Gumbel distribution {dprop}

Compute the distributional properties of the Gumbel 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 Gumbel distribution.

Usage

d_gumbel(alpha, beta)

Arguments

alpha

Location parameter of the Gumbel distribution (\alpha\in\left(-\infty,+\infty\right)).

beta

The strictly positive scale parameter of the Gumbel distribution (\beta > 0).

Details

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

f(x)=\frac{1}{\beta}e^{-(z+e^{-z})},

where z=\frac{x-\alpha}{\beta}, x\in\left(-\infty,+\infty\right), \alpha\in\left(-\infty,+\infty\right) and \beta > 0.

Value

d_gumbel 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 Gumbel distribution.

Author(s)

Muhammad Imran.

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

References

Gomez, Y. M., Bolfarine, H., & Gomez, H. W. (2019). Gumbel distribution with heavy tails and applications to environmental data. Mathematics and Computers in Simulation, 157, 115-129.

See Also

d_gompertz, d_fre

Examples

d_gumbel(1,2)