take.var.power10.RdEstimate standard deviation by the delta method
take.var.power10(var.result)which contains two matrix/data.frame:
mean: for the mean of log10 values,
var: for the variance of log10 values.
a list of mean and variance estimation.
mean: mean matrix
sd: standard deviation matrix
Say \(x \sim \mathcal{N}\!\left(\mu, \sigma^{2}\right)\) in its log10 scale. Let \(g(x) = 10^x\). Since \(g(x) = \exp(x \log(10))\) and \(g'(x) = \exp(x \log(10)) \log(10)\), by the delta method, we can approximate the distribution of \(g(x)\) around mean value \(\mu\). $$g(x) \sim \mathcal{N}\!\left(g(\mu), (g'(\mu))^2 \sigma^{2}\right)$$.