Random generation for the modified Asymmetric Power Distribution with parameters theta, phi, alpha and lambda.
This generator is called by function gensample to create random variables based on its parameters.
If theta, phi, alpha and lambda are not specified they assume the default values of 0, 1, 0.5 and 2, respectively.
The modified Asymmetric Power Distribution with parameters theta, phi, theta1 and theta2 has density:
$$f(x\mid\boldsymbol{\theta})=\frac{(\delta_{\boldsymbol{\theta}}/2)^{1/\theta_2}}{\Gamma(1+1/\theta_2)}\exp\left[-\left(\frac{2(\delta_{\boldsymbol{\theta}}/2)^{1/\theta_2}}{1+sign(x)(1-2\theta_1)}|x|\right)^{\theta_2}\right]$$ where \(\boldsymbol{\theta}=(\theta_2, \theta_1)^T\) is the vector of parameters, \(\theta_2>0, 0<\theta_1<1\) and $$\delta_{\boldsymbol{\theta}}=\frac{2(\theta_1)^{\theta_2} (1-\theta_1)^{\theta_2}}{(\theta_1)^{\theta_2}+(1-\theta_1)^{\theta_2}}$$.
The mean and variance of APD are defined respectively by $$E(U) = \theta + 2 ^ {1 / \theta_2} \phi \Gamma(2 / \theta_2) (1 - 2 \theta_1) \delta ^ {-1 / \theta_2} / \Gamma(1 / \theta_2)$$ and $$V(U) = 2 ^ {2 / \theta_2} \phi ^ 2 \left(\Gamma(3 / \theta_2) \Gamma(1 / \theta_2) (1 - 3 \theta_1 + 3 \theta_1 ^ 2) - \Gamma^2(2 / \theta_2) (1 - 2 \theta_1) ^ 2\right) \delta ^ {-2 / \theta_2} / \Gamma^2(1 / \theta_2).$$
Pierre Lafaye de Micheaux, Viet Anh Tran (2016). PoweR: A Reproducible Research Tool to Ease Monte Carlo Power Simulation Studies for Goodness-of-fit Tests in R. Journal of Statistical Software, 69(3), 1--42. doi:10.18637/jss.v069.i03
Desgagne, A. and Lafaye de Micheaux, P. and Leblanc, A. (2016), Test of normality based on alternate measures of skewness and kurtosis, ,
See Distributions for other standard distributions.
# NOT RUN {
res <- gensample(39, 10000, law.pars = c(3, 2, 0.5, 1))
res$law
res$law.pars
mean(res$sample)
sd(res$sample)
# }
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