Tweedie Family
Of course; Put p=2 and choose a(x, \theta) independently of x such that the integral of pdf be 1.
For more details see wikipedia article on "Tweedie distributions":
http://en.wikipedia.org/wiki/Tweedie_distributions
Beginner level books. High level books. Analytical Number Theory. Algebraic Number Theory. Combinatorical Number Theory. Books about partitions. Books about primes.
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