# estimateSumLognormalSample: Estimate the parameters of the lognormal approximation to the... In lognorm: Functions for the Lognormal Distribution

## Description

Estimate the parameters of the lognormal approximation to the sum

Estimate the parameters of the lognormal approximation to the sum

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```estimateSumLognormalSample( mu, sigma, resLog, effAcf = computeEffectiveAutoCorr(resLog), isGapFilled = logical(0), na.rm = TRUE ) estimateSumLognormalSampleExpScale(mean, sigmaOrig, ...) estimateSumLognormal( mu, sigma, effAcf = c(), corr = Diagonal(length(mu)), corrLength = if (inherits(corr, "ddiMatrix")) 0 else nTerm, sigmaSum = numeric(0), isStopOnNoTerm = FALSE, na.rm = isStopOnNoTerm ) ```

## Arguments

 `mu` numeric vector of center parameters of terms at log scale `sigma` numeric vector of scale parameter of terms at log scale `resLog` time series of model-residuals at log scale to estimate correlation `effAcf` numeric vector of effective autocorrelation This overrides arguments `corr` and `corrLength` `isGapFilled` logical vector whether entry is gap-filled rather than an original measurement, see details `na.rm` neglect terms with NA values in mu or sigma `mean` numeric vector of expected values `sigmaOrig` numeric vector of standard deviation at original scale `...` further arguments passed to `estimateSumLognormalSample` `corr` numeric matrix of correlations between the random variables `corrLength` integer scalar: set correlation length to smaller values to speed up computation by neglecting correlations among terms further apart. Set to zero to omit correlations. `sigmaSum` numeric scalar: possibility to specify a precomputed scale parameter instead of computing it. `isStopOnNoTerm` if no finite estimate is provided then by default NA is returned for the sum. Set this to TRUE to issue an error instead.

## Details

If there are no gap-filled values, i.e. `all(!isGapFilled)` or `!length(isGapFilled)` (the default), distribution parameters are estimated using all the samples. Otherwise, the scale parameter (uncertainty) is first estimated using only the non-gapfilled records.

Also use isGapFilled == TRUE for records, where sigma cannot be trusted. When setting sigma to missing, this is also affecting the expected value.

If there are only gap-filled records, assume uncertainty to be (before v0.1.5: the largest uncertainty of given gap-filled records.) the mean of the given multiplicative standard deviation

## Value

numeric vector with components `mu`, `sigma`, and `nEff`, i.e. the parameters of the lognormal distribution at log scale and the number of effective observations.

## Functions

• `estimateSumLognormalSample`: In addition to `estimateSumLognormal` take care of missing values and estimate correlation terms.

• `estimateSumLognormalSampleExpScale`: Before calling `estimateSumLognormalSample` estimate lognormal parameters from value and its uncertainty given on original scale.

• `estimateSumLognormal`: Estimate the parameters of the lognormal approximation to the sum

## References

```Lo C (2013) WKB approximation for the sum of two correlated lognormal random variables. Applied Mathematical Sciences, Hikari, Ltd., 7 , 6355-6367 10.12988/ams.2013.39511```

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ``` # distribution of the sum of two lognormally distributed random variables mu1 = log(110) mu2 = log(100) sigma1 = log(1.2) sigma2 = log(1.6) (coefSum <- estimateSumLognormal( c(mu1,mu2), c(sigma1,sigma2) )) # repeat with correlation (coefSumCor <- estimateSumLognormal( c(mu1,mu2), c(sigma1,sigma2), effAcf = c(1,0.9) )) # expected value is equal, but variance with correlated variables is larger getLognormMoments(coefSum["mu"],coefSum["sigma"]) getLognormMoments(coefSumCor["mu"],coefSumCor["sigma"]) ```

lognorm documentation built on Nov. 22, 2021, 1:07 a.m.