Kumaraswamy Burr XII distribution {dprop}

Compute the distributional properties of the Kumaraswamy Burr XII 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 Kumaraswamy Burr XII distribution.

Usage

d_kburr(a, b, k, c)

Arguments

a

The strictly positive parameter of the Kumaraswamy distribution (a > 0).

b

The strictly positive parameter of the Kumaraswamy distribution (b > 0).

k

The strictly positive parameter of the Burr XII distribution (k > 0).

c

The strictly positive parameter of the Burr XII distribution (c > 0).

Details

The following is the probability density function of the Kumaraswamy Burr XII distribution:

f(x)=\frac{abkcx^{c-1}}{\left(1+x^{c}\right)^{k+1}}\left[1-\left(1+x^{c}\right)^{-k}\right]^{a-1}\left\{ 1-\left[1-\left(1+x^{c}\right)^{-k}\right]^{a}\right\} ^{b-1},

where x > 0, a > 0, b > 0, k > 0 and c > 0.

Value

d_kburr 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 Kumaraswamy Burr XII distribution.

Author(s)

Muhammad Imran.

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

References

Paranaiba, P. F., Ortega, E. M., Cordeiro, G. M., & Pascoa, M. A. D. (2013). The Kumaraswamy Burr XII distribution: theory and practice. Journal of Statistical Computation and Simulation, 83(11), 2117-2143.

See Also

d_kum, d_kexp

Examples

d_kburr(1.5,1,1,7)