# 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>.

betafunctions is free open-source software and comes with absolutely no warranty.

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. No Results!