static public Tuple <double, double> ComputeParas(
IEnumerable <double> samples
)
{
var meanVar = Observations.GetMeanVar(samples);
var mean = meanVar.Item1;
var var = meanVar.Item2;
var p = ((1 - mean) / var - 1 / mean) / Math.Pow(mean, 2);
var q = p * (1 / mean - 1);
return(new Tuple <double, double>(p, q));
}
/// <summary>
///
/// </summary>
/// <param name="samples"></param>
/// <returns></returns>
/// <remarks>
/// if X~BetaSpanned(min,max,p,q) then
/// Y=(X-min)/(max-min) ~ BetaSpanned(0,1,p,q)=Beta(p,q)
/// accourding to std Beta,
/// E(Y)= p/(p+q), D(Y)=a * b / ((a + b) * (a + b) * (a + b + 1))
/// So
/// (E(X)-min)/(max-min)=p/(p+q), so E(x)=p/(p+q)*span+min
/// so E(x)= (aq+bp) / (p+q)
/// D(Y)=D(X)/span^2, so D(X)=D(Y)*span^2
///
/// </remarks>
static public Tuple <double, double> ComputeParas(
IEnumerable <double> samples
)
{
var min = samples.Min();
var max = samples.Max();
var span = max - min;
var meanVar = Observations.GetMeanVar(samples);
var mean = meanVar.Item1;
var var = meanVar.Item2;
var lambda = (mean - min) * (max - mean) / var - 1;
var p = lambda * (mean - min) / span;
var q = lambda * (max - min) / span;
return(new Tuple <double, double>(p, q));
}