Description Details Author(s) References See Also Examples
This package deals with the estimation of the jump rate for piecewise-deterministic Markov processes (PDMPs), from only one observation of the process within a long time. The main functions provide an estimate of this function. The state space may be discrete or continuous. The associated paper is given in References. Other functions provide a method to simulate random variables from their (conditional) hazard rate, and then to simulate PDMPs.
Package: | EstSimPDMP |
Type: | Package |
Version: | 1.2 |
Date: | Nov 2014 |
License: | GPL (>=2) |
Simu.Cond.HR(n,lambda,x)
CondPdf.DC.interval(data,x,tmin,tmax,N)
CondPdf.CC.interval(data,x,epsilon,tmin,tmax,N)
Romain AZAIS <romain.azais@gmail.com>
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
, CondPdf.CC.interval
, Simu.HR
, Simu.Cond.HR
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 | # Simu.Cond.HR
example<-function(x,t){
sqrt(sum(x^2))+t
}
# Simulations of 50 iid random variables with hazard rate=example given x=3
Simu.Cond.HR(50,example,3)
# Simulations of 50 iid random variables with hazard rate=example given x=0.5
# Simu.Cond.HR(50,example,0.5)
# CondPdf.DC.interval
# Simulation of a PDMP with discrete state space
dat<-Simu.PDMP.DC(1,500,verbose=FALSE)
# Estimation of the conditional density given state=2
CondPdf.DC.interval(dat,2,0.4,5.5,70,alpha=1/4,bound=5.8)
tmin<-0.4
tmax<-5.5
N<-70
a<-(N*tmin):(N*tmax)
a<-a/N
# Conditional density given state=2
gr<-exp(-a)
# Theoretical conditional pdf
points(a,gr,"l",col="blue")
# 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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