Meth of Moments: Uniform Dist | Real Statistics Using Excel

Approach

From Uniform Distribution, we know that the mean and the variance of the uniform distribution are (α + β)/2 and (β – α)²/12, respectively. Thus, x̄ ≈ (α + β)/2, and so β ≈ 2x̄ – α, from which it follows that

and so

Note that if we prefer to use the pure method of moments approach, then we need to substitute t for s in the above formulas.

Example

Example 1: Estimate the uniform distribution that fits the data in range B3:C12 of Figure 1.

Figure 1 – Fit for uniform distribution

We see from Figure 1 that the uniform distribution is over the interval [-.03587,1.0417]. In fact, the data in range B3:C12 was actually taken from the interval [0,1) using the formula =RAND(). There is also the possibility that there will be data elements outside the estimated interval.