A list
of class "ClarkLDF" with the components listed below.
("Key" to naming convention: all caps represent parameters;
mixed case represent origin-level amounts;
all-lower-case represent observation-level (origin, development age) results.)
method"LDF"
growthFunctionname of the growth function
Originnames of the rows of the triangle
CurrentValuethe most mature value for each row
CurrentAgethe most mature "age" for each row
CurrentAge.usedthe most mature age used; differs from "CurrentAge"
when adol=TRUE
MAXAGEsame as 'maxage' argument
MAXAGE.USEDthe maximum age for development
from the average date of loss;
differs from MAXAGE when adol=TRUE
FutureValuethe projected loss amounts ("Reserves" in Clark's paper)
ProcessSEthe process standard error of the FutureValue
ParameterSEthe parameter standard error of the FutureValue
StdErrorthe total standard error (process + parameter)
of the FutureValue
Totala list
with amounts that appear on the "Total" row
for components "Origin" (="Total"), "CurrentValue", "FutureValue",
"ProcessSE", "ParameterSE", and "StdError"
PARthe estimated parameters
THETAUthe estimated parameters for the "ultimate loss" by
origin year ("U" in Clark's notation)
THETAGthe estimated parameters of the growth function
GrowthFunctionvalue of the growth function as of the
CurrentAge.used
GrowthFunctionMAXAGEvalue of the growth function as of the
MAXAGE.used
SIGMA2the estimate of the sigma^2 parameter
Ldfthe "to-ultimate" loss development factor
(sometimes called the "cumulative development factor")
as defined in Clark's paper for each origin year
LdfMAXAGEthe "to-ultimate" loss development factor as of
the maximum age used in the model
TruncatedLdfthe "truncated" loss development factor for developing
the current diagonal to
the maximum age used in the model
FutureValueGradientthe gradient of the FutureValue function
originthe origin year corresponding to each observed value of incremental loss
agethe age of each observed value of incremental loss
fittedthe expected value of each observed value of incremental loss
(the "mu's" of Clark's paper)
residualsthe actual minus fitted value for
each observed incremental loss
stdresidthe standardized residuals for
each observed incremental loss
(= residuals/sqrt(sigma2*fitted),
referred to as "normalized residuals" in Clark's paper; see p. 62)
FIthe "Fisher Information" matrix as defined in Clark's paper
(i.e., without the sigma^2 value)
valuethe value of the loglikelihood function at the solution point
countsthe number of calls to the loglikelihood function
and its gradient function when numerical convergence was achieved