The standard Cauchy distribution (Student's

t-distribution with one degree of freedom) has neither a moment-generating function nor finite moments of order greater than or equal to one [Johnson et al.

An important parameter in the

t-distribution is the degrees of freedom.

18) The

t-distribution (also known as the Student's

t-distribution) is a probability distribution that is used to estimate population parameters when the sample size is small and/or when the population variance is unknown.

j] represents the offset of hidden layer node; u is the freedom degree of

T-distribution function which is used to control the change of distribution form; u/(u-2)is the variance yields of

T-distribution function.

Here we compare the results of the previous two sections using a specific non-Gaussian model, namely, Student's

t-distribution as an example.

c] under the multivariate

t-distribution assumption is different from the one under the multivariate normality assumption.

Since the effective degree of freedom is 6, from

t-distribution table at 95% CL the coverage factor K = 2.

For a finite number of degrees of freedom, k is estimated as the t-factor from the Student's

t-distribution based on the number of degrees of freedom and about a 95% confidence interval.

To do this, we estimate the degrees of freedom of the

t-distribution, v, as part of the analysis.

With the previously stated distributional assumptions, t has a central

t-distribution if [Rho] = [[Rho].

For the monotonically increasing calibration curve, the variable t has a noncentral

t-distribution, as described by Graybill (13) with noncentrality parameter:

The error for an estimated average is determined assuming that (X - [micro])/([sigma]/[square root]n) follows the

t-distribution (where [micro] = the population average, X = the sample average, [sigma] = the sample standard deviation, n = the sample size).