Facing the first times of occurence of events of a new type, such as seismic events, arrivals of individuals of a unknown species, occurrences of cases of a new disease..., it is crucial to predict if these events are only ?sporadic?, or if they announce an emerging phenomenon (earthquake, emergence of a population, epidemic). We propose here an exact nonparametric test statistic based on the number of lower records Nn in {?Tk}1 ≤ k ≤ n, ?Tk being the waiting time between two successive events. Under H0 (sporadic events), the {?Tk} are assumed i.i.d., while under H1 (emergent events), the {?Tk} are assumed independent with cdf?s (Cumulative Distributions Functions) {Gk} increasing with k. Under H0, the distribution of Nn is independent of Gk, thus allowing a nonparametric test of H0. To calculate the power of the test under the alternative hypothesis H1, we assume the particular family of cdf?s, , , where G is a continuous cdf on (0, ∞) and a > 1. These distributions represent an exponential occurrence rate of events. We show that the distribution of Nn under H1 depends only on a (and not on G). We estimate a by the Maximum Likelihood Estimator, and give the asymptotic properties of this estimator, as n ? ∞. Finally we illustrate the test on simulations and then on data concerning the atypical BSE (Bovine Spongiform Encephalopathy) in France.