Continuous Uniform

The continuous uniform distribution applies when the random variable can fall anywhere equally likely between two limits. The distribution is often called when an analyst does not have definitive information on the range and shape of the random variable. For example, management may estimate the time to finish a project is equally likely between 50 and 60 h. A baseball is hit for a homerun and the officials estimate the ball traveled somewhere between 410 and 430 feet. The amount of official snowfall at a location on a wintry day is predicted between 1 and 5 inches. The chapter lists the probability density, cumulative distribution, mean, variance and standard deviation of the random variable. Also described is the α-percent-point of x that identifies the value of x where the cumulative probability is α. When the parameter limit values are not known, and sample data is available, estimates of the parameter values are obtained. Two estimates are described, one by way of the maximum-likelihood method, and the other by the method-of-moments. When sample data is not available, experts are called to obtain the estimates. Often both of the limits are unknown and estimates on both are needed. Sometimes only the low limit is known, and on other occasions, only the upper limit is unknown. The way to estimate the parameter values is described for all three scenarios.