Using a novel approach we have reanalized the question of whether the extreme star forming galaxies known as HII galaxies are truly young or rejuvenated old systems. We first present a method of inversion that applies to any monotonic function of time describing the evolution of independent events. We show that, apart from a normalization constant, the ``true time dependence can be recovered from the inversion of its probability density function. We applied the inversion method to the observed equivalent width of Hbeta (EW(Hbeta)) distribution for objects in the Terlevich and collaborators Spectrophotometric Catalogue of HII galaxies and found that their global history of star formation behaves much closer to the expectations of a continuos star formation model than to an instantaneous one. On the other hand, when the inversion method is applied to samples within a restricted metallicity range we find that their history of star formation behaves much closer to what the instantaneous model predicts. Our main conclusion is that, globally, the evolution of HII galaxies seems consistent with a succession of short starbursts separated by quiescent periods and that, while the emission lines trace the properties of the present burst, the underlying stellar continuum traces the whole star formation history of the galaxy. Thus, observables like the EW(Hbeta) that combine an emission line flux, i.e. a parameter pertaining to the present burst, with the continuum flux, i.e. a parameter that traces the whole history of star formation, should not be used alone to characterize the present burst.
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