// BetaFromQtls finds the shape parameters of a beta density that matches knowledge of two quantiles of the distribution.
func BetaFromQtls(p1, x1, p2, x2 float64) (alpha, beta float64) {
// Arguments:
// p1 first probability
// x1 its quantile
// p2 second probability
// x2 its quantile
// Returns:
// alpha, beta params of the corresponding Beta distribution.
m := make([]float64, 100)
logK := make([]float64, 100)
k := make([]float64, 100)
for i := 0; i < 100; i++ {
v := -3.0 + 0.1111111*float64(i)
logK[i] = v
k[i] = exp(v)
m[i] = betaprior1(exp(v), x1, p1)
}
prob2 := make([]float64, 100)
for i, _ := range prob2 {
prob2[i] = dst.BetaCDFAt(k[i]*m[i], k[i]*(1-m[i]), x2)
}
yOut := linInt(prob2, logK, p2)
k0 := exp(yOut)
m0 := betaprior1(k0, x1, p1)
alpha = k0 * m0
beta = k0 * (1 - m0)
return
}
// betaprior1 returns the prior mean m given a beta(k*m, K*(1-m)) prior
// where the pth quantile is given by x.
func betaprior1(k, x, p float64) float64 {
var m0, p0 float64
mLo := 0.0
mHi := 1.0
rep := true
for rep == true {
m0 = (mLo + mHi) / 2.0
p0 = dst.BetaCDFAt(k*m0, k*(1-m0), x)
if p0 < p {
mHi = m0
} else {
mLo = m0
}
if abs(p0-p) < .0001 {
rep = false
}
}
return m0
}