is denoted by continuous probability distribution probability distribution scale parameter probability distribution shape parameter probability distribution location parameter Weibull probability distribution Weibull distribution Philippe Rocca-Serra Weibull probability distribution adapted from : https://en.wikipedia.org/wiki/Weibull_distribution and from http://www.engineeredsoftware.com/nasa/weibull.htm pweibull(q, shape, scale = 1, lower.tail = TRUE, log.p = FALSE) from: https://stat.ethz.ch/R-manual/R-devel/library/stats/html/Weibull.html scipy.stats.weibull_min from: https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.weibull_min.html#scipy.stats.weibull_min the Weibull probability distribution is continuous probabibility distribution which is used to model time to fail, time to repair and material strength in material science. In biomedicine, the Weibull probability is used to in determining 'hazard functions'. The 'location parameter' of the Weibull probability distribution can be used to define a failure-free zone. If the quantity X is a "time-to-failure", the Weibull distribution gives a distribution for which the failure rate is proportional to a power of time. The shape parameter, k, is that power plus one, and so this parameter can be interpreted directly as follows: A value of {\displaystyle k<1\,} {\displaystyle k<1\,} indicates that the failure rate decreases over time. This happens if there is significant "infant mortality", or defective items failing early and the failure rate decreasing over time as the defective items are weeded out of the population. In the context of the diffusion of innovations, this means negative word of mouth: the hazard function is a monotonically decreasing function of the proportion of adopters; A value of {\displaystyle k=1\,} {\displaystyle k=1\,} indicates that the failure rate is constant over time. This might suggest random external events are causing mortality, or failure. The Weibull distribution reduces to an exponential distribution; A value of {\displaystyle k>1\,} {\displaystyle k>1\,} indicates that the failure rate increases with time. This happens if there is an "aging" process, or parts that are more likely to fail as time goes on. In the context of the diffusion of innovations, this means positive word of mouth: the hazard function is a monotonically increasing function of the proportion of adopters. The function is first concave, then convex with an inflexion point at {\displaystyle (e^{1/k}-1)/e^{1/k},k>1\,} {\displaystyle (e^{1/k}-1)/e^{1/k},k>1\,}. ready for release