predDen {MRHawkes}

MRHawkes (bivariate) predictive density function

Description

Calculates the predictive density of the next event time after the censoring time cens based on the observations over the interval [0,cens].

Usage

predDen(x, data, cens, par, 
        h1.fn = function(x, p) 1 / p * exp( - x / p),
        h2.fn = function(x, p) 1 / p * exp( - x / p),
        mu1.fn = function(x, p){
          exp(dweibull(x, shape = p[1], scale = p[2], log = TRUE) -
               pweibull(x, shape = p[1], scale = p[2], lower.tail = FALSE, 
                        log.p = TRUE))
        },
        mu2.fn = function(x, p){
         exp(dweibull(x, shape = p[1], scale = p[2], log = TRUE) -
               pweibull(x, shape = p[1], scale = p[2], lower.tail = FALSE, 
                        log.p = TRUE))
        },
        H1.fn = function(x, p) pexp(x, rate = 1 / p),
        H2.fn = function(x, p) pexp(x, rate = 1 / p),
        Mu1.fn = function(x, p){
         - pweibull(x, shape = p[1], scale = p[2], lower.tail = FALSE, 
                    log.p = TRUE)
        },
        Mu2.fn = function(x, p){
         - pweibull(x, shape = p[1], scale = p[2], lower.tail = FALSE, 
                    log.p = TRUE)
        })

Arguments

x

A scalar. The amount of time after the censoring tine cens.

data

A two column matrix. The first column contains the event times sorted in ascending order. The second column contains the corresponding event type with the label one or two.

cens

A scalar. The censoring time.

par

A numeric vector containing the twelve parameters of the model, in order of the immigration parameters \mu(.) for the two component distributions, the four offspring parameters h(.) and lastly the four branching ratios \eta.

h1.fn

A (vectorized) function. The offspring density function for type one events.

h2.fn

A (vectorized) function. The offspring density function for type two events.

mu1.fn

A (vectorized) function. The immigration hazard function for events of type one.

mu2.fn

A (vectorized) function. The immigration hazard function for events of type two.

H1.fn

A (vectorized) function. Its value at t gives the integral of the offspring density function from 0 to t for type one events.

H2.fn

A (vectorized) function. Its value at t gives the integral of the offspring density function from 0 to t for type two events.

Mu1.fn

A (vectorized) function. Its value at t gives the integral of the immigrant hazard function from 0 to t for type one events.

Mu2.fn

A (vectorized) function. Its value at t gives the integral of the immigrant hazard function from 0 to t for type two events.

Value

The predictive density of the next event time evaluated at x.

Author(s)

Tom Stindl <[e-mail]> Feng Chen <[e-mail]>

Examples

  ## Magnitude 5.5 or greater earthquakes over the 25 year period from 
  ## 01/01/1991 to 31/12/2015.  
  data(fivaqks); 
  near.fiji <- grep("Fiji", fivaqks$place)
  near.vanuatu <- grep("Vanuatu", fivaqks$place)
  t.beg <- strptime("1991-01-01 00:00:00", "%Y-%m-%d %H:%M:%S", tz = "UTC")
  t.end <- strptime("2015-12-31 23:59:59", "%Y-%m-%d %H:%M:%S", tz = "UTC")
  t0 <- 0
  t1 <- as.numeric(t.end - t.beg)
  tms <- strptime(fivaqks$time, "%Y-%m-%dT%H:%M:%OSZ", tz = "UTC")
  ts <- as.numeric(tms[-1] - t.beg)
  ts <- c(as.numeric(tms[1] - t.beg)/24, ts)
  ts.fi <- ts[near.fiji]; ts.fi <- ts.fi[ts.fi >= 0 & ts.fi <= t1]
  ts.va <- ts[near.vanuatu]; ts.va <- ts.va[ts.va >=0 & ts.va <= t1]
  ts.c <- c(ts.fi, ts.va)
  z.c <- c(rep(1, times = length(ts.fi)), rep(2, times = length(ts.va)))
  o <- order(ts.c)
  data <- cbind(ts.c[o], z.c[o])
  curve(predDen(x, data = data, cens = t1, 
                 par = c(0.488, 20.10, 0.347, 9.53, 461, 720, 
                         0.472, 0.293, 0.399, -0.0774)) 
        ,0 ,200, col = "red", lwd = 2, ylab = "Density")