21.4.7.5. Uniform Distribution

Sometimes, there is not enough information available to determine the use of a particular standard distribution. From the empirical experience, one can have some guideline of the lower and upper bounds of a random variable, but there may not be enough data available between these two bounds to justify a specific distribution. In this situation, a uniform distribution is widely used even though any distribution can be used such as triangular, trapezoidal and uniform, etc. Figure 21.160 shows a uniform distribution with two limits \(a\) and \(b\).

Figure 21.160 Uniform distribution

Then, the mean and the coefficient of variance are specified as

\({{\mu }_{x}}=\frac{1}{2}\left( a+b \right)\) and \({{\sigma }_{x}}=\frac{2}{12}\left( \frac{b-a}{b+a} \right)\)