Flexible probability density function

Which is the most flexible probability distribution that spans from

(1) -inf to +inf
(2) zero to +inf

I am guessing Weibull could be a good choice for (2). Any ideas about (1)?

When I say flexible, the distribution should take symmetric as well skewed shape depending on the distribution parameters.

Any help is greatly appreciated.

regards,
Ramesh Rebba
.

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