Distribution function and quantile function
of the Wakeby distribution.
Usage
cdfwak(x, para = c(0, 1, 0, 0, 0))
quawak(f, para = c(0, 1, 0, 0, 0))
Arguments
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.
Details
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.
Value
cdfwak gives the distribution function;
quawak gives the quantile function.
Note
The functions expect the distribution parameters in a vector,
rather than as separate arguments as in the standard R
distribution functions pnorm, qnorm, etc.
References
Hosking, J. R. M. and Wallis, J. R. (1997).
Regional frequency analysis: an approach based on L-moments,
Cambridge University Press, Appendix A.11.
See Also
cdfgpa for the generalized Pareto distribution.
cdfexp for the exponential distribution.
Examples
# 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))