Bayesian Inference for Log-Normal Data
Addend SMNG density function
Addend SMNG moment generating function
Target functional to minimize with respect to delta
Target functional to minimize with respect to gamma
Integral of the target functional to minimize
Vectorization of the function g_V
GH Moment Generating Function
Summation SMNG density function
Summation SMNG moment generating function
Integrand SMNG density function
Integrand SMNG moment generating function
Numerical evaluation of the log-normal conditioned means posterior mom...
Bayesian estimation of a log - normal hierarchical model
Bayesian Estimate of the Log-normal Mean
Bayesian Estimate of the conditional Log-normal Mean
Bayesian estimate of the log-normal quantiles
Bayesian estimate of the log-normal conditioned quantiles
Recursion used for SMNG moments
Ratio of Bessel K functions
SMNG and logSMNG Distributions
SMNG Moments and Moment Generating Function
SMNG moments centered in mu
Function for finding SMNG quantiles
Function for finding logSMNG quantiles
Bayesian inference under log-normality assumption must be performed very carefully. In fact, under the common priors for the variance, useful quantities in the original data scale (like mean and quantiles) do not have posterior moments that are finite (Fabrizi et al. 2012 <doi:10.1214/12-BA733>). This package allows to easily carry out a proper Bayesian inferential procedure by fixing a suitable distribution (the generalized inverse Gaussian) as prior for the variance. Functions to estimate several kind of means (unconditional, conditional and conditional under a mixed model) and quantiles (unconditional and conditional) are provided.