Neutral-to-the-right processes

F(t) = 1 - exp(-M(t)) for M an independent-increment process. Neutral to the right means the relative survival fractions over disjoint intervals are INDEPENDENT, and that independence is what makes the class closed under right censoring – the property the Dirichlet process itself has and shares with the beta process.

Usage

Ghosalntrdef(increments, seed = 42)

Arguments

increments

Non-negative increments of M.

seed

Unused; kept for call compatibility.

Value

List with estimate (terminal CDF value), F_path, nondecreasing, method.

Details

Formula: F(t_k) = 1 - exp(-sum_{j <= k} inc_j).

References

Ghosal & van der Vaart (2017), Fundamentals of Nonparametric Bayesian Inference, CUP, section 13.4.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Ghosalntrdef(V)
#> $estimate
#> [1] 1
#> 
#> $F_path
#> [1] 0.6321206 0.9502129 0.9975212 0.9999546 0.9999997 1.0000000 1.0000000
#> [8] 1.0000000
#> 
#> $nondecreasing
#> [1] TRUE
#> 
#> $method
#> [1] "NTR construction (GvdV 2017 sec. 13.4)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"