When you ask for a random set of say 100 numbers between 1 and 10, you are looking for a sample from a uniform distribution, where α = 1 and β = 10 according to the following definition.
Definition 1: The uniform distribution has probability density function (pdf)
where α and β are any parameters with α < β.
Observation: The corresponding cumulative distribution function is
The inverse cumulative distribution function is
I(p) = α + p(β − α)
Other key statistical properties are:
- Mean = (α + β) / 2
- Median = (α + β) / 2
- Mode = any x, α ≤ x ≤ β
- Range = (-∞, ∞)
- Variance = (β – α)2 / 12
- Skewness = 0
- Kurtosis = -1.2
Real Statistics Functions: Excel doesn’t provide any functions for the uniform distribution. Instead you can use the following functions provided by the Real Statistics Resource Pack.
UNIFORM_DIST(x, α, β, cum) = the pdf of the uniform distribution f(x) at x when cum = FALSE and the corresponding cumulative distribution function F(x) when cum = TRUE.
UNIFORM_INV(p, α, β) = x such that UNIFORM_DIST(x, α, β, TRUE) = p. Thus UNIFORM_INV is the inverse of the cumulative distribution version of UNIFORM_DIST.