estTWL {windAC} | R Documentation |
Truncated Weighted Likelihood Estimation
Description
Maximum likelihood estimation of a (possibly truncated) probability density function is completed with weights on the likelihood.
Usage
estTWL(fatDist, fatW, distribution, plotBounds = NULL, ...)
weightedLikelihood(fatDist, fatW, distribution, plotBounds = NULL, ...)
Arguments
fatDist |
Vector of fatality distances from the turbine. |
fatW |
Vector of weights, to weight the likelihood for estimatation. This must be the same length as fatDist and is assumed to be in the same order as fatDist. |
distribution |
Character indicating the distribution for |
plotBounds |
Vector of length 1 or 2. If the length is 2 (or greater) the max value is used as the upper truncation bound and the min value is used as the lower truncation bound. If the length is 1 this value is taken as the upper truncation bound and zero is set as the lower truncation bound. The default is NULL, in which case the bounds are zero and positive infinity. |
... |
Additional arguments passed to |
Details
The truncated likelihood for a single observation is
L^*(\theta|x_i) = \frac{f(x_i|\theta)}{\int_{a}^{b}f(y|\theta)dy}
Where x_i
is fatDist
, \theta
is the vector of parameters to be estimated, a
and b
correspond to the plotBounds
and f()
is the distribution
chosen.
The truncated weighted likelihood is
TWL(\theta|\underbar{x}) = \prod_{i=1}^{n}L^*(\theta|x_i)^{w_i}
Where n=length(fatDist)
and w_i
is fatW
.
The truncated weighted likelihood is then estimated using standard maximum likelihood techniques.
See estTWL
for examples.
Value
Data frame of the parameter estimates for the distribution with fit statistics.
See Also
Examples
## load the data
data(carcassDistance)
data(proportionAreaSearched)
## add proportion of area searched to each carcass
carcDist <- merge(carcassDistance,proportionAreaSearched,
by=c('plotType','distanceFromTurbine'),all.x=TRUE)
## create the weight for each carcass
carcDist$w <- with(carcDist,1/(proportionAreaSearched*probabilityDetection))
twlOutput <- with(carcDist,estTWL(fatDist=distanceFromTurbine,fatW=w,plotBounds=c(0,100),
distribution=c('norm','weibull','gamma')))