"symmetric lambda distribution" in Lihn's former works. However, it has several more popular names such as "exponential power distribution", or the "generalized error/normal distribution", often referred to when . The n-th moment of is the -th moment of , All positive moments are finite. This in a way solves the thorny issue of diverging moments in the stable distribution. Properties All stable distributions are infinitely divisible. With the exception of the normal distribution (), stable distributions are leptokurtotic and heavy-tailed distributions. Closure under convolution Stable distributions are closed under convolution for a fixed value of . Since convolution is equivalent to multiplication of the Fourier-transformed function, it follows that the product of two stable characteristic functions with the same will yield another such characteristic function. The product of two stable characteristic functions is given by: Since is not a function of the μ, c or variables it follows that these parameters for the convolved function are given by: In each case, it can be shown that the resulting parameters lie within the required intervals for a stable distribution. A generalized central limit theorem Another important property of stable distributions is the role that they play in a generalized central limit theorem. The central limit theorem states that the sum of a number of independent and identically distributed (i.i.d.) random variables with finite non-zero variances will tend to a normal distribution as the number of variables grows. A generalization due to Gnedenko and Kolmogorov states that the sum of a number of random variables with symmetric distributions having power-law tails (Paretian tails), decreasing as where (and therefore having infinite variance), will tend to a stable distribution as the number of summands grows. If then the sum converges to a stable distribution with stability parameter equal to 2, i.e. a Gaussian distribution. There are other possibilities as well. For example, if the characteristic function of the random variable is asymptotic to for small t (positive or negative), then we may ask how t varies with n when the value of the characteristic function for the sum of n such random variables equals a given value u: Assuming for the moment that t → 0, we take the limit of the above as : Therefore: This shows that is asymptotic to so using the previous equation we have This implies that the sum divided by has a characteristic function whose value at some