module HLearn.Models.Distributions.Univariate.Normal
( Normal (..)
)
where
import Control.DeepSeq
import GHC.TypeLits
import qualified Data.Vector.Unboxed as U
import Data.Vector.Unboxed.Deriving
import HLearn.Algebra
import HLearn.Models.Distributions.Common
import HLearn.Models.Distributions.Univariate.Internal.Moments
import HLearn.Models.Distributions.Visualization.Gnuplot
newtype Normal prob = Normal (Moments3 prob)
deriving (Read,Show,Eq,Ord,Monoid,Group,Abelian,Module,NumDP,NFData)
instance (Num prob) => HomTrainer (Normal prob) where
type Datapoint (Normal prob) = prob
train1dp dp = Normal $ train1dp dp
instance (Num prob) => HasRing (Normal prob) where
type Ring (Normal prob) = prob
instance (Num prob) => Probabilistic (Normal prob) where
type Probability (Normal prob) = prob
instance (Floating prob) => PDF (Normal prob) where
pdf dist dp = (1 / (sqrt $ sigma2 * 2 * pi))*(exp $ (1)*(dpmu)*(dpmu)/(2*sigma2))
where
sigma2 = variance dist
mu = mean dist
instance (Fractional prob) => Mean (Normal prob) where
mean (Normal dist) = m1 dist / m0 dist
instance (Fractional prob) => Variance (Normal prob) where
variance normal@(Normal dist) = m2 dist / m0 dist (mean normal)*(mean normal)
instance
( Floating prob
, Enum prob
, Show prob
, Ord prob
) => PlottableDistribution (Normal prob) where
plotType _ = Continuous
samplePoints dist = samplesFromMinMax min max
where
numsamples = 1000
min = (mean dist)5*(sqrt $ variance dist)
max = (mean dist)+5*(sqrt $ variance dist)