  We present a statistical analysis of time-resolved spontaneous emission decay
curves from ensembles of emitters, such as semiconductor quantum dots, with the
aim to interpret ubiquitous non-single-exponential decay. Contrary to what is
widely assumed, the density of excited emitters and the intensity in an
emission decay curve are not proportional, but the density is a time-integral
of the intensity. The integral relation is crucial to correctly interpret
non-single-exponential decay. We derive the proper normalization for both a
discrete, and a continuous distribution of rates, where every decay component
is multiplied with its radiative decay rate. A central result of our paper is
the derivation of the emission decay curve in case that both radiative and
non-radiative decays are independently distributed. In this case, the
well-known emission quantum efficiency can not be expressed by a single number
anymore, but it is also distributed. We derive a practical description of
non-single-exponential emission decay curves in terms of a single distribution
of decay rates; the resulting distribution is identified as the distribution of
total decay rates weighted with the radiative rates. We apply our analysis to
recent examples of colloidal quantum dot emission in suspensions and in
photonic crystals, and we find that this important class of emitters is well
described by a log-normal distribution of decay rates with a narrow and a broad
distribution, respectively. Finally, we briefly discuss the Kohlrausch
stretched-exponential model, and find that its normalization is ill-defined for
emitters with a realistic quantum efficiency of less than 100 %.
