Calculate fitted probabilities or quantiles from a (weighted) linear pool

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Description

Calculates a linear pool given a set of elicited judgements in a fit object. Then calculates required probabilities or quantiles from the pooled cumulative distribution function.

Usage

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plinearpool(fit, x, d = "best", w = 1)
qlinearpool(fit, q, d = "best", w = 1)

Arguments

fit

The output of a fitdist command.

x

A vector of required cumulative probabilities P(X<=x)

d

The distribution fitted to each expert's probabilities. This must either be the same distribution for each expert, or the best fitting distribution for each expert. Options are "normal", "t", "gamma", "lognormal", "logt","beta", "best".

w

A vector of weights to be used in the weighted linear pool.

q

A vector of required quantiles

Details

Quantiles are calculate by first calculating the pooled cumulative distribution function at 100 points, and then using linear interpolation to invert the CDF.

Value

A probability or quantile, calculate from a (weighted) linear pool (arithmetic mean) of the experts' individual fitted probability.

Author(s)

Jeremy Oakley <j.oakley@sheffield.ac.uk>

Examples

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## Not run: 
# Expert 1 states P(X<30)=0.25, P(X<40)=0.5, P(X<50)=0.75
# Expert 2 states P(X<20)=0.25, P(X<25)=0.5, P(X<35)=0.75
# Both experts state 0<X<100.

v <- matrix(c(30, 40, 50, 20, 25, 35), 3, 2)
p <- c(0.25, 0.5, 0.75)
myfit <- fitdist(vals = v, probs = p, lower = 0, upper = 100)

plinearpool(myfit, x=c(20, 50, 80))
qlinearpool(myfit, q=c(0.05, 0.5, 0.95))

# give more weight to first expert
plinearpool(myfit, x=c(20, 50, 80), w=c(0.7, 0.3)) 

# force the use of gamma distributions for each expert
qlinearpool(myfit, q=c(0.05, 0.5, 0.95), d="gamma") 

## End(Not run)