In probability theory and statistics, the<unk>  (named after Waloddi<unk>  is a continuous probability distribution with the probability density function
for 
x
≥
0
{\displaystyle x\geq 0}
 and f(x; k, λ) = 0 for x < 0, where 
k
>
0
{\displaystyle k>0}
 is the shape parameter and 
λ
>
0
{\displaystyle \lambda >0}
 is the scale parameter of the distribution. Its complementary cumulative distribution function is a stretched exponential.
The<unk>  is often used in the field of life data analysis due to its flexibility—it can mimic the behavior of other statistical distributions such as the normal and the exponential.  If the failure rate decreases over time, then k < 1.  If the failure rate is constant over time, then k = 1. If the failure rate increases over time, then k > 1.
An understanding of the failure rate may provide insight as to what is causing the failures:
A decreasing failure rate would suggest "infant mortality".  That is, defective items fail early and the failure rate decreases over time as they fall out of the population.
A constant failure rate suggests that items are failing from random events.
An increasing failure rate suggests "wear out" - parts are more likely to fail as time goes on.
When k = 3.4, then the<unk>  appears similar to the normal distribution.
When k = 1, then the<unk>  reduces to the exponential distribution.
Weibull distribution
Degrees of freedom 
Absolute deviation
Binomial distribution
Ancillary statistic
Covariance matrix
Allan variance
Dominance relationship