BirnbaumSaundersDistribution

Generate a set of pseudorandom numbers that are Birnbaum-Saunders distributed:

Compare its histogram to the CDF:

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 depends only on the shape parameter :

The limiting value:

Kurtosis depends only on the shape parameter :

The limiting value:

Different moments with closed forms as functions of parameters:

Moment:

Closed form for symbolic order:

CentralMoment:

FactorialMoment:

Cumulant:

Closed form for symbolic order:

Hazard function:

Quantile function:

The lifetime in hours of a component has a Birnbaum-Saunders distribution with and . Find the probability the component survives 300 hours:

Find the probability that the component is still working after 500 hours, after it has survived 300 hours:

Find the mean time to failure:

Simulate the failure times for 30 independent components like this:

The time to failure of a component A follows a Birnbaum-Saunders distribution with and , while the failure rate of component B is . Find the mean time to failure for both components:

Find the probability that component A fails before component B:

Although they have the same mean lifetime, a Birnbaum-Saunders distribution tends to fail early:

The lifetime of a device has a Birnbaum-Saunders distribution. Find the reliability of the device:

The hazard function has horizontal asymptote :

Find the reliability of two such devices in series:

Find the reliability of two such devices in parallel:

Compare the reliability of both systems for and :

Parameter influence on the CDF for each :

Birnbaum-Saunders distribution is closed under scaling by a positive factor:

If has a Birnbaum-Saunders distribution, then also has a Birnbaum-Saunders distribution:

Birnbaum-Saunders distribution is related to NormalDistribution: