Question

Refer to the air-conditioning data set aircondit provided in the boot package. The 12 observations are the times in hours between failures of air-conditioning equipment

3, 5, 7, 18, 43, 85, 91, 98, 100, 130, 230, 487.

Assume that the times between failures follow an exponential model Exp(λ). Obtain the MLE of the hazard rate λ and use bootstrap to estimate the bias and standard error of the estimate

Use R software .

Answer 1

For bias and SE using bootstrap, we use R package "boot".

We obtain bootstrap estimate of bias as  0.001353666 and SE as 0.004556693

R Program

library(boot)
x=c(3, 5, 7, 18, 43, 85, 91, 98, 100, 130, 230, 487)
f=function(data, indices)
{
d=data[indices] # allows boot to select sample
y=1/mean(d)
return(y)
}
bootmle=boot(x,f,R=10000)
bootmle

R Output

ORDINARY NONPARAMETRIC BOOTSTRAP

Call:
boot(data = x, statistic = f, R = 10000)

Bootstrap Statistics :
original bias std. error
t1* 0.00925212 0.001353666 0.004556693