Log CDFs for the ode function

Helper function to compute the log CDF for the delay distribution. More...

Collaboration diagram for Log CDFs for the ode function:

Functions
real	gengamma_lcdf (real y, real shape, real scale, real k)
int	dist_has_positive_support (data int dist_id)
int	lognormal_lcdf_underflows (real y, real mu, real sigma)
real	dist_lcdf (real delay, array[] real params, int dist_id)

Description

Helper function to compute the log CDF for the delay distribution.

Function Documentation

dist_has_positive_support()

int dist_has_positive_support

(

data int

dist_id

)

Test whether a delay distribution has support only on the non-negative reals

Used internally to decide whether to short-circuit dist_lcdf at delay <= 0 and whether the ODE / nested CDF calls need to integrate over negative arguments. Returns 1 for distributions with strictly non-negative support, 0 otherwise. IDs match pcd_distributions$stan_id in R.

Parameters

dist_id

Distribution identifier

Returns

1 if the delay distribution has non-negative support, 0 otherwise.

Definition at line 33 of file primarycensored_ode.stan.

Here is the caller graph for this function:

dist_lcdf()

real dist_lcdf	(	real	delay,
		array[]real	params,
		int	dist_id )

Compute the log CDF of the delay distribution

Parameters

delay	Time delay
params	Distribution parameters
dist_id	Distribution identifier matching pcd_distributions in R: 1: Lognormal, 2: Gamma, 3: Weibull, 4: Exponential, 5: Generalised gamma, 9: Beta, 12: Cauchy, 13: Chi-square, 15: Gumbel, 16: Inverse Gamma, 17: Logistic, 18: Normal, 19: Inverse Chi-square, 20: Double Exponential, 21: Pareto, 22: Scaled Inverse Chi-square, 23: Student's t, 24: Uniform, 25: von Mises, 26: Non-parametric step (params = [boundaries (K+1), pmf (K)], length 2*K + 1), 27/28: Non-parametric discrete hazard (params = [boundaries (K+1), hazards (K)], length 2*K + 1; hazards[K] must equal 1). 27 and 28 share this likelihood and only differ in the prior on the hazards (random walk for 27, IID random effect for 28).

Returns

Log CDF of the delay distribution

// Example: Lognormal distribution
real delay = 5.0;
array[2] real params = {0.0, 1.0}; // mean and standard deviation on log scale
int dist_id = 1; // Lognormal
real log_cdf = dist_lcdf(delay, params, dist_id);

Definition at line 107 of file primarycensored_ode.stan.

Here is the call graph for this function:

Here is the caller graph for this function:

gengamma_lcdf()

real gengamma_lcdf	(	real	y,
		real	shape,
		real	scale,
		real	k )

Compute the log CDF of the generalised gamma distribution

Uses the Stacy parameterisation of flexsurv::pgengamma.orig() in R. The CDF is the regularised lower incomplete gamma function P(k, (y / scale)^shape), so the Gamma (shape = 1) and Weibull (k = 1) distributions are special cases.

Parameters

y	Value at which to evaluate the log CDF (y > 0)
shape	Shape (power) parameter
scale	Scale parameter
k	Shape parameter of the underlying Gamma distribution

Returns

Log CDF of the generalised gamma distribution

Definition at line 17 of file primarycensored_ode.stan.

Here is the caller graph for this function:

lognormal_lcdf_underflows()

int lognormal_lcdf_underflows	(	real	y,
		real	mu,
		real	sigma )

Test whether lognormal_lcdf underflows to -inf at these arguments

Underflow makes the autodiff partial 0 / 0, and Stan's reverse pass chains that NaN into mu and sigma whatever weight the term is later given. Callers must therefore test this before calling lognormal_lcdf, rather than checking its result.

The threshold is -38 on the standardised scale (log(y) - mu) / sigma, inside the region where the CDF is still representable: log F(y) is below -726 there, so a term dropped on this test cannot change a result at double precision.

Parameters

y	Value at which the log CDF would be evaluated
mu	Location parameter on the log scale
sigma	Scale parameter on the log scale

Returns

1 if lognormal_lcdf would underflow or y is non-positive, 0 otherwise

Definition at line 69 of file primarycensored_ode.stan.

Here is the caller graph for this function: