st: Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto...

In shannon: Computation of Entropy Measures and Relative Loss

Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Student's t distribution

Description

Compute the Shannon, Rényi, Havrda and Charvat, and Arimoto entropies of the Student's t distribution.

Usage

se_st(v)
re_st(v, delta)
hce_st(v, delta)
ae_st(v, delta)

Arguments

v	The strictly positive parameter of the Student's t distribution (v > 0), also called a degree of freedom.
delta	The strictly positive parameter (\delta > 0) and (\delta \ne 1).

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, and \Gamma(a) is the standard gamma function.

Value

The functions se_st, re_st, hce_st, and ae_st provide the Shannon entropy, Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Student's t distribution and \delta.

Author(s)

Muhammad Imran, Christophe Chesneau and Farrukh Jamal

R implementation and documentation: Muhammad Imran <[e-mail]>, Christophe Chesneau <[e-mail]> and Farrukh Jamal [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.

Arimoto, S. (1971). Information-theoretical considerations on estimation problems. Inf. Control, 19, 181–194.

See Also

re_exp, re_gamma

Examples

se_st(4)
delta <- c(1.5, 2, 3)
re_st(4, delta)
hce_st(4, delta)
ae_st(4, delta)

shannon documentation built on Sept. 11, 2024, 7:48 p.m.