Student's t distribution {dprop}

Compute the distributional properties of the Student distribution

Description

Compute the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Student t distribution.

Usage

d_st(v)

Arguments

v

The strictly positive parameter of the Student distribution (v > 0), it is also called a degree of freedom.

Details

The following is the probability density function of the Student t distribution:

f(x)=\frac{\Gamma(\frac{v+1}{2})}{\sqrt{v\pi}\Gamma(\frac{v}{2})}\left(1+\frac{x^{2}}{v}\right)^{-(v+1)/2},

where x\in\left(-\infty,+\infty\right) and v > 0.

Value

d_st gives the first four ordinary moments, central moments, mean, and variance, Pearson's coefficient of skewness and kurtosis, coefficient of variation, median and quartile deviation based on the selected parametric values of the Student t distribution.

Author(s)

Muhammad Imran.

R implementation and documentation: Muhammad Imran [e-mail].

References

Yang, Z., Fang, K. T., & Kotz, S. (2007). On the Student's t-distribution and the t-statistic. Journal of Multivariate Analysis, 98(6), 1293-1304.

Ahsanullah, M., Kibria, B. G., & Shakil, M. (2014). Normal and Student's t distributions and their applications (Vol. 4). Paris, France: Atlantis Press.

See Also

d_chi

Examples

d_st(6)