# linear.kernel: Integration with respect to locally weighted kernel In seismic: Predict Information Cascade by Self-Exciting Point Process

## Description

Integration with respect to locally weighted kernel

## Usage

 ```1 2 3 4 5 6 7``` ```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 =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=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`:

• `integral.memory.kernel`:

`memory.pdf`