Description Usage Arguments Author(s) References See Also Examples
This is the main function of the package EstSimPDMP. It computes the estimation of the density associated to the jump rate for a piecewise-deterministic Markov process (PDMP) whose state space is continuous. Details about the estimator are given in the paper mentioned in References.
1 | CondPdf.CC.interval(dat,x,epsilon,tmin,tmax,nbre,h,alpha,verbose,bound)
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dat |
data from which the estimator is to be computed. It corresponds to the observation of a PDMP within a long time. dat is a matrix such that the last column contains the interarrival times, while the other columns contain the post-jump locations of the process. |
x |
the conditional probability density function is estimated given state is around x. |
epsilon |
the probability density function is estimated given the distance between state and x is less than epsilon. If epsilon is small, this is an approximation of the exact density. |
tmin |
the probability density function is estimated between tmin and tmax. |
tmax |
the probability density function is estimated between tmin and tmax. In addition, tmax must be less than bound. |
nbre |
size of the grid plot. |
h |
bandwith |
alpha |
strictly positive real number. If h is NULL, the bandwith is 1/n^alpha where n is the number of data. |
verbose |
if TRUE, add a plot between tmin and tmax. |
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 |
Romain Azais
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.interval
, Simu.PDMP
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | # CondPdf.CC.interval
# Simulation of a PDMP with continuous state space
dat<-Simu.PDMP(2.3,500,verbose=FALSE)
# Estimation of the conditional density given state=1.8
CondPdf.CC.interval(dat,1.8,0.3,0.5,7.5,70,h=1/3,bound=7.8)
tmin<-0.5
tmax<-7.5
N<-70
a<-tmin:N*tmax
a<-a/N
x<-1.8
# Theoretical conditional pdf given state=1.8
grid<-(1/(1+x))*exp(-(1/(1+x))*a)
points(a,grid,"l",col="blue")
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