An random number generator can be used for many analytical purposes, with a heavy focus on the distribution it generates. This article will provide some examples to help guide you in choosing the best option for your needs.
Binomial distributions are one use for Random Number Generators. This distribution shows the number of successful observations in a set number of independent trials. The only options for each observation being success or failure. This distribution shows the expected number of trials with success. This distribution can be used for answering questions like “What is the probability that a coin will flip 30 times?” Or “How many defects are most likely to be found in a batch 2500 computer chips?” Binomial distributions allow you to calculate probabilities for win/loss, success/failure, yes/no and win/loss.
Triangular distributions can also be produced by a random number generator. These are useful for analyzing small amounts of data, such as the number and severity of recent hurricanes or auto accidents on a country road. Triangular distributions require the minimum and maximum values to establish the range of possible values and the peak, or center value. The distribution can be tilted to the right or left depending on the location of the peak. This distribution allows for fast processing of large numbers of cases (e.g. 100,000 towns could have been affected by a hurricane. This does not assume any real-life distribution shapes, though many triangular distributions could lead to a distribution with greater density across larger populations.
Another output that a random generator can produce is the Chi-Square distribution. This distribution can be used to test proportional differences among different distributions with different variances. It tends to be positive when there are lower degrees of freedom. Lower sample sizes result in a longer left tail distribution, but it becomes more normal with increasing numbers of samples.
These are just some of the many capabilities available to statisticians and analysts who use random number generators to solve real-world problems.