Exponentiated Weibull distribution {dprop}

Compute the distributional properties of the exponentiated Weibull 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 exponentiated Weibull distribution.

Usage

d_EW(a, beta, zeta)

Arguments

a

The strictly positive shape parameter of the exponentiated Weibull distribution (a > 0).

beta

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

zeta

The strictly positive shape parameter of the baseline Weibull distribution (\zeta > 0).

Details

The following is the probability density function of the exponentiated Weibull distribution:

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

where x > 0, a > 0, \beta > 0 and \zeta > 0.

Value

d_EW 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 exponentiated Weibull distribution.

Author(s)

Muhammad Imran.

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

References

Nadarajah, S., Cordeiro, G. M., & Ortega, E. M. (2013). The exponentiated Weibull distribution: a survey. Statistical Papers, 54, 839-877.

See Also

d_EE, d_wei

Examples

d_EW(1,1,0.5)