Frechet distribution {dprop}

Compute the distributional properties of the Frechet 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 Frechet distribution.

Usage

d_fre(alpha, beta, zeta)

Arguments

alpha

The parameter of the Frechet distribution (\alpha>0).

beta

The parameter of the Frechet distribution (\beta\in\left(-\infty,+\infty\right)).

zeta

The parameter of the Frechet distribution (\zeta>0).

Details

The following is the probability density function of the Frechet distribution:

f(x)=\frac{\alpha}{\zeta}\left(\frac{x-\beta}{\zeta}\right)^{-1-\alpha}e^{-(\frac{x-\beta}{\zeta})^{-\alpha},}

where x>\beta, \alpha>0, \zeta>0 and \beta\in\left(-\infty,+\infty\right). The Frechet distribution is also known as inverse Weibull distribution and special case of the generalized extreme value distribution.

Value

d_fre 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 Frechet distribution.

Author(s)

Muhammad Imran.

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

References

Abbas, K., & Tang, Y. (2015). Analysis of Frechet distribution using reference priors. Communications in Statistics-Theory and Methods, 44(14), 2945-2956.

See Also

d_wei

Examples

d_fre(5,1,0.5)