LN_Quant {BayesLN} | R Documentation |

## Bayesian estimate of the log-normal quantiles

### Description

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

.

### Usage

```
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 |

`x_transf` |
Logical. If |

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

`CI` |
Logical. With the default choice |

`alpha_CI` |
Level of alpha that determines the credibility (1- |

`type_CI` |
String that indicates the type of interval to compute: |

`method_CI` |
String that indicates if the limits should be computed through the logSMNG
quantile function |

`rel_tol_CI` |
Level of relative tolerance required for the |

`nrep_CI` |
Number of simulations in case of |

### 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.

### Value

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.

### Source

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

### 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
```

*BayesLN*version 0.2.10 Index]