estimateSumLognormalSample {lognorm}

Estimate the parameters of the lognormal approximation to the sum

Description

Estimate the parameters of the lognormal approximation to the sum

Estimate the parameters of the lognormal approximation to the sum

Usage

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

  # 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"])