runiform

runiform is a statistical distribution. It is a continuous probability distribution that describes outcomes that are equally likely over a given range. The most common form is the uniform distribution over the interval [0, 1], where any value between 0 and 1 is equally probable. This means that the probability of observing a value in any subinterval of [0, 1] is proportional to the length of that subinterval.

The probability density function (PDF) for a continuous uniform distribution over an interval [a, b] is given by:

f(x) = 1 / (b - a) for a <= x <= b, and 0 otherwise.

This means that the probability density is constant within the specified interval and zero outside of it.

The uniform distribution is often used as a starting point for generating random numbers in computer simulations and statistical modeling. When no prior information about the distribution of data is available, a uniform distribution can serve as a naive or uninformative prior distribution. It is also fundamental in understanding more complex probability distributions. For example, certain transformations of uniform random variables can be used to generate random variables following other distributions, such as the normal or exponential distribution. Its simplicity makes it a key concept in introductory probability and statistics.