  Daily precipitation time series are composed of null entries corresponding to
dry days and nonzero entries that describe the rainfall amounts on wet days.
Assuming that wet days follow a Bernoulli process with success probability $p$,
we show that the presence of dry days induces negative correlations between
record-breaking precipitation events. The resulting non-monotonic behavior of
the Fano factor of the record counting process is recovered in empirical data.
We derive the full probability distribution $P(R,n)$ of the number of records
$R_n$ up to time $n$, and show that for large $n$, its large deviation form
coincides with that of a Poisson distribution with parameter $\ln(p\,n)$. We
also study in detail the joint limit $p \to 0$, $n \to \infty$, which yields a
random record model in continuous time $t = pn$.
