UniformSumDistribution

Generate a set of pseudorandom numbers that are uniform sum distributed:

Compare its histogram to the PDF:

Distribution parameters estimation:

Estimate the distribution parameters from sample data:

Compare the density histogram of the sample with the PDF of the estimated distribution:

Skewness is zero because of the symmetry:

Kurtosis does not depend on the range:

Kurtosis tends to the kurtosis of NormalDistribution:

Different moments with closed forms as functions of parameters:

Moment:

CentralMoment:

FactorialMoment:

Cumulant:

Hazard function does not have a closed form but can be computed numerically:

Quantile function:

A device has three lifetime stages: A, B, and C. The time spent in each phase follows uniform distribution over ; after phase C, failure occurs. Find the distribution of the time to failure of this device:

Find the mean time to failure:

Find the probability that such a device would be operational for at least 20 hours:

Simulate time to failure for 30 independent devices:

The CDF of the mean of 3 independent uniformly distributed random variables:

The CDF can also be derived from the UniformSumDistribution:

Show that they are the same:

Get the corresponding PDFs by taking derivatives:

Generate random numbers from its definition:

Compare the histogram with the PDF:

Find parameters min and max to approximate standard normal distribution using the method of moments:

Compare densities of the standard normal distribution and its approximation:

Parameter influence on the CDF for each :

UniformSumDistribution is closed under scaling:

Assumption on the sign of the scaling factor or numeric value is required:

Relationships to other distributions:

Sum of n uniform random variables follows UniformSumDistribution:

The mean of n uniform variables follows BatesDistribution:

The mean of two uniform variables follows TriangularDistribution:

UniformSumDistribution illustrates the central limit theorem: