Skip to contents

Score function (gradient of log-likelihood) for exponential series system (C1,C2,C3)

Source: R/md_candidate_set_models.R
md_score_exp_series_C1_C2_C3.Rd

Returns the score function (gradient of log-likelihood with respect to theta) for an exponential series system with masked data under C1, C2, C3 conditions.

Usage

md_score_exp_series_C1_C2_C3(
  md,
  sysvar = "t",
  setvar = "x",
  deltavar = "delta"
)

Arguments

md

Masked data frame containing:

  • System lifetime column (default: "t")

  • Candidate set columns (default: "x1", "x2", ..., "xm")

  • Optional right-censoring indicator (default: "delta")

sysvar

Column name for system lifetime. Default is "t".

setvar

Column prefix for candidate set (Boolean matrix). Default is "x".

deltavar

Column name for right-censoring indicator. Default is "delta". If NULL or column doesn't exist, assumes no censoring.

Value

A function g(theta) that computes the score (gradient) vector at parameter values theta = (lambda_1, ..., lambda_m).

Details

The score for component j is: $$\frac{\partial \ell}{\partial \lambda_j} = -\sum_i s_i + \sum_{i: \delta_i=0} \frac{I(j \in C_i)}{\sum_{k \in C_i} \lambda_k}$$

where I(j in C_i) is 1 if component j is in candidate set C_i, 0 otherwise.

Examples

if (FALSE) { # \dontrun{
md <- tibble::tibble(
  t = c(0.5, 1.2, 0.8),
  x1 = c(TRUE, TRUE, FALSE),
  x2 = c(TRUE, FALSE, TRUE),
  x3 = c(FALSE, TRUE, TRUE)
)
score <- md_score_exp_series_C1_C2_C3(md)
score(c(1, 1.5, 2))
} # }