Search Results for ""

Let phi(t) be the characteristic function, defined as the Fourier transform of the probability density function P(x) using Fourier transform parameters a=b=1, phi(t) = ...

Defined for samples x_i, i=1, ..., N by alpha_r=1/Nsum_(i=1)^Nz_i^r=(mu_r)/(sigma^r), (1) where z_i=(x_i-x^_)/(s_x). (2) The first few are alpha_1 = 0 (3) alpha_2 = 1 (4) ...

alpha=1/Nsum_(i=1)^N|x_i-mu|=<|x_i-mu|>.

nu_((r))=sum_(x)x^((r))f(x), where x^((r))=x(x-1)...(x-r+1).

gamma_r=(kappa_r)/(sigma^(r+2)), where kappa_r are cumulants and sigma is the standard deviation.

A set of statistical distributions having different variances.

A set of statistical distributions having the same variance.

A type of statistic which can be useful for determining asymmetry and tailedness of a population.

A distribution with a high peak so that the kurtosis excess satisfies gamma_2>0.

A distribution with zero kurtosis excess, i.e., gamma_2=0.