rectangular(uniform) distribution - coverage factor

[elektr0]

Hello,

consider a total measurement uncertainty M that is given with a defined confidence level of 95%
(95% of all measured values are within plus/minus M).

If the error of the physical quantity has Gaussian distribution, the corresponding variance (σ²) is calculated

σ² = (M/C)²

with σ being the standard deviation and C being the coverage factor.
C = 1.96 in case of 95%.

So my question is, how to determine the variance σ² if the error of the measured physical quantity follows uniform (rectangular) distribution.

Which coverage factor has to be used ?

Thanks for any reply.

-e

 

[elektr0]

According to
https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)
the variance in case of uniform distribution is given by
VAR=σ²=1/12 (b-a)^2
if b is the uppper limit of the measurement results and a is the lower limit.
If all measurement results (100%) lie within E plus/minus e.
The variance is given by
VAR=σ²=1/12 (E+e - (E-e))^2 = (2e)²/(12) = e²/3

If we know the total measurement uncertainty M is valid for a confidence level of 95%.
In case of uniform distribution I would expect M*(1/0.95) is the corresponding uncertainty with 100% confidence level.
Hence,
VAR=σ²=[M*(1/0.5)]²/3

May be somone can comment on this.