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 →It is hard to quickly evaluate data in an everyday situation, but a nifty shortcut I saw on the R-bloggers aggregator can help.
read more →This analysis models the survival of 1,000 US men aged 60 who carry a life-limiting diagnosis (let’s say IPF) with:
read more →Information theoretic approaches view inference as a problem of model selection. The best model is the one that has the least information loss relative to the true model. Information criteria (IC) are estimates of the Kullback Leibler information loss, which cannot be calculated in real life mode...
read more →The hypergeometric distribution is used to solve the classic “balls in an urn” proble. Suppose one has 7 red balls and 3 white ball in an urn, and draws 2 balls. What is the probability that both balls are white?
read more →The binomial distribution is used when there are n (a fixed number) independent trials with two possible outcomes (“success” and “failure”) with a probability that is constant.
read more →The Poisson distribution is the workhorse for count data — the number of times something happens in a fixed interval of time, space, or volume. Named after French mathematician Siméon Denis Poisson (1837), it appears everywhere: call-centre arrivals, radioactive decay counts, hospital admissions,...
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