| Continuous uniform distribution | CDF | { 0 for x < a x − a b − a for x ∈ [ a , b ] 1 for x > b {\displaystyle {\begin{cases}0&{\text{for }}x<a\\{\frac {x-a}{b-a}}&{\text{for }}x\in [a,b]\\1&{\text{for }}x>b\end{cases}}} | 1.00 | infobox |
| Continuous uniform distribution | CF | { e i t b − e i t a i t ( b − a ) for t ≠ 0 1 for t = 0 {\displaystyle {\begin{cases}{\frac {\mathrm {e} ^{\mathrm {i} tb}-\mathrm {e} ^{\mathrm {i} ta}}{\mathrm {i} t(b-a)}}&{\… | 1.00 | infobox |
| Continuous uniform distribution | Entropy | log ( b − a ) {\displaystyle \log(b-a)} | 1.00 | infobox |
| Continuous uniform distribution | Excess kurtosis | − 6 5 {\displaystyle -{\tfrac {6}{5}}} | 1.00 | infobox |
| Continuous uniform distribution | MAD | 1 4 ( b − a ) {\displaystyle {\tfrac {1}{4}}(b-a)} | 1.00 | infobox |
| Continuous uniform distribution | Mean | 1 2 ( a + b ) {\displaystyle {\tfrac {1}{2}}(a+b)} | 1.00 | infobox |
| Continuous uniform distribution | Median | 1 2 ( a + b ) {\displaystyle {\tfrac {1}{2}}(a+b)} | 1.00 | infobox |
| Continuous uniform distribution | MGF | { e t b − e t a t ( b − a ) for t ≠ 0 1 for t = 0 {\displaystyle {\begin{cases}{\frac {\mathrm {e} ^{tb}-\mathrm {e} ^{ta}}{t(b-a)}}&{\text{for }}t\neq 0\\1&{\text{for }}t=0\end… | 1.00 | infobox |
| Continuous uniform distribution | Mode | any value in ( a , b ) {\displaystyle {\text{any value in }}(a,b)} | 1.00 | infobox |
| Continuous uniform distribution | Notation | U [ a , b ] {\displaystyle {\mathcal {U}}_{[a,b]}} | 1.00 | infobox |
| Continuous uniform distribution | Parameters | − ∞ < a < b < ∞ {\displaystyle -\infty <a<b<\infty } | 1.00 | infobox |
| Continuous uniform distribution | PDF | { 1 b − a for x ∈ [ a , b ] 0 otherwise {\displaystyle {\begin{cases}{\frac {1}{b-a}}&{\text{for }}x\in [a,b]\\0&{\text{otherwise}}\end{cases}}} | 1.00 | infobox |
| Continuous uniform distribution | Skewness | 0 {\displaystyle 0} | 1.00 | infobox |
| Continuous uniform distribution | Support | [ a , b ] {\displaystyle [a,b]} | 1.00 | infobox |
| Continuous uniform distribution | Variance | 1 12 ( b − a ) 2 {\displaystyle {\tfrac {1}{12}}(b-a)^{2}} | 1.00 | infobox |
