LN_Mean {BayesLN} | R Documentation |

## Bayesian Estimate of the Log-normal Mean

### Description

This function produces a Bayesian estimate of the log-normal mean, assuming a GIG prior for the variance and an improper flat prior for the mean in the log scale.

### Usage

```
LN_Mean(
x,
method = "weak_inf",
x_transf = TRUE,
CI = TRUE,
alpha_CI = 0.05,
type_CI = "two-sided",
nrep = 1e+05
)
```

### Arguments

`x` |
Vector containing the sample. |

`method` |
String that indicates the prior setting to adopt. Choosing |

`x_transf` |
Logical. If |

`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: |

`nrep` |
Number of simulations for the computation of the credible intervals. |

### Details

Summarizing the posterior mean of the log-normal expectation might be delicate since several
common priors used for the variance do not produces posteriors with finite moments. The proposal by Fabrizi and Trivisano (2012) of adopting a generalized inverse Gaussian (GIG)
prior for the variance in the log scale `\sigma^2`

has been implemented. Moreover, they discussed how to specify the hyperparameters according to two different aims.

Firstly, a weakly informative
prior allowed to produce posterior credible intervals with good frequentist properties, whereas a prior aimed at minimizing the point estimator
MSE was proposed too. The choice between the two priors can be made through the argument `method`

.

The point estimates are exact values, whereas the credible intervals are provided through simulations from the posterior distribution.

### Value

The function returns a list which includes the prior and posterior parameters, the point estimate of the log-normal mean that consists in the mean of the posterior
distribution of the functional `\exp\{\mu+\sigma^2/2\}`

and the posterior variance.

### Source

Fabrizi, E., & Trivisano, C. *Bayesian estimation of log-normal means with finite quadratic expected loss*. Bayesian Analysis, 7(4), 975-996. (2012).

### Examples

```
# Load data
data("NCBC")
# Optimal point estimator
LN_Mean(x = NCBC$al, x_transf = FALSE, method = "optimal", CI = FALSE)
# Weakly informative prior and interval estimation
LN_Mean(x = NCBC$al, x_transf = FALSE, type_CI = "UCL")
```

*BayesLN*version 0.2.10 Index]