draw_cumulative_intensity

Sample NHPPP times using the inversion method

Simulates events from one dimensional nonhomogeneous Poisson point processes (NHPPPs) as per Trikalinos and Sereda (2024, <doi:10.48550/arXiv.2402.00358> and 2024, <doi:10.1371/journal.pone.0311311>). Functions are based on three algorithms that provably sample from a target NHPPP: the time-transformation of a homogeneous Poisson process (of intensity one) via the inverse of the integrated intensity function (Cinlar E, "Theory of stochastic processes" (1975, ISBN:0486497996)); the generation of a Poisson number of order statistics from a fixed density function; and the thinning of a majorizing NHPPP via an acceptance-rejection scheme (Lewis PAW, Shedler, GS (1979) <doi:10.1002/nav.3800260304>).

Thomas Trikalinos

nhppp

Simulating Nonhomogeneous Poisson Point Processes

Yuliia Sereda

draw_cumulative_intensity function

<dl><dt>Lambda</dt>
<dd>(function, double vector) a continuous increasing R to R map
which is the integrated rate of the NHPPP</dd>
<dt>Lambda_inv</dt>
<dd>(function, double vector) the inverse of <code>Lambda()</code></dd>
<dt>t_min</dt>
<dd>(double) the lower bound of the time interval</dd>
<dt>t_max</dt>
<dd>(double) the upper bound of the time interval</dd>
<dt>atmost1</dt>
<dd>boolean, draw at most 1 event time</dd></dl>

Arguments

Simulate from a non homogeneous Poisson Point Process (NHPPP)
over an interval when you know the cumulative intensity and its inverse. — draw_cumulative_intensity

<dl>

<dt>Lambda</dt>
<dd>(function, double vector) a continuous increasing R to R map
which is the integrated rate of the NHPPP</dd>


<dt>Lambda_inv</dt>
<dd>(function, double vector) the inverse of <code>Lambda()</code></dd>


<dt>t_min</dt>
<dd>(double) the lower bound of the time interval</dd>


<dt>t_max</dt>
<dd>(double) the upper bound of the time interval</dd>


<dt>atmost1</dt>
<dd>boolean, draw at most 1 event time</dd>

</dl>

draw_cumulative_intensity: Simulate from a non homogeneous Poisson Point Process (NHPPP) over an interval when you know the cumulative intensity and its inverse.

Description

Usage

Value

Arguments