LN_Quant function

Bayesian estimate of the log-normal quantiles

This function produces an estimate for the log-normal distribution quantile of fixed level quant.

Source

Gardini, A., C. Trivisano, and E. Fabrizi. Bayesian inference for quantiles of the log-normal distribution. Biometrical Journal (2020).

LN_Quant(
  x,
  quant,
  method = "weak_inf",
  x_transf = TRUE,
  guess_s2 = NULL,
  CI = TRUE,
  alpha_CI = 0.05,
  type_CI = "two-sided",
  method_CI = "exact",
  rel_tol_CI = 1e-05,
  nrep_CI = 1e+06
)

Arguments

• x: Vector of data used to estimate the quantile.

• quant: Number between 0 and 1 that indicates the quantile of interest.

• method: String that indicates the prior setting to adopt. Choosing "weak_inf"

  a weakly informative prior setting is adopted, whereas selecting "optimal" the hyperparameters are fixed trough a numerical optimization algorithm aimed at minimizing the frequentist MSE.

• x_transf: Logical. If TRUE, the x vector is assumed already log-transformed.

• guess_s2: Specification of a guess for the variance if available. If not, the sample estimate is used.

• CI: Logical. With the default choice TRUE, the posterior credibility interval is computed.

• alpha_CI: Level of alpha that determines the credibility (1-alpha_CI) of the posterior interval.

• type_CI: String that indicates the type of interval to compute: "two-sided" (default), "UCL" (i.e. Upper Credible Limit) for upper one-sided intervals or "LCL" (i.e. Lower Credible Limit) for lower one-sided intervals.

• method_CI: String that indicates if the limits should be computed through the logSMNG quantile function qlSMNG (option "exact", default), or by randomly generating a sample ("simulation") using the function rlSMNG.

• rel_tol_CI: Level of relative tolerance required for the integrate procedure or for the infinite sum. Default set to 1e-5.

• nrep_CI: Number of simulations in case of method="simulation".

Returns

The function returns the prior parameters and their posterior values, summary statistics of the log-scale parameters and the estimate of the specified quantile: the posterior mean and variance are provided by default. Moreover, the user can control the computation of posterior intervals.

Details

The function allows to carry out Bayesian inference for the unconditional quantiles of a sample that is assumed log-normally distributed.

A generalized inverse Gaussian prior is assumed for the variance in the log scale $\sigma^2$, whereas a flat improper prior is assumed for the mean in the log scale $\xi$.

Two alternative hyperparamters setting are implemented (choice controlled by the argument method): a weakly informative proposal and an optimal one.

Examples

library(BayesLN)
data("EPA09")
# The optimization algorithm might require time:
# LN_Quant(x = EPA09, x_transf = FALSE, quant = 0.95, method = "optimal", CI = FALSE)
LN_Quant(x = EPA09, x_transf = FALSE, quant = 0.95, method = "weak_inf",
        alpha_CI = 0.05, type_CI = "UCL", nrep_CI = 1e3) # increase nrep_CI