Uniform Law – Udomore®

Parameters	$$-\infty < min < max < +\infty $$
Support	$$x \in [min,max ] \quad and \quad p \in \:]0,1 [$$
PDF	$$ PDF = \left\{ \begin{array}{rl} \frac{1}{(max-min)}, &\mbox{ for $x \in$ [min,max]}\\ 0 \qquad, &\mbox{ otherwise} \end{array} \right. $$
CDF	$$ CDF = \left\{ \begin{array}{rl} 0 \qquad, &\mbox{ for x < min}\\ \frac{(x-min)}{(max-min)}, &\mbox{ for $x \in$ [min,max]}\\ 1 \qquad, &\mbox{ for x $\ge$ max} \end{array} \right. $$
CDF^-1	$$ CDF^{-1} = \left\{ \begin{array}{rl} min \qquad \qquad, &\mbox{ for p $\le $ 0}\\ min+p \times (max-min), &\mbox{ for $0< p <1$ }\\ max \qquad \qquad, &\mbox{ for p $ \ge $ 1} \end{array} \right. $$