just adding three random numbers. Create a gaussian random number distribution using the java Random. This site describes functions for generating random variates and computing their probability distributions.