Is the Weibull Distribution Effective for β < 1 Despite Divergence at t=0?

[free_electron]

When the weibull shape parameter beta is <1, the pdf is divergent at t=0 due to negative exponent of beta -1. With such a divergent distribution is it meaningful to use Weibull for beta <1?

 

[john.phillip]

"The Weibull failure rate for 0 < β < 1 is unbounded at T = 0 (or γ). The failure rate, λ(T), decreases thereafter monotonically and is convex, approaching the value of zero as MATH or λ() = 0. This behavior makes it suitable for representing the failure rate of units exhibiting early-type failures, for which the failure rate decreases with age. When encountering such behavior in a manufactured product, it may be indicative of problems in the production process, inadequate burn-in, substandard parts and components, or problems with packaging and shipping."

http://www.weibull.com/LifeDataWeb/characteristics_of_the_weibull_distribution.htm