In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an … See more

Probability density function
The probability density function of the continuous uniform distribution is
$${\displaystyle f(x)={\begin{cases}{\frac {1}{b-a}}&{\text{for }}a\leq x\leq b,\\[8pt]0&{\text{for }}x<a\ {\text{ or }}\ x>b.\end{cases}}}$$ See more

Estimation of parameters
Estimation of maximum
Given a uniform distribution on $${\displaystyle [0,b]}$$ See more

The probabilities for uniform distribution function are simple to calculate due to the simplicity of the function form. Therefore, there are various … See more

Moments
The mean (first raw moment) of the continuous uniform distribution is:
The second raw … See more

• If X has a standard uniform distribution, then by the inverse transform sampling method, Y = − λ ln(X) has an exponential distribution with … See more

There are many applications in which it is useful to run simulation experiments. Many programming languages come with implementations to generate pseudo-random numbers which … See more