gonum.org/v1/gonum@v0.14.0/mathext/betainc.go (about) 1 // Copyright ©2016 The Gonum Authors. All rights reserved. 2 // Use of this source code is governed by a BSD-style 3 // license that can be found in the LICENSE file. 4 5 package mathext 6 7 import "gonum.org/v1/gonum/mathext/internal/cephes" 8 9 // RegIncBeta returns the value of the regularized incomplete beta function 10 // I(x;a,b). It is defined as 11 // 12 // I(x;a,b) = B(x;a,b) / B(a,b) 13 // = Γ(a+b) / (Γ(a)*Γ(b)) * int_0^x u^(a-1) * (1-u)^(b-1) du. 14 // 15 // The domain of definition is 0 <= x <= 1, and the parameters a and b must be positive. 16 // For other values of x, a, and b RegIncBeta will panic. 17 func RegIncBeta(a, b float64, x float64) float64 { 18 return cephes.Incbet(a, b, x) 19 } 20 21 // InvRegIncBeta computes the inverse of the regularized incomplete beta function. 22 // It returns the x for which 23 // 24 // y = I(x;a,b) 25 // 26 // The domain of definition is 0 <= y <= 1, and the parameters a and b must be 27 // positive. For other values of x, a, and b InvRegIncBeta will panic. 28 func InvRegIncBeta(a, b float64, y float64) float64 { 29 if y < 0 || 1 < y { 30 panic("mathext: parameter out of range") 31 } 32 return cephes.Incbi(a, b, y) 33 }