Calculates the excess kurtosis of the Student's tDistribution.
Syntax
TDIST_XKURT(v)
v is the degrees of freedom of the Student's tDistribution (v > 4).
Remarks
 TDIST_XKURT is declared as deprecated. Please, use DIST_XKURT as TDIST_XKURT is listed here only for backward compatibility.
 The probability density function of the Student's tDistribution is defined as:
$$f(t) = \frac{\Gamma(\frac{\nu+1}{2})} {\sqrt{\nu\pi}\,\Gamma(\frac{\nu}{2})} \left(1+\frac{t^2}{\nu} \right)^{(\nu+1)/2} $$
Where:
 $\Gamma (.)$ is the gamma function.
 $\nu $ is the degrees of freedom (i.e. shape parameter).
 The excess kurtosis of tDistribution is defined as:
$$\gamma_2= \frac{6}{\nu4}$$
Where:
 $\nu$ is the degrees of freedom.
 IMPORTANT The Student's tDistribution kurtosis is only defined for degrees of freedom values greater than 4.
 Special Cases:
 $ \nu\to 4^+$
$$\lim_{\nu\to 4^+}\gamma_2(\nu)=+\infty$$  $ \nu\to \infty $
$$\lim_{\nu\to +\infty}\gamma_2(\nu)=0$$
 $ \nu\to 4^+$
Examples
Student's tDistribution XKurtosis Plot
Example 1:


Files Examples
References
 K.L. Lange, R.J.A. Little and J.M.G. Taylor. "Robust Statistical Modeling Using the t Distribution." Journal of the American Statistical Association 84, 881896, 1989
 Hurst, Simon, The Characteristic Function of the Studentt Distribution, Financial Mathematics Research Report No. FMRR00695, Statistics Research Report No. SRR04495
0 Comments