  Suppose that $n$ drivers each choose a preferred parking space in a linear
car park with $m$ spaces. Each driver goes to the chosen space and parks there
if it is free, and otherwise takes the first available space with larger number
(if any). If all drivers park successfully, the sequence of choices is called a
parking function. In general, if $k$ drivers fail to park, we have a
\emph{defective parking function} of \emph{defect} $k$. Let $\cp(n,m,k)$ be the
number of such functions.
  In this paper, we establish a recurrence relation for the numbers
$\cp(n,m,k)$, and express this as an equation for a three-variable generating
function. We solve this equation using the kernel method, and extract the
coefficients explicitly: it turns out that the cumulative totals are partial
sums in Abel's binomial identity. Finally, we compute the asymptotics of
$\cp(n,m,k)$. In particular, for the case $m=n$, if choices are made
independently at random, the limiting distribution of the defect (the number of
drivers who fail to park), scaled by the square root of $n$, is the Rayleigh
distribution. On the other hand, in case $m=\omega(n)$, the probability that
all spaces are occupied tends asymptotically to one.
