Wakeby distribution
Distribution function and quantile function of the Wakeby distribution.
cdfwak(x, para = c(0, 1, 0, 0, 0)) quawak(f, para = c(0, 1, 0, 0, 0))
x |
Vector of quantiles. |
f |
Vector of probabilities. |
para |
Numeric vector containing the parameters of the distribution, in the order xi, alpha, beta, gamma, delta. |
The Wakeby distribution with parameters xi, alpha, beta, gamma and delta has quantile function
x(F) = xi + alpha {1-(1-F)^beta}/beta - gamma {1-(1-F)^(-delta)}/delta .
The parameters are restricted as in Hosking and Wallis (1997, Appendix A.11):
either beta + delta > 0 or beta = gamma = delta = 0;
if alpha = 0 then beta = 0;
if gamma = 0 then delta = 0;
gamma >= 0;
alpha + gamma >= 0.
The distribution has a lower bound at xi and, if delta<0, an upper bound at xi+alpha/beta-gamma/delta.
The generalized Pareto distribution is the special case alpha=0 or gamma=0. The exponential distribution is the special case beta=gamma=delta=0. The uniform distribution is the special case beta=1, gamma=delta=0.
cdfwak gives the distribution function;
quawak gives the quantile function.
The functions expect the distribution parameters in a vector,
rather than as separate arguments as in the standard R
distribution functions pnorm, qnorm, etc.
Hosking, J. R. M. and Wallis, J. R. (1997). Regional frequency analysis: an approach based on L-moments, Cambridge University Press, Appendix A.11.
cdfgpa for the generalized Pareto distribution.
cdfexp for the exponential distribution.
# Random sample from the Wakeby distribution # with parameters xi=0, alpha=30, beta=20, gamma=1, delta=0.3. quawak(runif(100), c(0,30,20,1,0.3))
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