Description Usage Arguments Value Author(s) See Also Examples

This function estimates the lower and upper limits of a specified confidence interval for aribitrary quantile values for a sample *x* and a specified distribution form. The estimation is based on the sample variance-covariance structure of the L-moments (`lmoms.cov`

) through a Monte Carlo approach. The quantile values, actually the nonexceedance probabilities (*F* for *0 ≤ F ≤ 1*), are specified by the user. The user provides type of parent distribution distribution and this form which will be fitted internal to the function.

1 2 3 4 |

`x` |
A real value vector. |

`f` |
Nonexceedance probabilities ( |

`type` |
Three character distribution type (for example, type='gev'). |

`nsim` |
The number of simulations to perform. Large numbers produce more refined confidence limit estimates at the cost of CPU time. The default is anticipated to be large enough to semi-quantitatively interpret results without too much computational delay. Larger simulation numbers are recommended. |

`interval` |
The type of interval to compute. If |

`level` |
The confidence interval ( |

`asnorm` |
Use the mean and standard deviation of the simulated quantiles as parameters of the Normal distribution to estimate the confidence interval. Otherwise, a Bernstein polynomial approximation ( |

`altlmoms` |
Alternative L-moments to rescale the simulated L-moments from the variance-covariance structure of the sample L-moments in |

`flip` |
A flipping or reflection value denoted as |

`dimless` |
Perform the simulations in dimensionless space meaning that values in |

`usefastlcov` |
A logical to use the function |

`nmom` |
The number of L-moments involved. This argument needs to be high enough to permit parameterization of the distribution in |

`getsimlmom` |
A logical controlling whether the simulated L-moment matrix having |

`verbose` |
The verbosity of the operation of the function. |

`...` |
Additional arguments to pass such as to |

An **R** `data.frame`

is returned.

`lwr` |
The lower value of the confidence interval having nonexceedance probability equal to |

`fit` |
The fit of the quantile based on the L-moments of |

`upr` |
The upper value of the confidence interval having nonexceedance probability equal to |

`qua_med` |
The median of the simulated quantiles. |

`qua_mean` |
The mean of the simulated quantiles for which the median and mean should be very close if the simulation size is large enough and the quantile distribution is symmetrical. |

`qua_var` |
The variance ( |

`qua_lam2` |
The L-scale ( |

W.H. Asquith

`lmoms`

, `lmoms.cov`

, `qua2ci.simple`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 | ```
## Not run:
samsize <- 128; nsim <- 2000; f <- 0.999
wei <- parwei(vec2lmom(c(100,75,-.3)))
set.seed(1734); X <- rlmomco(samsize, wei); set.seed(1734)
tmp <- qua2ci.cov(X, f, type="wei", nsim=nsim)
print(tmp) # show results of one 2000 replicated Monte Carlo
# nonexceed lwr fit upr qua_med qua_mean qua_var qua_lam2
# 0.999 310.4 333.2 360.2 333.6 334.3 227.3 8.4988
set.seed(1734)
qf <- qua2ci.cov(X, f, type="wei", nsim=nsim, interval="none") # another
boxplot(qf)
message(" quantile variance: ", round(tmp$qua_var, digits=2),
" compared to ", round(var(qf, na.rm=TRUE), digits=2))
set.seed(1734)
genci.simple(wei, n=samsize, f=f)
# nonexceed lwr fit upr qua_med qua_mean qua_var qua_lam2
# 0.999 289.7 312.0 337.7 313.5 313.6 213.5 8.2330
#----------------------------------------
# Using X from above example, demonstrate that using dimensionless
# simulation that the results are the same.
set.seed(145); qua2ci.cov(X, 0.1, type="wei") # both outputs same
set.seed(145); qua2ci.cov(X, 0.1, type="wei", dimless=TRUE)
# nonexceed lwr fit upr qua_med qua_mean qua_var qua_lam2
# 0.1 -78.62 -46.01 -11.39 -43.58 -44.38 416.04 11.54
#----------------------------------------
# Using X again, demonstration application of the flip and notice that just
# simple reversal is occurring and that the Weibull is a reversed GEV.
eta <- 0
set.seed(145); qua2ci.cov(X, 0.9, type="wei", nsim=nsim)
# nonexceed lwr fit upr qua_med qua_mean qua_var qua_lam2
# 0.9 232.2 244.2 255.9 244.3 244.1 51.91 4.0635
set.seed(145); qua2ci.cov(X, 0.9, type="gev", nsim=nsim, flip=eta)
# nonexceed lwr fit upr qua_med qua_mean qua_var qua_lam2
# 0.9 232.2 244.2 256.2 244.2 244.3 53.02 4.1088
# The values are slightly different, which likely represents a combination
# of numerics of the variance-covariance matrix because the Monte Carlo
# is seeded the same.
#----------------------------------------
# Using X again, removed dimension and have the function add it back.
lmr <- lmoms(X); Y <- (X - lmr$lambdas[1])/lmr$lambdas[2]
set.seed(145); qua2ci.cov(Y, 0.9, type="wei", altlmoms=lmr, nsim=nsim)
# nonexceed lwr fit upr qua_med qua_mean qua_var qua_lam2
# 0.9 232.2 244.2 255.9 244.3 244.1 51.91 4.0635
## End(Not run)
``` |

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