This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

Birnbaum-Saunders Distribution


The Birnbaum-Saunders distribution has the density function


with scale parameter β > 0 and shape parameter γ > 0, for x > 0.

If x has a Birnbaum-Saunders distribution with parameters β and γ, then


has a standard normal distribution.


The Birnbaum-Saunders distribution was originally proposed as a lifetime model for materials subject to cyclic patterns of stress and strain, where the ultimate failure of the material comes from the growth of a prominent flaw. In materials science, Miner's Rule suggests that the damage occurring after n cycles, at a stress level with an expected lifetime of N cycles, is proportional to n / N. Whenever Miner's Rule applies, the Birnbaum-Saunders model is a reasonable choice for a lifetime distribution model.


To estimate distribution parameters, us mle or the Distribution Fitter app.

See Also

Related Topics