# Calculate the parameters of a Beta distribution based on expert information

### Description

The `betaExpert`

function fits a (standard) Beta distribution to expert opinion. The expert provides information on a best-guess estimate (mode or mean), and an uncertainty range:

The parameter value is with

`100*p%`

certainty greater than`lower`

The parameter value is with

`100*p%`

certainty smaller than`upper`

The parameter value lies with

`100*p%`

in between`lower`

and`upper`

### Usage

1 2 3 4 5 6 | ```
betaExpert(best, lower, upper, p = 0.95, method = "mode")
## S3 method for class 'betaExpert'
print(x, conf.level = .95, ...)
## S3 method for class 'betaExpert'
plot(x, y, ...)
``` |

### Arguments

`best` |
Best-guess estimate; see argument |

`lower` |
Lower uncertainty limit |

`upper` |
Upper uncertainty limit |

`p` |
Expert's certainty level |

`method` |
Does best-guess estimate correspond to the |

`x` |
Object of class |

`y` |
Currently not implemented |

`conf.level` |
Confidence level used in printing quantiles of resulting Beta distribution |

`...` |
Other arguments to pass to function |

### Details

The methodology behind the `betaExpert`

function is presented by Branscum et al. (2005) and implemented in the *BetaBuster* software, written by Chun-Lung Su.

The parameters of a standard Beta distribution are calculated based on a best-guess estimate and a 100(*p*)% uncertainty range, defined by a lower and/or upper limit. The `betaExpert`

function uses minimization (`optimize`

) to derive *α* and *β* from this best guess and lower and/or upper limit. The resulting distribution is a standard 2-parameter Beta distribution: Beta(*α*, *β*).

### Value

A list of class `"betaExpert"`

:

`alpha ` |
Parameter |

`beta ` |
Parameter |

The `print`

method for `"betaExpert"`

additionally calculates the mean, median, mode, variance and range of the corresponding Beta distribution.

### Author(s)

Brecht Devleesschauwer <brechtdv@gmail.com>

### References

Branscum AJ, Gardner IA, Johnson WO (2005) Estimation of diagnostic-test sensitivity and specificity through Bayesian modeling. *Prev Vet Med* **68**:145-163.

### See Also

Package rriskDistributions, which provides a collection of functions for fitting distributions to given data or by known quantiles.

`betaPERT`

, for modelling a generalized Beta distribution based on expert opinion

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
## Most likely value (mode) is 90%
## Expert states with 95% certainty that true value is larger than 70%
betaExpert(best = 0.90, lower = 0.70, p = 0.95)
## Most likely value (mode) is 0%
## Expert states with 95% certainty that true value is smaller than 40%
betaExpert(best = 0, upper = 0.40, p = 0.95)
## Most likely value (mode) is 80%
## Expert states with 90% certainty that true value lies in between 40% and 90%
betaExpert(best = 0.80, lower = 0.40, upper = 0.90, p = 0.90)
## Mean value is assumed to be 80%
## Expert states with 90% certainty that true value lies in between 40% and 90%
betaExpert(best = 0.80, lower = 0.40, upper = 0.90, p = 0.90, method = "mean")
``` |