Read the equation
This relation defines (1 based, index m-1 in the returned vector), hazard[m] in the source section “survival · (1 based, index m-1 in the returned vector), hazard[m]”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.
Terms & definitions
The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.
How it works
Read (1 based, index m-1 in the returned vector), hazard[m] as the quantity being defined or updated by this relation.
Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.
Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.
Assumptions & limits
This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.
Original context
Read the surrounding source passage
// at the last period (Filled false). Periods is at least 1.
type Duration struct {
Periods int
Filled bool
}
// EmpiricalHazard estimates the discrete time hazard per period from right censored durations. For each period m
// (1 based, index m-1 in the returned vector), hazard[m] = events at m / at risk at m, where at risk at m counts
// every observation whose Periods is at least m (it reached period m still open at the start of it), and events
// at m counts the observations that Filled exactly at period m. A still open (censored) observation contributes
// to every at risk denominator through its observed periods but to no event numerator. The returned vector has
// length maxPeriod; a period with no one at risk has hazard 0 (no evidence of filling then). maxPeriod at most 1
// returns a single period.
func EmpiricalHazard(durations []Duration, maxPeriod int) []float64 {
if maxPeriod < 1 {
maxPeriod = 1
}
events := make([]float64, maxPeriod)Exact original notation
(1 based, index m-1 in the returned vector), hazard[m] = events at m / at risk at m, where at risk at m counts