BatesDistribution

Generate a set of pseudorandom numbers that are Bates distributed:

Compare the 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:

Kurtosis does not depend on the domain:

In the limit, kurtosis is the same as kurtosis of NormalDistribution:

Different moments with closed forms as functions of parameters:

Moment:

Closed form for symbolic order:

CentralMoment:

Closed form for symbolic order:

FactorialMoment:

Cumulant:

Closed form for symbolic order:

Hazard function:

Quantile function:

The mean of a uniform distribution follows a Bates distribution:

A device has 3 lifetime phases: A, B, and C. The time spent in each phase follows uniform distribution over , and after phase C, failure occurs. Find the distribution of the average time spent in the same phase:

Find the mean average time spent in the same phase:

Find the probability that on average the device will stay in the same stage for more than 4 hours:

Simulate the average time spent in the same phase for 30 such devices:

Parameter influence on the CDF for each :

Bates distribution is closed under translation and scaling:

Scaling with a negative factor:

The default domain is interval :

Relationships to other distributions:

The distribution of the mean of n uniformly distributed variables follows the Bates distribution:

The triangular distribution is a special case of the Bates distribution: