Survival function of posting durations — duration

From a table of duration counts, returns per group the share of postings still open j days after their start, for j = 0, ..., max_duration.

Usage

duration_survival(
  durations,
  by = NULL,
  duration_col = "duration",
  n_col = "n",
  max_duration = NULL
)

Arguments

durations: A data.frame or data.table of durations, one row per duration value (and group), or one row per posting when n_col is NULL.
by: Character vector of grouping columns, or NULL for no grouping.
duration_col: Name of the duration column (non-negative integer days).
n_col: Name of the count column (number of postings with that duration), or NULL to count each row once.
max_duration: Last value of j in the output (single non-negative integer). Default: the largest observed duration over all groups, so that every group has the same grid.

Value

A data.table with columns by, j (integer, 0..max_duration) and surv (double, in [0, 1]), ordered by by and j.

Details

The duration is end - start in days, so a posting open on start..end (end inclusive) stays in the stock for duration + 1 days. The function returns surv(j) = P(duration >= j), the share of postings still open on day start + j; surv(0) = 1 and the curve is non-increasing. Used as weights G(j) by standardized_stock().

When max_duration is smaller than the largest observed duration, longer durations count as max_duration: the values of surv for j <= max_duration are unchanged, only the grid is truncated.

Examples

d <- data.table::data.table(
  source = c("a", "a", "b"),
  duration = c(2L, 5L, 3L),
  n = c(30L, 70L, 10L)
)
duration_survival(d, by = "source")
#>     source     j  surv
#>     <char> <int> <num>
#>  1:      a     0   1.0
#>  2:      a     1   1.0
#>  3:      a     2   1.0
#>  4:      a     3   0.7
#>  5:      a     4   0.7
#>  6:      a     5   0.7
#>  7:      b     0   1.0
#>  8:      b     1   1.0
#>  9:      b     2   1.0
#> 10:      b     3   1.0
#> 11:      b     4   0.0
#> 12:      b     5   0.0