Random Variables Generator

 Original: English

Here you can generate a set of values according to a selected probability distribution function, such as: Normal, Lognormal, Gamma, Exponential, Weibull, Uniform, Student’s, Binomial, Geometric, Negative Binomial and Poisson. Information about these distributions are provided in the section "Summary of Distribution Functions" below in this page.

To generate values just follow the steps below:

Step 1)  Select a probability distribution function:

Step 2)  Enter the parameter(s) for the selected distribution.

 Parameter 1 Parameter 2 Parameter 3

Step 3) Specify the quantity of values you would lile to generate:

Quantity:     (up to 10000)

Summary of Distribution Functions

The Cumulative Distribution Function (CDF) is the probability that the random variable X will take a value less than or equal to x. The following table summarizes common continuous and discrete distributions, showing the cumulative function and its parameters. In this table, the continuous distributions are: Normal, Lognormal, Gamma, Exponential, and Student’s. The discrete distributions are: Binomial, Geometric, Negative Binomial and Poisson.

 Normal Returns the probability 'p' that a single observation from a Normal distribution with parameters µ and σ falls in the interval (-∞,x]. The normal distribution is a two-parameter family of curves. The first parameter, µ, is the mean. The second parameter, σ, is the standard deviation. Lognormal Returns values at x of the Lognormal cumulative distribution function with distribution parameters µ and σ, where µ and σ are the mean and standard deviation, respectively, of the associated normal distribution. A lognormal distribution with mean m and variance v has parameters µ and σ. Gamma Returns the Gamma cumulative distribution function at value x using the corresponding shape parameters in a and scale parameters in b. Exponential Computes the Exponential cumulative distribution function at value x using the corresponding mean parameter µ. Student's Computes a Student’s cumulative distribution function at value x where ν is the degrees of freedom and Γ( · ) is the Gamma function. The result p is the probability that a single observation from the t distribution with ν degrees of freedom will fall in the interval [–∞, x]. Binomial Computes a binomial cumulative distribution function at value x using the corresponding number of trials in N and probability of success for each trial in p. Geometric Computes a Geometric cumulative distribution where p is the probability of success, and x is the number of failures before the first success. The result y is the probability of observing up to x trials before a success, when the probability of success in any given trial is p. Negative Binomial Computes the Negative binomial cumulative distribution at value x using the corresponding number of successes (R) and probability of success in a single trial (p). Poisson Returns the Poisson cumulative distribution function at value x using the corresponding mean parameter in lambda.