What is the official name of this distribution, $$k\exp(-\lambda|x|^\alpha),$$ where $\alpha$ is usually less than 1, but greater than 0? More importantly, could anyone tell me what the variance of this distribution is? Thank you very much.

(Edit: Oct 7 '13 at 21:37) Thank you all.

This distribution can be called generalized normal distribution, whose standard form is

$$f(x)=\beta/2\alpha\Gamma(1/\beta)\exp(-|(x-\mu)/\alpha|^\beta)$$

whose variance is $$\alpha^2 \Gamma(3/\beta)/\Gamma(1/\beta)$$