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Tilt transforms of delay distributions

Source: R/tilt_transform.R
pcens_tilt.Rd

Internal generics for the delay part of the analytical solutions with an exponentially tilted primary event window, see pcens_cdf_exptilt. They are built from the tilt transform \(T_f(\xi; \tau) = \int e^{\xi u} f(u) du\) up to \(\tau\), from 0 for delays on the non-negative reals. A delay is added with a method for each generic, dispatched on the delay class of a pcens object. The Stan equivalents are check_for_tilt_transform(), log_tilt_transform_pair() and primarycensored_tilt_moments().

Usage

.pcens_tilt_transform(object, t, xi, upper = FALSE)

.pcens_tilt_available(object, xi)

.pcens_tilt_lower(object)

.pcens_tilt_moments(object, t)

Arguments

object

A pcens object.

t

Numeric vector of points.

xi

The tilt, a single number or, for .pcens_tilt_transform(), a vector of the length of t. A window with tilt \(\rho\) needs xi = -rho.

upper

Logical. If TRUE, the transform over (t, Inf) rather than up to t.

Value

  • .pcens_tilt_transform(): the log of the transform at each t.

  • .pcens_tilt_available(): whether the transform is closed form and the tilted delay exists for xi. If not, the numerical method is used.

  • .pcens_tilt_lower(): the lower end of the support, 0 or -Inf.

  • .pcens_tilt_moments(): a matrix with columns G1, G2 and G3, the log of \(G_k(t) = \int (t - u)^k f(u) du\) up to t, -Inf below the support.