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gamma.scala
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gamma.scala
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/*
* Copyright 2021 Arman Bilge
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package schrodinger
package stats
import cats.Applicative
import cats.syntax.all.*
import schrodinger.kernel.Gamma
import schrodinger.math.LogDouble
import schrodinger.math.special
object gamma:
given [F[_]](using F: Applicative[F]): Gamma[Density[F, LogDouble, _], Double] with
def gamma(shape: Double, rate: Double) =
val `β^α/Γ(α)` = LogDouble(rate) ** shape / special.gamma(shape)
Density { x =>
F.pure(`β^α/Γ(α)` * LogDouble(x) ** (shape - 1) * LogDouble.exp(-rate * x))
}