--
--  Given the parameters of Alpha and Beta to define the shape of
--  the distribution, BETA.DIST returns the value of the probability
--  density function or the cumulative distribution function, depending
--  on the fourth argument.
--
--      BETA.DIST ( [Value], Alpha, Beta, Cumulative, LowerBound, UpperBound )
--
--  BETA.INV returns the inverse of BETA.DIST
--
--  https://en.wikipedia.org/wiki/Beta_distribution
--
DEFINE
    VAR Vals            = GENERATESERIES ( 0.01, 1, 0.02 )
    VAR Alpha           = 3.51
    VAR Beta            = 4.02
    VAR CumulativeTrue  = TRUE   -- Cumulative distribution function
    VAR CumulativeFalse = FALSE  -- Probability density function
    VAR LowerBound      = 0
    VAR UpperBound      = 1
EVALUATE
ADDCOLUMNS ( 
    Vals, 
    "Beta Dist",             -- Probability density function
        FORMAT ( 
            BETA.DIST ( [Value], Alpha, Beta, CumulativeFalse, LowerBound, UpperBound ),
            "#,0.0####"
        ),
    "Beta Dist Cumulative",  -- Cumulative distribution function
        FORMAT ( 
            BETA.DIST ( [Value], Alpha, Beta, CumulativeTrue, LowerBound, UpperBound ),
            "#,0.0####"
        ),
    "Beta Inv Cumulative",
        BETA.INV (  
            BETA.DIST ( [Value], Alpha, Beta, CumulativeTrue, LowerBound, UpperBound ),
            Alpha,
            Beta,
            LowerBound,
            UpperBound 
        )           
    )