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

### 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

1 2 | ```
plinearpool(fit, x, d = "best", w = 1)
qlinearpool(fit, q, d = "best", w = 1)
``` |

### Arguments

`fit` |
The output of a |

`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 |

`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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
## 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)
``` |

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