linear.kernel: Integration with respect to locally weighted kernel

In seismic: Predict Information Cascade by Self-Exciting Point Process

Integration with respect to locally weighted kernel

Description

Integration with respect to locally weighted kernel

Usage

linear.kernel(t1, t2, ptime, slope, c = 0.0006265725)

power.kernel(
  t1,
  t2,
  ptime,
  share.time,
  slope,
  theta = 0.2314843,
  cutoff = 300,
  c = 0.0006265725
)

integral.memory.kernel(
  p.time,
  share.time,
  slope,
  window,
  theta = 0.2314843,
  cutoff = 300,
  c = 0.0006265725
)

Arguments

t1	a vector of integral lower limit
t2	a vector of integral upper limit
ptime	the time (a scalar) to estimate infectiousness and predict for popularity
slope	slope of the linear kernel
c	the constant density when t is less than the cutoff
share.time	observed resharing times, sorted, share.time[1] =0
theta	exponent of the power law
cutoff	the cutoff value where the density changes from constant to power law
p.time	equally spaced vector of time to estimate the infectiousness, p.time[1]=0
window	size of the linear kernel

Value

linear.kernel returns the integral from vector t1 to vector t2 of c*[slope(t-ptime) + 1]; power.kernel returns the integral from vector t1 to vector 2 of c*((t-share.time)/cutoff)^(-(1+theta))[slope(t-ptime) + 1]; integral.memory.kernel returns the vector with ith entry being integral_-inf^inf phi_share.time[i]*kernel(t-p.time)

Functions

• power.kernel: Power-law kernel

• integral.memory.kernel: Integral of the kernel

See Also

memory.pdf

seismic documentation built on May 21, 2022, 1:05 a.m.