# betafunctions v1.2.2

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## Functions for Working with Two- And Four-Parameter Beta Probability Distributions

Package providing a number of functions for working with the Two- and Four-
parameter Beta distributions, including alternative parameterizations and calculation
of moments. Includes functions for estimating classification accuracy, diagnostic
performance and consistency, using what's known as the Livingston and Lewis approach
in the educational-measurement literature as the base method.
Livingston and Lewis (1995) <doi:10.1111/j.1745-3984.1995.tb00462.x>.
Hanson (1991) <https://files.eric.ed.gov/fulltext/ED344945.pdf>.
Glas, Lijmer, Prins, Bonsel and Bossuyt (2003) <doi:10.1016/S0895-4356(03)00177-X>.

## Readme

betafunctions is free open-source software and comes with absolutely no warranty. If any bugs or errors are encountered, please contact Haakon Haakstad at h.t.haakstad@cemo.uio.no. Suggestions for improvements and additional functionalities are welcome and encouraged.

## Functions in betafunctions

Name | Description | |

Beta.2p.fit | Method of Moment Estimates of Shape-Parameters of the Two-Parameter (Standard) Beta Distribution. | |

LL.CA | An Implementation of the Livingston and Lewis (1995) Approach to Estimate Classification Consistency and Accuracy based on Observed Test Scores and Test Reliability. | |

Beta.gfx.poly.cdf | Coordinate Generation for Marking an Area Under the Curve for the Beta Cumulative Probability Density Distribution. | |

Beta.gfx.poly.qdf | Coordinate Generation for Marking an Area Under the Curve for the Beta Quantile Density Distribution. | |

Beta.4p.fit | Method of Moment Estimates of Shape- and Location Parameters of the Four-Parameter Beta Distribution. | |

ETL | Livingston and Lewis' "Effective Test Length". | |

Beta.gfx.poly.pdf | Coordinate Generation for Marking an Area Under the Curve for the Beta Probability Density Distribution. | |

BMS | Beta Shape Parameter Given Mean and Variance of a Standard Beta PDD. | |

MLB | Most Likely True Beta Value Given Observed Outcome. | |

AMS | Alpha Shape Parameter Given Mean and Variance of a Standard Beta PDD. | |

AUC | Area Under the ROC Curve. | |

dBeta.pBeta | An implementation of the Beta-density Compound Cumulative-Beta Distribution. | |

dBeta.pBinom | An implementation of the Beta-density Compound Cumulative-Binomial Distribution. | |

dBetaMS | Density Under a Specific Point of the Standard Beta PDD with Specific Mean and Variance or Standard Deviation. | |

dBeta.4P | Probability Density under the Four-Parameter Beta PDD. | |

pBeta.4P | Cumulative Probability Function under the Four-Parameter Beta Probability Density Distribution. | |

observedmoments | Compute Moments of Observed Value Distribution. | |

LL.ROC | ROC curves for the Livingston and Lewis approach. | |

MLA | Most Likely True Alpha Value Given Observed Outcome. | |

betamoments | Compute Moments of Two-to-Four Parameter Beta Probability Density Distributions. | |

caStats | Classification Accuracy Statistics. | |

MLM | Most Likely Mean of the Standard Beta PDD, Given that the Observation is Considered the Most Likely Observation of the Standard Beta PDD (i.e., Mode). | |

rBetaMS | Random Draw from the Standard Beta PDD With Specific Mean and Variance. | |

cba | Calculate Cronbach's Alpha from supplied variables. | |

qBetaMS | Quantile Containing Specific Proportion of the Distribution, Given a Specific Probability of the Standard Beta PDD with Specific Mean and Variance or Standard Deviation. | |

ccStats | Classification Consistency Statistics. | |

rBeta.4P | Random Number Generation under the Four-Parameter Beta Probability Density Distribution. | |

pBetaMS | Probability of Some Specific Observation under the Standard Beta PDD with Specific Mean and Variance. | |

qBeta.4P | Quantile Given Probability Under the Four-Parameter Beta Distribution. | |

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## Details

Type | Package |

License | CC0 |

Encoding | UTF-8 |

LazyData | true |

RoxygenNote | 7.1.0 |

NeedsCompilation | no |

Packaged | 2020-09-16 09:46:19 UTC; thorb |

Repository | CRAN |

Date/Publication | 2020-09-16 10:00:02 UTC |

Contributors | Haakon Haakstad |

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