Uniform

Uniform⁡‾(min,max)\underline{\operatorname{Uniform}}(\mathrm{min}, \mathrm{max})
  • min\mathrm{min}: lower bound of the support interval
  • max\mathrm{max}: upper bound of the support interval (max>min\mathrm{max} > \mathrm{min})

  • Formation: all values within a bounded interval have equal probability.
  • Origin: represents complete uncertainty within known bounds.
  • Properties: rectangular probability density, finite support with hard boundaries.
  • Applications: random number generation, round-off errors, arrival times within known intervals.
  • Characteristics: symmetric, bounded, no tail behavior.
  • Note: traditional estimators work reasonably well due to symmetry and bounded nature.