# cdffeedback: Feedback for the elicited distribution of the population CDF In OakleyJ/SHELF: Tools to Support the Sheffield Elicitation Framework

## Description

Report the median and 100(1-alpha)% credible interval for point on the population CDF

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```cdffeedback( medianfit, precisionfit, quantiles = c(0.05, 0.95), vals = NA, alpha = 0.05, median.dist = "best", precision.dist = "gamma", n.rep = 10000 ) ```

## Arguments

 `medianfit` The output of a fitdist command following elicitation of the expert's beliefs about the population median. `precisionfit` The output of a fitprecision command following elicitation of the expert's beliefs about the population precision. `quantiles` A vector of quantiles q_1, …,q_n required for feedback `vals` A vector of population values x_1,…,x_n required for feedback `alpha` The size of the 100(1-alpha)% credible interval `median.dist` The fitted distribution for the population median. Can be one of `"normal"`, `"lognormal"` or `"best"`, where `"best"` will select the best fitting out of normal and lognormal. `precision.dist` The fitted distribution for the population precision. Can either be `"gamma"` or `"lognormal"`. `n.rep` The number of randomly sampled CDFs used to estimated the median and credible interval.

## Details

Denote the uncertain population CDF by

P(X ≤ x | μ, σ^2),

where μ is the uncertain population median and σ^(-2) is the uncertain population precision. Feedback can be reported in the form of the median and 100(1-alpha)% credible interval for (a) an uncertain probability P(X ≤ x | μ, σ^2), where x is a specified population value and (b) an uncertain quantile x_q defined by P(X ≤ x_q | μ, σ^2) = q, where q is a specified population probability.

## Value

Fitted median and 100(1-alpha)% credible interval for population quantiles and probabilities.

 `\$quantiles` Each row gives the fitted median and 100(1-alpha)% credible interval for each uncertain population quantile specified in `quantiles`: the fitted median and 100(1-alpha)% credible interval for the value of x_{q_i} where P(X≤ x_{q_i} | μ, σ^2) = q_i. `\$probs` Each row gives the fitted median and 100(1-alpha)% credible interval for each uncertain population probability specified in `probs`: the fitted median and 100(1-alpha)% credible interval for the value of P(X≤ x_i | μ, σ^2).

## Examples

 ```1 2 3 4 5 6 7``` ```## Not run: prfit <- fitprecision(interval = c(60, 70), propvals = c(0.2, 0.4), trans = "log") medianfit <- fitdist(vals = c(50, 60, 70), probs = c(0.05, 0.5, 0.95), lower = 0) cdffeedback(medianfit, prfit, quantiles = c(0.01, 0.99), vals = c(65, 75), alpha = 0.05, n.rep = 10000) ## End(Not run) ```

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