This function estimates the lower and upper limits of a specified confidence interval for a vector of nonexceedance probabilities \(F\) of a specified parent distribution [quantile function \(Q(F,\theta)\) with parameters \(\theta\)] using Monte Carlo simulation. The \(F\) are specified by the user. The user also provides \(\Theta\) of the parent distribution (see lmom2par). This function is a wrapper on qua2ci.simple; please consult the documentation for that function for further details of the simulations.
genci.simple(para, n, f=NULL, level=0.90, edist="gno", nsim=1000,
expand=FALSE, verbose=FALSE, showpar=FALSE, quiet=FALSE)An R
data.frame or list is returned (see discussion of argument expand). The following elements could be available.
A vector of \(F\) values, which is returned for convenience so that post operations such as plotting are easily coded.
The lower value of the confidence interval having nonexceedance probability equal to (1-level)/2.
The true quantile value from \(Q(F,\theta)\) for the corresponding \(F\) value.
The upper value of the confidence interval having \(F\) equal to 1-(1-level)/2.
The second L-moment (L-scale, \(\lambda_2\)) of the distribution of quantiles for the corresponding \(F\). This value is included in the primary returned data.frame because it measures the fundamental sampling variability.
The paraments of the parent distribution if expand=TRUE.
The type of error distribution used to model the confidence interval if the argument expand=TRUE is set.
The L-moment of the distribution of quantiles for the corresponding \(F\) if the argument expand=TRUE is set.
An environment containing the parameter lists of the error distribution fit to the elmoms for each of the f if the argument expand=TRUE is set.
A failure integer.
Text message associated with ifail.
The parameters from lmom2par or similar.
The sample size for each Monte Carlo simulation will use.
Vector of nonexceedance probabilities (\(0 \le f \le 1\)) of the quantiles for which the confidence interval are needed. If NULL, then the vector as returned by nonexceeds is used.
The confidence interval (\(0 \le \) level \( < 1\)). The interval is specified as the size of the interval. The default is 0.90 or the 90th percentile. The function will return the 5th (\((1-0.90)/2\)) and 95th (\(1-(1-0.90)/2\)) percentile cumulative probability of the error distribution for the parent quantile as specified by the nonexceedance probability argument (f). This argument is passed unused to qua2ci.simple.
The model for the error distribution. Although the Normal (the default) commonly is assumed in error analyses, it need not be, as support for other distributions supported by lmomco is available. The default is the Generalized Normal so the not only is the Normal possible but asymmetry is also accomodated (lmomgno). For example, if the L-skew (\(\tau_4\)) or L-kurtosis (\(\tau_4\)) values depart considerably from those of the Normal (\(\tau_3 = 0\) and \(\tau_4 = 0.122602\)), then the Generalized Normal or some alternative distribution would likely provide more reliable confidence interval estimation. This argument is passed unused to qua2ci.simple.
The number of simulations (replications) for the sample size n to perform. Much larger simulation numbers are recommended---see discussion about
qua2ci.simple. This argument is passed unused to qua2ci.simple. Users are encouraged to experiment with qua2ci.simple to get a feel for the value of edist and nsim.
Should the returned values be expanded to include information relating to the distribution type and L-moments of the distribution at the corresponding nonexceedance probabilities---in other words the information necessary to reconstruct the reported confidence interval. The default is FALSE. If expand=FALSE then a single data.frame of the lower and upper limits along with the true quantile value of the parent is returned. If expand=TRUE, then a more complicated list containing multiple data.frames is returned.
The verbosity of the operation of the function. This argument is passed unused to qua2ci.simple.
The parameters of the edist for each simulation for each \(F\) value passed to qua2ci.simple are printed. This argument is passed unused to qua2ci.simple.
Suppress incremental counter for a count down of the \(F\) values.
W.H. Asquith
genci, gen.freq.curves