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M_inf_sigc <- function(rlmc, df, alpha=0.5, truncation=5*10^6){
# inputs:
# rlmc: target RLMC value
# df: data frame in bayesmeta format
# alpha: quantile of the SGC distribution to use as reference threshold U_ref
# truncation: upper bound for the parameter value to aviod numberical problems
# output:
# parameter m of the SGC distribution with C=sigma_ref^{-2}
sigma.ref <- sigma_ref(df)
log.quot <- -6*log(sigma.ref) + 2*log(1-rlmc) -2*log(rlmc)
# return(1- log(alpha)/log(1+exp(log.quot)))
log.res <- log(-log(1-alpha)) - log(log(1+exp(log.quot)))
res <- 1 + exp(log.res)
return(min(res, truncation))
}
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