Takes elicited probabilities as inputs, and fits parametric distributions using least squares on the cumulative distribution function. If separate judgements from multiple experts are specified, the function will fit one set of distributions per expert.
fitdist(
vals,
probs,
lower = -Inf,
upper = Inf,
weights = 1,
tdf = 3,
expertnames = NULL,
excludelogt = FALSE
)An object of class elicitation. This is a list containing the elements
Parameters of the fitted normal distributions.
Parameters of the fitted t distributions. Note that (X -
location) / scale has a standard t distribution. The degrees of freedom is
not fitted; it is specified as an argument to fitdist.
Parameters of the fitted skew-normal distribution. The skew-normal distribution is implemented using the sn package. See sn::dsn for details. This distribution requires at least three elicited probabilities, including at least one in each interval (0, 0.4) and (0.6, 1).
Parameters of the fitted gamma distributions. Note that E(X - lower) =
shape / rate.
Parameters of the fitted log normal
distributions: the mean and standard deviation of log (X - lower).
Parameters of the fitted log student t distributions.
Note that (log(X- lower) - location) / scale has a standard t distribution. The
degrees of freedom is not fitted; it is specified as an argument to
fitdist.
Parameters of the fitted beta distributions. X
is scaled to the interval [0,1] via Y = (X - lower)/(upper -
lower), and E(Y) = shape1 / (shape1 + shape2).
Parameters of ('mirror') gamma distributions fitted to Y = upper - X. Note that E(Y) =
shape / rate.
Parameters of ('mirror') log normal distributions
fitted to Y = upper - X.
Parameters of ('mirror') log Student-t distributions fitted to Y = upper - X.
Note that (log(Y) - location) / scale has a standard t distribution. The
degrees of freedom is not fitted; it is specified as an argument to
fitdist.
Sum of squared errors for each fitted distribution and expert. Each error is the difference between an elicited cumulative probability and the corresponding fitted cumulative probability.
The best fitting distribution for each expert, determined by the smallest sum of squared errors. Note that with three judgements only, this is likely to be the skew-normal, as this is a three parameter distribution.
The elicited values used to fit the distributions.
The elicited probabilities used to fit the distributions.
The lower and upper limits specified by each expert (+/- Inf if not specified).
A vector of elicited values for one expert, or a matrix of elicited values for multiple experts (one column per expert). Note that the an elicited judgement about X should be of the form P(X<= vals[i,j]) = probs[i,j]
A vector of elicited probabilies for one expert, or a matrix of
elicited values for multiple experts (one column per expert). A single
vector can be used if the probabilities are the same for each expert. For
each expert, there should be at least one non-zero probability less than 0.4, and
at least one elicited probability less and 1 and greater than 0.6. Exponential distributions
can be fitted by specifying one limit (lower or upper) and one probability between 0 and 1.
A single lower limit for the uncertain quantity X, or a vector of different lower limits for each expert. Specifying a lower limit will allow the fitting of distributions bounded below.
A single upper limit for the uncertain quantity X, or a vector of different lower limits for each expert. Specifying both a lower limit and an upper limit will allow the fitting of a Beta distribution.
A vector or matrix of weights corresponding to vals if weighted least squares is to be used in the parameter fitting.
The number of degrees of freedom to be used when fitting a t-distribution.
Vector of names to use for each expert.
Set to TRUE to exclude log-t and mirror log-t when identifying best fitting distribution.
Jeremy Oakley <j.oakley@sheffield.ac.uk>
if (FALSE) {
# One expert, with elicited probabilities
# P(X<20)=0.25, P(X<30)=0.5, P(X<50)=0.75
# and X>0.
v <- c(20,30,50)
p <- c(0.25,0.5,0.75)
fitdist(vals=v, probs=p, lower=0)
# Now add a second expert, with elicited probabilities
# P(X<55)=0.25, P(X<60=0.5), P(X<70)=0.75
v <- matrix(c(20,30,50,55,60,70),3,2)
p <- c(0.25,0.5,0.75)
fitdist(vals=v, probs=p, lower=0)
# Two experts, different elicited quantiles and limits.
# Expert A: P(X<50)=0.25, P(X<60=0.5), P(X<65)=0.75, and provides bounds 10Run the code above in your browser using DataLab