Compute count probabilities based on modified renewal process (bi)

Compute count probabilities based on modified renewal process using dePril algorithm. dmodifiedCount_bi does it for the builtin distributions.

dmodifiedCount_user does the same for a user specified distribution.

dmodifiedCount_bi(
  x,
  distPars,
  dist,
  distPars0,
  dist0,
  nsteps = 100L,
  time = 1,
  extrap = TRUE,
  cdfout = FALSE,
  logFlag = FALSE
)

dmodifiedCount_user(
  x,
  distPars,
  survR,
  distPars0,
  survR0,
  extrapolPars,
  nsteps = 100L,
  time = 1,
  extrap = TRUE,
  cdfout = FALSE,
  logFlag = FALSE
)

Arguments

x: integer (vector), the desired count values.
distPars0, distPars: Rcpp::List with distribution specific slots for the first arrival and the rest of the process respectively.
dist0, dist: character, name of the first and following survival distributions.
nsteps: unsiged integer number of steps used to compute the integral.
time: double time at wich to compute the probabilities. Set to 1 by default.
extrap: logical if TRUE, Richardson extrapolation will be applied to improve accuracy.
cdfout: TODO
logFlag: logical if TRUE the log-probability will be returned.
survR0, survR: user supplied survival function; should have signature function(t, distPars), where t is a positive real number (the time at which the survival function is evaluated) and distPars is a list of distribution parameters. It should return a double value (first arrival and following arrivals respectively).
extrapolPars: list of same length as x, where each slot is a vector of length 2 (the extrapolation values to be used) corresponding to x[i].

Value

vector of probabilities P(x(i)) for i = 1, ..., n where n is the length of x.

Details

For the modified renewal process the first arrival is allowed to have a different distribution from the time between subsequent arrivals. The renewal assumption is kept.