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We present analytical reconstructions of type Ia supernova (SN Ia) delay time distributions (DTDs) by way of two independent methods: by a Markov chain Monte Carlo best-fit technique comparing the volumetric SN Ia rate history to today's compendium cosmic star-formation history, and secondly through a maximum likelihood analysis of the star formation rate histories of individual galaxies in the GOODS/CANDELS field, in comparison to their resultant SN Ia yields. We adopt a flexible skew-normal DTD model, which could match a wide range of physically motivated DTD forms. We find a family of solutions that are essentially exponential DTDs, similar in shape to the $β\approx-1$ power-law DTDs, but with more delayed events (>1 Gyr in age) than prompt events (<1 Gyr). Comparing these solutions to delay time measures separately derived from field galaxies and galaxy clusters, we find the skew-normal solutions can accommodate both without requiring a different DTD form in different environments. These model fits are generally inconsistent with results from single-degenerate binary population synthesis models, and are seemingly supportive of double-degenerate progenitors for most SN Ia events.