// Copyright 2015 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package stats

import (
	"math"

	"github.com/aclements/go-moremath/mathx"
)

// A TDist is a Student's t-distribution with V degrees of freedom.
type TDist struct {
	V float64
}

func lgamma(x float64) float64 {
	y, _ := math.Lgamma(x)
	return y
}

func (t TDist) PDF(x float64) float64 {
	return math.Exp(lgamma((t.V+1)/2)-lgamma(t.V/2)) /
		math.Sqrt(t.V*math.Pi) * math.Pow(1+(x*x)/t.V, -(t.V+1)/2)
}

func (t TDist) CDF(x float64) float64 {
	if x == 0 {
		return 0.5
	} else if x > 0 {
		return 1 - 0.5*mathx.BetaInc(t.V/(t.V+x*x), t.V/2, 0.5)
	} else if x < 0 {
		return 1 - t.CDF(-x)
	} else {
		return math.NaN()
	}
}

func (t TDist) Bounds() (float64, float64) {
	return -4, 4
}