Description Usage Arguments Details Value Author(s) See Also Examples
Estimate refractory exponential model parameters by the maximum likelihood method using possibly censored data.
1 2 |
yi |
vector of (possibly binned) observations or a
|
ni |
vector of counts for each value of |
si |
vector of counts of uncensored observations for each
value of |
The MLE are available in closed form even in the censored case for
this model. The likelihood function cannot be differentiated with
respect to the rp
(refractory period) parameter at the
maximum. COnfidence intervals for this parameter are therefore not
available.
A list of class durationFit
with the following components:
estimate |
the estimated parameters, a named vector. |
se |
the standard errors, a named vector. |
logLik |
the log likelihood at maximum. |
r |
a function returning the log of the relative likelihood function. |
mll |
a function returning the opposite of the log likelihood function using the log of the parameters. |
call |
the matched call. |
Christophe Pouzat christophe.pouzat@gmail.com
drexp
,
invgaussMLE
,
lnormMLE
,
gammaMLE
,
weibullMLE
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 | ## Not run:
## Simulate sample of size 100 from a refractory exponential distribution
set.seed(1102006,"Mersenne-Twister")
sampleSize <- 100
rate.true <- 20
rp.true <- 0.01
sampRE <- rrexp(sampleSize,rate=rate.true,rp=rp.true)
sampREmleRE <- rexpMLE(sampRE)
rbind(est = sampREmleRE$estimate,se = sampREmleRE$se,true = c(rate.true,rp.true))
## make a parametric boostrap to check the distribution of the deviance
nbReplicate <- 10000
system.time(
devianceRE100 <- replicate(nbReplicate,{
sampRE <- rrexp(sampleSize,rate=rate.true,rp=rp.true)
sampREmleRE <- rexpMLE(sampRE)
-2*sampREmleRE$r(rate.true,rp.true)
}
)
)[3]
## Get 95 and 99% confidence intervals for the QQ plot
ci <- sapply(1:nbReplicate,
function(idx) qchisq(qbeta(c(0.005,0.025,0.975,0.995),
idx,
nbReplicate-idx+1),
df=2)
)
## make QQ plot
X <- qchisq(ppoints(nbReplicate),df=2)
Y <- sort(devianceRE100)
X11()
plot(X,Y,type="n",
xlab=expression(paste(chi[2]^2," quantiles")),
ylab="MC quantiles",
main="Deviance with true parameters after ML fit of refractory Poisson data",
sub=paste("sample size:", sampleSize,"MC replicates:", nbReplicate)
)
abline(a=0,b=1)
lines(X,ci[1,],lty=2)
lines(X,ci[2,],lty=2)
lines(X,ci[3,],lty=2)
lines(X,ci[4,],lty=2)
lines(X,Y,col=2)
## End(Not run)
|
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