Statistical Methods
Interpret a Weibull shape through survival and cumulative hazard
Define the task
A Weibull model needs a positive shape and a positive scale in time units. Preserve parameter names when transferring estimates between packages. A coefficient called scale in an accelerated failure-time model can use a different convention. Confirm the survival equation before inserting any exported number into a calculator.
Carry out the check
Using shape k and time scale s, cumulative hazard at t is (t/s)^k and survival is exp(−(t/s)^k). At t=s, survival equals exp(−1) for every positive shape. For positive times, the hazard decreases when k is below one, is constant at one, and increases above one. These statements describe the specified distribution and should be checked against the generating process.
Worked hypothetical example
For hypothetical shape 2 and scale 10 days, cumulative hazard at day 5 is 0.25 and survival is approximately 0.7788. At day 10, survival is approximately 0.3679. The scale is therefore not generally a median. The median here is 10 times the square root of log(2), about 8.326 days. Censoring and uncertainty need a separate fitted-model analysis.
Method checked 11 November 2026 against R documentation: The Weibull Distribution.