# betafunctions v1.4.0

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

Package providing a number of functions for working with Two- and
Four-parameter Beta distributions, including alternative parameterizations,
calculation of moments, and fitting of Beta distributions to vectors of
values. Also includes functions for estimating classification accuracy,
diagnostic performance and consistency, using what is generally known as
the "Livingston and Lewis approach" in the psychometric literature as the
foundational method, which makes extensive use of the Beta distribution.
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 identified, please contact Haakon Haakstad at h.t.haakstad at cemo.uio.no.

Suggestions for improvements and additional functionalities are welcome and encouraged.

Experimental versions and versions under development might be found at github: https://github.com/hthaa/betafunctions.

## Functions in betafunctions

Name | Description | |

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

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

UABMSL | Upper Location Parameter Given Shape Parameters, Mean, Variance, and Lower Location Parameter of a Four-Parameter Beta PDD. | |

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

caStats | Classification Accuracy Statistics. | |

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. | |

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

observedmoments | Compute Moments of Observed Value Distribution. | |

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

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

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

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. | |

LABMSU | Lower Location Parameter Given Shape Parameters, Mean, Variance, and Upper Location Parameter of a Four-Parameter Beta PDD. | |

ccStats | Classification Consistency Statistics. | |

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

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

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

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). | |

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

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

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

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

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

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

Beta.tp.fit | Estimate Beta true-score distribution based on observed-score raw-moments and the effective test length. | |

BMS | Beta Shape-Parameter Given Location-Parameters, Mean, Variance, Skewness, Kurtosis and Alpha Shape-Parameter of a Four-Parameter Beta PDD. | |

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

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

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

AMS | Alpha Shape-Parameter Given Location-Parameters, Mean, Variance, Skewness, Kurtosis and Beta Shape-Parameter of a Four-Parameter Beta PDD. | |

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

AUC | Area Under the ROC Curve. | |

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## Last month downloads

## Details

Type | Package |

License | CC0 |

Encoding | UTF-8 |

LazyData | true |

RoxygenNote | 7.1.0 |

NeedsCompilation | no |

Packaged | 2020-10-18 15:28:25 UTC; thorb |

Repository | CRAN |

Date/Publication | 2020-10-18 21:40:11 UTC |

Contributors | Haakon Haakstad |

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