The Weibull distribution is exceptionally well-suited to clinical and biomedical research because its shape parameter \(k\) carries direct interpretive meaning: whether the hazard of an event is decreasing (\(k < 1\)), constant (\(k = 1\)), or increasing (\(k > 1\)) over time. Below are thr...
read more →The Weibull distribution is one of the most widely used distributions in reliability engineering, survival analysis, and failure-time modelling. Named after Swedish engineer Waloddi Weibull (1951), it is prized for its flexibility: by tuning just two parameters it can mimic an exponential, a norm...
read more →An elegant way to demonstrate the Monte Carlo technique is by estimating \(\pi\) in a simple geometry problem. Given a circle of radius r inscribed in a square of side 2r, the area of the circle is \(\pi*r^2\) and the area of the square is \(4r^2\). The ratio of those areas is \(\pi /4\), so if y...
read more →This analysis models the survival of 1,000 US men aged 60 who carry a life-limiting diagnosis (letโs say IPF) with:
read more →