F distribution {dprop}

Compute the distributional properties of the F 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 F distribution.

Usage

d_F(alpha, beta)

Arguments

alpha

The strictly positive parameter of the F distribution (\alpha > 0).

beta

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

Details

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

f(x)=\frac{1}{B(\frac{\alpha}{2},\frac{\beta}{2})}\left(\frac{\alpha}{\beta}\right)^{\frac{\alpha}{2}}x^{\frac{\alpha}{2}-1}\left(1+\frac{\alpha}{\beta}x\right)^{-\left(\frac{\alpha+\beta}{2}\right)},

where x > 0, \alpha > 0 and \beta > 0.

Value

d_F 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 F distribution.

Author(s)

Muhammad Imran.

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

References

Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995). Continuous univariate distributions, volume 2 (Vol. 289). John Wiley & Sons.

See Also

d_gamma

Examples

d_F(2,10)