The coverage factor in a Flatten-Gaussian distribution

According to the Guide to the Expression of Uncertainty in Measurement, a coverage factor that produces an expanded uncertainty having an approximate level of confidence is recommended in the final expression of the measurement result. The numerical value for the coverage factor depends on the probability density function. When a Type A evaluation following a Gaussian (normal) distribution is combined with a Type B one following a rectangular distribution, the resulting probability density function is neither Gaussian nor rectangular, but similar to both, which we term a Flatten-Gaussian probability density function. The variance of such a function is the combined variance in the usual way, but the coverage factor must be calculated.