CondPdf.DC: Estimation of the density associated to the jump rate for piecewise-deterministic Markov processes (discrete state space)
Description
This function computes the estimation of the density associated to the jump rate for a piecewise-deterministic Markov process whose state space is finite. The estimator is given in the paper mentioned in References.
Usage
CondPdf.DC(dat,x,t,h,alpha,bound)
Arguments
dat
data from which the estimator is to be computed. It corresponds to the observation of a process within a long time. dat is a matrix such that the last column contains the interarrival times, while the other columns contain the states.
x
the conditional probability density function is estimated given state=x.
t
the conditional probability density function is estimated at time t. In addition, t must be less than bound.
h
bandwith
alpha
strictly positive real number. If h is NULL, the bandwith is 1/n^alpha where n is the number of data.
bound
the estimator is computed as an integral between the times 0 and bound. bound must be less than the deterministic exit time function tstar computed at state x
References
Azais R., Dufour F., and Gegout-Petit A. Nonparametric estimation of the conditional distribution of the inter-jumping times for piecewise-deterministic Markov processes Scandinavian Journal of Statistics, 2014.
# CondPdf.DC# Simulation of a PDMP with discrete state spacedat<-Simu.PDMP.DC(1,200,verbose=FALSE)
# Estimation of the conditional density given state=2 at time 2CondPdf.DC(dat,2,2,bound=5.8)