# fitprecision: Fit a distribution to judgements about a population precision In OakleyJ/SHELF: Tools to Support the Sheffield Elicitation Framework

## Description

Takes elicited probabilities about proportion of a population lying in a specfied interval as inputs, converts the judgements into probability judgements about the population precision, and fits gamma and lognormal distributions to these judgements using the fitdist function.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```fitprecision( interval, propvals, propprobs = c(0.05, 0.95), med = interval, trans = "identity", pplot = TRUE, tdf = 3, fontsize = 12 ) ```

## Arguments

 `interval` A vector specifying the endpoints of an interval [k_1, k_2]. `propvals` A vector specifying two values θ_1, θ_2 for the proportion. `propprobs` A vector specifying two probabilities p_1, p_2. `med` The hypothetical value of the population median. `trans` A string variable taking the value `"identity"`, `"log"` or `"logit"` corresponding to whether the population distribution is normal, lognormal or logit-normal respectively. `pplot` Plot the population distributions with median set at k_1 and precision fixed at the two elicited quantiles implied by `propvals` and `propprobs`. `tdf` Degrees of freedom in the fitted log Student-t distribution. `fontsize` Font size used in the plots.

## Details

The expert provides a pair of probability judgements

P(θ < θ_1 ) = p_1,

and

P(θ < θ_2) = p_2,

where θ is the proportion of the population that lies in the interval [k_1, k_2], conditional on the population median taking some hypothetical value (k_1 by default). k_1 can be set to `-Inf`, or k_2 can be set to `Inf`; in either case, the hypothetical median value must be specified. If both k_1 and k_2 are finite, the hypothetical median must be one of the interval endpoints. Note that, unlike the fitdist command, a 'best fitting' distribution is not reported, as the distributions are fitted to two elicited probabilities only.

## Value

 `Gamma` Parameters of the fitted gamma distribution. Note that E(precision) = shape / rate. `Log.normal` Parameters of the fitted log normal distribution: the mean and standard deviation of log precision. `Log.Student.t` 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 input argument. `vals` The elicited values θ_1, θ_2 `probs` The elicited probabilities p_1, p_2 `limits` The lower and upper limits specified by each expert (+/- Inf if not specified). `transform` Transformation used for a normal population distribution.

## Examples

 ```1 2 3 4``` ```## Not run: fitprecision(interval=c(60, 70), propvals=c(0.2, 0.4), trans = "log") ## End(Not run) ```

OakleyJ/SHELF documentation built on June 21, 2021, 1:24 a.m.