Type   II and III solar radio bursts involve streaming electrons that produce   Langmuir waves that then couple wave energy into radio emission. These Langmuir waves can be driven to large enough amplitudes that they undergo electrostatic (ES) decay into   a backward propagating Langmuir wave and forward propagating ion acoustic wave. The forward and backwards propagating Langmuir waves can then “beat” together to produce   characteristic Langmuir waveforms and spectra, plus radio emission. Stochastic growth   theory (SGT) predicts that the probability distribution of the Langmuir wave electric   field strength should be lognormal, with known modifications if nonlinear processes like ES decay are occurring.

   Other analyses suggest Pearson distributions may be relevant. Here,   previous work on Langmuir waves in type II and III source regions is generalized and tested by analysing the probability distributions of the waveforms of Langmuir waves observed by   the STEREO spacecraft. The focus is on a set of published events identified using   spectral analyses to have or not have spectral evidence for ES decay. For events for which spectral  analyses provide   evidence of ES decay, 86%of the probability distributions are consistent   with the combination of SGT and a nonlinear process like ES decay, while of those without  spectral evidence for ES    decay 78% of the probability distributions are well fitted by pure SGT.   Moreover, better fits with stronger statistical significance are obtained for pure and nonlinear   SGT than for Pearson distributions in the majority of events (-90%). These results provide   strong evidence for SGT  and ES decay proceeding in type II and III source regions.