# betafunctions v1.2.2

0

0th

Percentile

## 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>.

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. No Results!