{-# LANGUAGE OverloadedStrings #-}{-# LANGUAGE DeriveDataTypeable, DeriveGeneric #-}-- |-- Module : Statistics.Distribution.Geometric-- Copyright : (c) 2009 Bryan O'Sullivan-- License : BSD3---- Maintainer : bos@serpentine.com-- Stability : experimental-- Portability : portable---- The Geometric distribution. There are two variants of-- distribution. First is the probability distribution of the number-- of Bernoulli trials needed to get one success, supported on the set-- [1,2..] ('GeometricDistribution'). Sometimes it's referred to as-- the /shifted/ geometric distribution to distinguish from another-- one.---- Second variant is probability distribution of the number of-- failures before first success, defined over the set [0,1..]-- ('GeometricDistribution0').moduleStatistics.Distribution.Geometric(GeometricDistribution ,GeometricDistribution0 -- * Constructors,geometric ,geometricE ,geometric0 ,geometric0E -- ** Accessors,gdSuccess ,gdSuccess0 )whereimportControl.ApplicativeimportControl.Monad(liftM)importData.Aeson(FromJSON(..),ToJSON,Value(..),(.:))importData.Binary(Binary(..))importData.Data(Data,Typeable)importGHC.Generics(Generic)importNumeric.MathFunctions.Constants(m_neg_inf)importNumeric.SpecFunctions(log1p,expm1)importqualifiedSystem.Random.MWC.DistributionsasMWCimportqualifiedStatistics.Distribution asDimportStatistics.Internal ------------------------------------------------------------------ | Distribution over [1..]newtypeGeometricDistribution =GD {GeometricDistribution -> Double
gdSuccess ::Double}deriving(GeometricDistribution -> GeometricDistribution -> Bool
(GeometricDistribution -> GeometricDistribution -> Bool)
-> (GeometricDistribution -> GeometricDistribution -> Bool)
-> Eq GeometricDistribution
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
$c== :: GeometricDistribution -> GeometricDistribution -> Bool
== :: GeometricDistribution -> GeometricDistribution -> Bool
$c/= :: GeometricDistribution -> GeometricDistribution -> Bool
/= :: GeometricDistribution -> GeometricDistribution -> Bool
Eq,Typeable,Typeable GeometricDistribution
Typeable GeometricDistribution =>
(forall (c :: * -> *).
 (forall d b. Data d => c (d -> b) -> d -> c b)
 -> (forall g. g -> c g)
 -> GeometricDistribution
 -> c GeometricDistribution)
-> (forall (c :: * -> *).
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 -> (forall r. r -> c r) -> Constr -> c GeometricDistribution)
-> (GeometricDistribution -> Constr)
-> (GeometricDistribution -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
 Typeable t =>
 (forall d. Data d => c (t d)) -> Maybe (c GeometricDistribution))
-> (forall (t :: * -> * -> *) (c :: * -> *).
 Typeable t =>
 (forall d e. (Data d, Data e) => c (t d e))
 -> Maybe (c GeometricDistribution))
-> ((forall b. Data b => b -> b)
 -> GeometricDistribution -> GeometricDistribution)
-> (forall r r'.
 (r -> r' -> r)
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 -> (forall d. Data d => d -> r')
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-> (forall r r'.
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-> (forall u.
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-> (forall u.
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-> (forall (m :: * -> *).
 Monad m =>
 (forall d. Data d => d -> m d)
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-> (forall (m :: * -> *).
 MonadPlus m =>
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-> (forall (m :: * -> *).
 MonadPlus m =>
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 -> GeometricDistribution -> m GeometricDistribution)
-> Data GeometricDistribution
GeometricDistribution -> Constr
GeometricDistribution -> DataType
(forall b. Data b => b -> b)
-> GeometricDistribution -> GeometricDistribution
forall a.
Typeable a =>
(forall (c :: * -> *).
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-> (forall u. (forall d. Data d => d -> u) -> a -> [u])
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-> (forall (m :: * -> *).
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-> (forall (m :: * -> *).
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forall u.
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forall r r'.
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forall r r'.
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forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d)
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forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> GeometricDistribution -> m GeometricDistribution
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c GeometricDistribution
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
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-> c GeometricDistribution
forall (t :: * -> *) (c :: * -> *).
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(forall d. Data d => c (t d)) -> Maybe (c GeometricDistribution)
forall (t :: * -> * -> *) (c :: * -> *).
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(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c GeometricDistribution)
$cgfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g)
-> GeometricDistribution
-> c GeometricDistribution
gfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g)
-> GeometricDistribution
-> c GeometricDistribution
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c GeometricDistribution
gunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c GeometricDistribution
$ctoConstr :: GeometricDistribution -> Constr
toConstr :: GeometricDistribution -> Constr
$cdataTypeOf :: GeometricDistribution -> DataType
dataTypeOf :: GeometricDistribution -> DataType
$cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c GeometricDistribution)
dataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c GeometricDistribution)
$cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
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(forall d e. (Data d, Data e) => c (t d e))
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dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c GeometricDistribution)
$cgmapT :: (forall b. Data b => b -> b)
-> GeometricDistribution -> GeometricDistribution
gmapT :: (forall b. Data b => b -> b)
-> GeometricDistribution -> GeometricDistribution
$cgmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> GeometricDistribution -> r
gmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> GeometricDistribution -> r
$cgmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> GeometricDistribution -> r
gmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> GeometricDistribution -> r
$cgmapQ :: forall u.
(forall d. Data d => d -> u) -> GeometricDistribution -> [u]
gmapQ :: forall u.
(forall d. Data d => d -> u) -> GeometricDistribution -> [u]
$cgmapQi :: forall u.
Int -> (forall d. Data d => d -> u) -> GeometricDistribution -> u
gmapQi :: forall u.
Int -> (forall d. Data d => d -> u) -> GeometricDistribution -> u
$cgmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d)
-> GeometricDistribution -> m GeometricDistribution
gmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d)
-> GeometricDistribution -> m GeometricDistribution
$cgmapMp :: forall (m :: * -> *).
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(forall d. Data d => d -> m d)
-> GeometricDistribution -> m GeometricDistribution
gmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> GeometricDistribution -> m GeometricDistribution
$cgmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> GeometricDistribution -> m GeometricDistribution
gmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> GeometricDistribution -> m GeometricDistribution
Data,(forall x. GeometricDistribution -> Rep GeometricDistribution x)
-> (forall x. Rep GeometricDistribution x -> GeometricDistribution)
-> Generic GeometricDistribution
forall x. Rep GeometricDistribution x -> GeometricDistribution
forall x. GeometricDistribution -> Rep GeometricDistribution x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
$cfrom :: forall x. GeometricDistribution -> Rep GeometricDistribution x
from :: forall x. GeometricDistribution -> Rep GeometricDistribution x
$cto :: forall x. Rep GeometricDistribution x -> GeometricDistribution
to :: forall x. Rep GeometricDistribution x -> GeometricDistribution
Generic)instanceShowGeometricDistribution whereshowsPrec :: Int -> GeometricDistribution -> ShowS
showsPrec Int
i (GD Double
x )=[Char] -> Double -> Int -> ShowS
forall a. Show a => [Char] -> a -> Int -> ShowS
defaultShow1 [Char]
"geometric"Double
x Int
i instanceReadGeometricDistribution wherereadPrec :: ReadPrec GeometricDistribution
readPrec =[Char]
-> (Double -> Maybe GeometricDistribution)
-> ReadPrec GeometricDistribution
forall a r. Read a => [Char] -> (a -> Maybe r) -> ReadPrec r
defaultReadPrecM1 [Char]
"geometric"Double -> Maybe GeometricDistribution
geometricE instanceToJSONGeometricDistribution instanceFromJSONGeometricDistribution whereparseJSON :: Value -> Parser GeometricDistribution
parseJSON (ObjectObject
v )=doDouble
x <-Object
v Object -> Key -> Parser Double
forall a. FromJSON a => Object -> Key -> Parser a
.:Key
"gdSuccess"Parser GeometricDistribution
-> (GeometricDistribution -> Parser GeometricDistribution)
-> Maybe GeometricDistribution
-> Parser GeometricDistribution
forall b a. b -> (a -> b) -> Maybe a -> b
maybe([Char] -> Parser GeometricDistribution
forall a. [Char] -> Parser a
forall (m :: * -> *) a. MonadFail m => [Char] -> m a
fail([Char] -> Parser GeometricDistribution)
-> [Char] -> Parser GeometricDistribution
forall a b. (a -> b) -> a -> b
$Double -> [Char]
errMsg Double
x )GeometricDistribution -> Parser GeometricDistribution
forall a. a -> Parser a
forall (m :: * -> *) a. Monad m => a -> m a
return(Maybe GeometricDistribution -> Parser GeometricDistribution)
-> Maybe GeometricDistribution -> Parser GeometricDistribution
forall a b. (a -> b) -> a -> b
$Double -> Maybe GeometricDistribution
geometricE Double
x parseJSONValue
_=Parser GeometricDistribution
forall a. Parser a
forall (f :: * -> *) a. Alternative f => f a
emptyinstanceBinaryGeometricDistribution whereput :: GeometricDistribution -> Put
put (GD Double
x )=Double -> Put
forall t. Binary t => t -> Put
putDouble
x get :: Get GeometricDistribution
get =doDouble
x <-Get Double
forall t. Binary t => Get t
getGet GeometricDistribution
-> (GeometricDistribution -> Get GeometricDistribution)
-> Maybe GeometricDistribution
-> Get GeometricDistribution
forall b a. b -> (a -> b) -> Maybe a -> b
maybe([Char] -> Get GeometricDistribution
forall a. [Char] -> Get a
forall (m :: * -> *) a. MonadFail m => [Char] -> m a
fail([Char] -> Get GeometricDistribution)
-> [Char] -> Get GeometricDistribution
forall a b. (a -> b) -> a -> b
$Double -> [Char]
errMsg Double
x )GeometricDistribution -> Get GeometricDistribution
forall a. a -> Get a
forall (m :: * -> *) a. Monad m => a -> m a
return(Maybe GeometricDistribution -> Get GeometricDistribution)
-> Maybe GeometricDistribution -> Get GeometricDistribution
forall a b. (a -> b) -> a -> b
$Double -> Maybe GeometricDistribution
geometricE Double
x instanceD.Distribution GeometricDistribution wherecumulative :: GeometricDistribution -> Double -> Double
cumulative =GeometricDistribution -> Double -> Double
cumulative complCumulative :: GeometricDistribution -> Double -> Double
complCumulative =GeometricDistribution -> Double -> Double
complCumulative instanceD.DiscreteDistr GeometricDistribution whereprobability :: GeometricDistribution -> Int -> Double
probability (GD Double
s )Int
n |Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<Int
1=Double
0|Double
s Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
>=Double
0.5=Double
s Double -> Double -> Double
forall a. Num a => a -> a -> a
*(Double
1Double -> Double -> Double
forall a. Num a => a -> a -> a
-Double
s )Double -> Int -> Double
forall a b. (Num a, Integral b) => a -> b -> a
^(Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
-Int
1)|Bool
otherwise=Double
s Double -> Double -> Double
forall a. Num a => a -> a -> a
*(Double -> Double
forall a. Floating a => a -> a
exp(Double -> Double) -> Double -> Double
forall a b. (a -> b) -> a -> b
$Double -> Double
forall a. Floating a => a -> a
log1p(-Double
s )Double -> Double -> Double
forall a. Num a => a -> a -> a
*(Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegralInt
n Double -> Double -> Double
forall a. Num a => a -> a -> a
-Double
1))logProbability :: GeometricDistribution -> Int -> Double
logProbability (GD Double
s )Int
n |Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<Int
1=Double
m_neg_inf|Bool
otherwise=Double -> Double
forall a. Floating a => a -> a
logDouble
s Double -> Double -> Double
forall a. Num a => a -> a -> a
+Double -> Double
forall a. Floating a => a -> a
log1p(-Double
s )Double -> Double -> Double
forall a. Num a => a -> a -> a
*(Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegralInt
n Double -> Double -> Double
forall a. Num a => a -> a -> a
-Double
1)instanceD.Mean GeometricDistribution wheremean :: GeometricDistribution -> Double
mean (GD Double
s )=Double
1Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/Double
s instanceD.Variance GeometricDistribution wherevariance :: GeometricDistribution -> Double
variance (GD Double
s )=(Double
1Double -> Double -> Double
forall a. Num a => a -> a -> a
-Double
s )Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/(Double
s Double -> Double -> Double
forall a. Num a => a -> a -> a
*Double
s )instanceD.MaybeMean GeometricDistribution wheremaybeMean :: GeometricDistribution -> Maybe Double
maybeMean =Double -> Maybe Double
forall a. a -> Maybe a
Just(Double -> Maybe Double)
-> (GeometricDistribution -> Double)
-> GeometricDistribution
-> Maybe Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.GeometricDistribution -> Double
forall d. Mean d => d -> Double
D.mean instanceD.MaybeVariance GeometricDistribution wheremaybeStdDev :: GeometricDistribution -> Maybe Double
maybeStdDev =Double -> Maybe Double
forall a. a -> Maybe a
Just(Double -> Maybe Double)
-> (GeometricDistribution -> Double)
-> GeometricDistribution
-> Maybe Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.GeometricDistribution -> Double
forall d. Variance d => d -> Double
D.stdDev maybeVariance :: GeometricDistribution -> Maybe Double
maybeVariance =Double -> Maybe Double
forall a. a -> Maybe a
Just(Double -> Maybe Double)
-> (GeometricDistribution -> Double)
-> GeometricDistribution
-> Maybe Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.GeometricDistribution -> Double
forall d. Variance d => d -> Double
D.variance instanceD.Entropy GeometricDistribution whereentropy :: GeometricDistribution -> Double
entropy (GD Double
s )|Double
s Double -> Double -> Bool
forall a. Eq a => a -> a -> Bool
==Double
1=Double
0|Bool
otherwise=-(Double
s Double -> Double -> Double
forall a. Num a => a -> a -> a
*Double -> Double
forall a. Floating a => a -> a
logDouble
s Double -> Double -> Double
forall a. Num a => a -> a -> a
+(Double
1Double -> Double -> Double
forall a. Num a => a -> a -> a
-Double
s )Double -> Double -> Double
forall a. Num a => a -> a -> a
*Double -> Double
forall a. Floating a => a -> a
log1p(-Double
s ))Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/Double
s instanceD.MaybeEntropy GeometricDistribution wheremaybeEntropy :: GeometricDistribution -> Maybe Double
maybeEntropy =Double -> Maybe Double
forall a. a -> Maybe a
Just(Double -> Maybe Double)
-> (GeometricDistribution -> Double)
-> GeometricDistribution
-> Maybe Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.GeometricDistribution -> Double
forall d. Entropy d => d -> Double
D.entropy instanceD.DiscreteGen GeometricDistribution wheregenDiscreteVar :: forall g (m :: * -> *).
StatefulGen g m =>
GeometricDistribution -> g -> m Int
genDiscreteVar (GD Double
s )g
g =Double -> g -> m Int
forall g (m :: * -> *). StatefulGen g m => Double -> g -> m Int
MWC.geometric1Double
s g
g instanceD.ContGen GeometricDistribution wheregenContVar :: forall g (m :: * -> *).
StatefulGen g m =>
GeometricDistribution -> g -> m Double
genContVar GeometricDistribution
d g
g =Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegral(Int -> Double) -> m Int -> m Double
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
`liftM`GeometricDistribution -> g -> m Int
forall d g (m :: * -> *).
(DiscreteGen d, StatefulGen g m) =>
d -> g -> m Int
forall g (m :: * -> *).
StatefulGen g m =>
GeometricDistribution -> g -> m Int
D.genDiscreteVar GeometricDistribution
d g
g cumulative ::GeometricDistribution ->Double->Doublecumulative :: GeometricDistribution -> Double -> Double
cumulative (GD Double
s )Double
x |Double
x Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
<Double
1=Double
0|Double -> Bool
forall a. RealFloat a => a -> Bool
isInfiniteDouble
x =Double
1|Double -> Bool
forall a. RealFloat a => a -> Bool
isNaNDouble
x =[Char] -> Double
forall a. HasCallStack => [Char] -> a
error[Char]
"Statistics.Distribution.Geometric.cumulative: NaN input"|Double
s Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
>=Double
0.5=Double
1Double -> Double -> Double
forall a. Num a => a -> a -> a
-(Double
1Double -> Double -> Double
forall a. Num a => a -> a -> a
-Double
s )Double -> Int -> Double
forall a b. (Num a, Integral b) => a -> b -> a
^Int
k |Bool
otherwise=Double -> Double
forall a. Num a => a -> a
negate(Double -> Double) -> Double -> Double
forall a b. (a -> b) -> a -> b
$Double -> Double
forall a. Floating a => a -> a
expm1(Double -> Double) -> Double -> Double
forall a b. (a -> b) -> a -> b
$Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegralInt
k Double -> Double -> Double
forall a. Num a => a -> a -> a
*Double -> Double
forall a. Floating a => a -> a
log1p(-Double
s )wherek :: Int
k =Double -> Int
forall b. Integral b => Double -> b
forall a b. (RealFrac a, Integral b) => a -> b
floorDouble
x ::IntcomplCumulative ::GeometricDistribution ->Double->DoublecomplCumulative :: GeometricDistribution -> Double -> Double
complCumulative (GD Double
s )Double
x |Double
x Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
<Double
1=Double
1|Double -> Bool
forall a. RealFloat a => a -> Bool
isInfiniteDouble
x =Double
0|Double -> Bool
forall a. RealFloat a => a -> Bool
isNaNDouble
x =[Char] -> Double
forall a. HasCallStack => [Char] -> a
error[Char]
"Statistics.Distribution.Geometric.complCumulative: NaN input"|Double
s Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
>=Double
0.5=(Double
1Double -> Double -> Double
forall a. Num a => a -> a -> a
-Double
s )Double -> Int -> Double
forall a b. (Num a, Integral b) => a -> b -> a
^Int
k |Bool
otherwise=Double -> Double
forall a. Floating a => a -> a
exp(Double -> Double) -> Double -> Double
forall a b. (a -> b) -> a -> b
$Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegralInt
k Double -> Double -> Double
forall a. Num a => a -> a -> a
*Double -> Double
forall a. Floating a => a -> a
log1p(-Double
s )wherek :: Int
k =Double -> Int
forall b. Integral b => Double -> b
forall a b. (RealFrac a, Integral b) => a -> b
floorDouble
x ::Int-- | Create geometric distribution.geometric ::Double-- ^ Success rate->GeometricDistribution geometric :: Double -> GeometricDistribution
geometric Double
x =GeometricDistribution
-> (GeometricDistribution -> GeometricDistribution)
-> Maybe GeometricDistribution
-> GeometricDistribution
forall b a. b -> (a -> b) -> Maybe a -> b
maybe([Char] -> GeometricDistribution
forall a. HasCallStack => [Char] -> a
error([Char] -> GeometricDistribution)
-> [Char] -> GeometricDistribution
forall a b. (a -> b) -> a -> b
$Double -> [Char]
errMsg Double
x )GeometricDistribution -> GeometricDistribution
forall a. a -> a
id(Maybe GeometricDistribution -> GeometricDistribution)
-> Maybe GeometricDistribution -> GeometricDistribution
forall a b. (a -> b) -> a -> b
$Double -> Maybe GeometricDistribution
geometricE Double
x -- | Create geometric distribution.geometricE ::Double-- ^ Success rate->MaybeGeometricDistribution geometricE :: Double -> Maybe GeometricDistribution
geometricE Double
x |Double
x Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
>Double
0Bool -> Bool -> Bool
&&Double
x Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
<=Double
1=GeometricDistribution -> Maybe GeometricDistribution
forall a. a -> Maybe a
Just(Double -> GeometricDistribution
GD Double
x )|Bool
otherwise=Maybe GeometricDistribution
forall a. Maybe a
NothingerrMsg ::Double->StringerrMsg :: Double -> [Char]
errMsg Double
x =[Char]
"Statistics.Distribution.Geometric.geometric: probability must be in (0,1] range. Got "[Char] -> ShowS
forall a. [a] -> [a] -> [a]
++Double -> [Char]
forall a. Show a => a -> [Char]
showDouble
x ------------------------------------------------------------------ | Distribution over [0..]newtypeGeometricDistribution0 =GD0 {GeometricDistribution0 -> Double
gdSuccess0 ::Double}deriving(GeometricDistribution0 -> GeometricDistribution0 -> Bool
(GeometricDistribution0 -> GeometricDistribution0 -> Bool)
-> (GeometricDistribution0 -> GeometricDistribution0 -> Bool)
-> Eq GeometricDistribution0
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
$c== :: GeometricDistribution0 -> GeometricDistribution0 -> Bool
== :: GeometricDistribution0 -> GeometricDistribution0 -> Bool
$c/= :: GeometricDistribution0 -> GeometricDistribution0 -> Bool
/= :: GeometricDistribution0 -> GeometricDistribution0 -> Bool
Eq,Typeable,Typeable GeometricDistribution0
Typeable GeometricDistribution0 =>
(forall (c :: * -> *).
 (forall d b. Data d => c (d -> b) -> d -> c b)
 -> (forall g. g -> c g)
 -> GeometricDistribution0
 -> c GeometricDistribution0)
-> (forall (c :: * -> *).
 (forall b r. Data b => c (b -> r) -> c r)
 -> (forall r. r -> c r) -> Constr -> c GeometricDistribution0)
-> (GeometricDistribution0 -> Constr)
-> (GeometricDistribution0 -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
 Typeable t =>
 (forall d. Data d => c (t d)) -> Maybe (c GeometricDistribution0))
-> (forall (t :: * -> * -> *) (c :: * -> *).
 Typeable t =>
 (forall d e. (Data d, Data e) => c (t d e))
 -> Maybe (c GeometricDistribution0))
-> ((forall b. Data b => b -> b)
 -> GeometricDistribution0 -> GeometricDistribution0)
-> (forall r r'.
 (r -> r' -> r)
 -> r
 -> (forall d. Data d => d -> r')
 -> GeometricDistribution0
 -> r)
-> (forall r r'.
 (r' -> r -> r)
 -> r
 -> (forall d. Data d => d -> r')
 -> GeometricDistribution0
 -> r)
-> (forall u.
 (forall d. Data d => d -> u) -> GeometricDistribution0 -> [u])
-> (forall u.
 Int -> (forall d. Data d => d -> u) -> GeometricDistribution0 -> u)
-> (forall (m :: * -> *).
 Monad m =>
 (forall d. Data d => d -> m d)
 -> GeometricDistribution0 -> m GeometricDistribution0)
-> (forall (m :: * -> *).
 MonadPlus m =>
 (forall d. Data d => d -> m d)
 -> GeometricDistribution0 -> m GeometricDistribution0)
-> (forall (m :: * -> *).
 MonadPlus m =>
 (forall d. Data d => d -> m d)
 -> GeometricDistribution0 -> m GeometricDistribution0)
-> Data GeometricDistribution0
GeometricDistribution0 -> Constr
GeometricDistribution0 -> DataType
(forall b. Data b => b -> b)
-> GeometricDistribution0 -> GeometricDistribution0
forall a.
Typeable a =>
(forall (c :: * -> *).
 (forall d b. Data d => c (d -> b) -> d -> c b)
 -> (forall g. g -> c g) -> a -> c a)
-> (forall (c :: * -> *).
 (forall b r. Data b => c (b -> r) -> c r)
 -> (forall r. r -> c r) -> Constr -> c a)
-> (a -> Constr)
-> (a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
 Typeable t =>
 (forall d. Data d => c (t d)) -> Maybe (c a))
-> (forall (t :: * -> * -> *) (c :: * -> *).
 Typeable t =>
 (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
-> ((forall b. Data b => b -> b) -> a -> a)
-> (forall r r'.
 (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall r r'.
 (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
-> (forall u. (forall d. Data d => d -> u) -> a -> [u])
-> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
-> (forall (m :: * -> *).
 Monad m =>
 (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
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-> (forall (m :: * -> *).
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-> Data a
forall u.
Int -> (forall d. Data d => d -> u) -> GeometricDistribution0 -> u
forall u.
(forall d. Data d => d -> u) -> GeometricDistribution0 -> [u]
forall r r'.
(r -> r' -> r)
-> r
-> (forall d. Data d => d -> r')
-> GeometricDistribution0
-> r
forall r r'.
(r' -> r -> r)
-> r
-> (forall d. Data d => d -> r')
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-> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d)
-> GeometricDistribution0 -> m GeometricDistribution0
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> GeometricDistribution0 -> m GeometricDistribution0
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c GeometricDistribution0
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g)
-> GeometricDistribution0
-> c GeometricDistribution0
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c GeometricDistribution0)
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c GeometricDistribution0)
$cgfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g)
-> GeometricDistribution0
-> c GeometricDistribution0
gfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g)
-> GeometricDistribution0
-> c GeometricDistribution0
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c GeometricDistribution0
gunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c GeometricDistribution0
$ctoConstr :: GeometricDistribution0 -> Constr
toConstr :: GeometricDistribution0 -> Constr
$cdataTypeOf :: GeometricDistribution0 -> DataType
dataTypeOf :: GeometricDistribution0 -> DataType
$cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c GeometricDistribution0)
dataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c GeometricDistribution0)
$cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c GeometricDistribution0)
dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c GeometricDistribution0)
$cgmapT :: (forall b. Data b => b -> b)
-> GeometricDistribution0 -> GeometricDistribution0
gmapT :: (forall b. Data b => b -> b)
-> GeometricDistribution0 -> GeometricDistribution0
$cgmapQl :: forall r r'.
(r -> r' -> r)
-> r
-> (forall d. Data d => d -> r')
-> GeometricDistribution0
-> r
gmapQl :: forall r r'.
(r -> r' -> r)
-> r
-> (forall d. Data d => d -> r')
-> GeometricDistribution0
-> r
$cgmapQr :: forall r r'.
(r' -> r -> r)
-> r
-> (forall d. Data d => d -> r')
-> GeometricDistribution0
-> r
gmapQr :: forall r r'.
(r' -> r -> r)
-> r
-> (forall d. Data d => d -> r')
-> GeometricDistribution0
-> r
$cgmapQ :: forall u.
(forall d. Data d => d -> u) -> GeometricDistribution0 -> [u]
gmapQ :: forall u.
(forall d. Data d => d -> u) -> GeometricDistribution0 -> [u]
$cgmapQi :: forall u.
Int -> (forall d. Data d => d -> u) -> GeometricDistribution0 -> u
gmapQi :: forall u.
Int -> (forall d. Data d => d -> u) -> GeometricDistribution0 -> u
$cgmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d)
-> GeometricDistribution0 -> m GeometricDistribution0
gmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d)
-> GeometricDistribution0 -> m GeometricDistribution0
$cgmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> GeometricDistribution0 -> m GeometricDistribution0
gmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> GeometricDistribution0 -> m GeometricDistribution0
$cgmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> GeometricDistribution0 -> m GeometricDistribution0
gmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> GeometricDistribution0 -> m GeometricDistribution0
Data,(forall x. GeometricDistribution0 -> Rep GeometricDistribution0 x)
-> (forall x.
 Rep GeometricDistribution0 x -> GeometricDistribution0)
-> Generic GeometricDistribution0
forall x. Rep GeometricDistribution0 x -> GeometricDistribution0
forall x. GeometricDistribution0 -> Rep GeometricDistribution0 x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
$cfrom :: forall x. GeometricDistribution0 -> Rep GeometricDistribution0 x
from :: forall x. GeometricDistribution0 -> Rep GeometricDistribution0 x
$cto :: forall x. Rep GeometricDistribution0 x -> GeometricDistribution0
to :: forall x. Rep GeometricDistribution0 x -> GeometricDistribution0
Generic)instanceShowGeometricDistribution0 whereshowsPrec :: Int -> GeometricDistribution0 -> ShowS
showsPrecInt
i (GD0 Double
x )=[Char] -> Double -> Int -> ShowS
forall a. Show a => [Char] -> a -> Int -> ShowS
defaultShow1 [Char]
"geometric0"Double
x Int
i instanceReadGeometricDistribution0 wherereadPrec :: ReadPrec GeometricDistribution0
readPrec=[Char]
-> (Double -> Maybe GeometricDistribution0)
-> ReadPrec GeometricDistribution0
forall a r. Read a => [Char] -> (a -> Maybe r) -> ReadPrec r
defaultReadPrecM1 [Char]
"geometric0"Double -> Maybe GeometricDistribution0
geometric0E instanceToJSONGeometricDistribution0 instanceFromJSONGeometricDistribution0 whereparseJSON :: Value -> Parser GeometricDistribution0
parseJSON(ObjectObject
v )=doDouble
x <-Object
v Object -> Key -> Parser Double
forall a. FromJSON a => Object -> Key -> Parser a
.:Key
"gdSuccess0"Parser GeometricDistribution0
-> (GeometricDistribution0 -> Parser GeometricDistribution0)
-> Maybe GeometricDistribution0
-> Parser GeometricDistribution0
forall b a. b -> (a -> b) -> Maybe a -> b
maybe([Char] -> Parser GeometricDistribution0
forall a. [Char] -> Parser a
forall (m :: * -> *) a. MonadFail m => [Char] -> m a
fail([Char] -> Parser GeometricDistribution0)
-> [Char] -> Parser GeometricDistribution0
forall a b. (a -> b) -> a -> b
$Double -> [Char]
errMsg Double
x )GeometricDistribution0 -> Parser GeometricDistribution0
forall a. a -> Parser a
forall (m :: * -> *) a. Monad m => a -> m a
return(Maybe GeometricDistribution0 -> Parser GeometricDistribution0)
-> Maybe GeometricDistribution0 -> Parser GeometricDistribution0
forall a b. (a -> b) -> a -> b
$Double -> Maybe GeometricDistribution0
geometric0E Double
x parseJSONValue
_=Parser GeometricDistribution0
forall a. Parser a
forall (f :: * -> *) a. Alternative f => f a
emptyinstanceBinaryGeometricDistribution0 whereput :: GeometricDistribution0 -> Put
put(GD0 Double
x )=Double -> Put
forall t. Binary t => t -> Put
putDouble
x get :: Get GeometricDistribution0
get=doDouble
x <-Get Double
forall t. Binary t => Get t
getGet GeometricDistribution0
-> (GeometricDistribution0 -> Get GeometricDistribution0)
-> Maybe GeometricDistribution0
-> Get GeometricDistribution0
forall b a. b -> (a -> b) -> Maybe a -> b
maybe([Char] -> Get GeometricDistribution0
forall a. [Char] -> Get a
forall (m :: * -> *) a. MonadFail m => [Char] -> m a
fail([Char] -> Get GeometricDistribution0)
-> [Char] -> Get GeometricDistribution0
forall a b. (a -> b) -> a -> b
$Double -> [Char]
errMsg Double
x )GeometricDistribution0 -> Get GeometricDistribution0
forall a. a -> Get a
forall (m :: * -> *) a. Monad m => a -> m a
return(Maybe GeometricDistribution0 -> Get GeometricDistribution0)
-> Maybe GeometricDistribution0 -> Get GeometricDistribution0
forall a b. (a -> b) -> a -> b
$Double -> Maybe GeometricDistribution0
geometric0E Double
x instanceD.Distribution GeometricDistribution0 wherecumulative :: GeometricDistribution0 -> Double -> Double
cumulative (GD0 Double
s )Double
x =GeometricDistribution -> Double -> Double
cumulative (Double -> GeometricDistribution
GD Double
s )(Double
x Double -> Double -> Double
forall a. Num a => a -> a -> a
+Double
1)complCumulative :: GeometricDistribution0 -> Double -> Double
complCumulative (GD0 Double
s )Double
x =GeometricDistribution -> Double -> Double
complCumulative (Double -> GeometricDistribution
GD Double
s )(Double
x Double -> Double -> Double
forall a. Num a => a -> a -> a
+Double
1)instanceD.DiscreteDistr GeometricDistribution0 whereprobability :: GeometricDistribution0 -> Int -> Double
probability (GD0 Double
s )Int
n =GeometricDistribution -> Int -> Double
forall d. DiscreteDistr d => d -> Int -> Double
D.probability (Double -> GeometricDistribution
GD Double
s )(Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1)logProbability :: GeometricDistribution0 -> Int -> Double
logProbability (GD0 Double
s )Int
n =GeometricDistribution -> Int -> Double
forall d. DiscreteDistr d => d -> Int -> Double
D.logProbability (Double -> GeometricDistribution
GD Double
s )(Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1)instanceD.Mean GeometricDistribution0 wheremean :: GeometricDistribution0 -> Double
mean (GD0 Double
s )=Double
1Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/Double
s Double -> Double -> Double
forall a. Num a => a -> a -> a
-Double
1instanceD.Variance GeometricDistribution0 wherevariance :: GeometricDistribution0 -> Double
variance (GD0 Double
s )=GeometricDistribution -> Double
forall d. Variance d => d -> Double
D.variance (Double -> GeometricDistribution
GD Double
s )instanceD.MaybeMean GeometricDistribution0 wheremaybeMean :: GeometricDistribution0 -> Maybe Double
maybeMean =Double -> Maybe Double
forall a. a -> Maybe a
Just(Double -> Maybe Double)
-> (GeometricDistribution0 -> Double)
-> GeometricDistribution0
-> Maybe Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.GeometricDistribution0 -> Double
forall d. Mean d => d -> Double
D.mean instanceD.MaybeVariance GeometricDistribution0 wheremaybeStdDev :: GeometricDistribution0 -> Maybe Double
maybeStdDev =Double -> Maybe Double
forall a. a -> Maybe a
Just(Double -> Maybe Double)
-> (GeometricDistribution0 -> Double)
-> GeometricDistribution0
-> Maybe Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.GeometricDistribution0 -> Double
forall d. Variance d => d -> Double
D.stdDev maybeVariance :: GeometricDistribution0 -> Maybe Double
maybeVariance =Double -> Maybe Double
forall a. a -> Maybe a
Just(Double -> Maybe Double)
-> (GeometricDistribution0 -> Double)
-> GeometricDistribution0
-> Maybe Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.GeometricDistribution0 -> Double
forall d. Variance d => d -> Double
D.variance instanceD.Entropy GeometricDistribution0 whereentropy :: GeometricDistribution0 -> Double
entropy (GD0 Double
s )=GeometricDistribution -> Double
forall d. Entropy d => d -> Double
D.entropy (Double -> GeometricDistribution
GD Double
s )instanceD.MaybeEntropy GeometricDistribution0 wheremaybeEntropy :: GeometricDistribution0 -> Maybe Double
maybeEntropy =Double -> Maybe Double
forall a. a -> Maybe a
Just(Double -> Maybe Double)
-> (GeometricDistribution0 -> Double)
-> GeometricDistribution0
-> Maybe Double
forall b c a. (b -> c) -> (a -> b) -> a -> c
.GeometricDistribution0 -> Double
forall d. Entropy d => d -> Double
D.entropy instanceD.DiscreteGen GeometricDistribution0 wheregenDiscreteVar :: forall g (m :: * -> *).
StatefulGen g m =>
GeometricDistribution0 -> g -> m Int
genDiscreteVar (GD0 Double
s )g
g =Double -> g -> m Int
forall g (m :: * -> *). StatefulGen g m => Double -> g -> m Int
MWC.geometric0Double
s g
g instanceD.ContGen GeometricDistribution0 wheregenContVar :: forall g (m :: * -> *).
StatefulGen g m =>
GeometricDistribution0 -> g -> m Double
genContVar GeometricDistribution0
d g
g =Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegral(Int -> Double) -> m Int -> m Double
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
`liftM`GeometricDistribution0 -> g -> m Int
forall d g (m :: * -> *).
(DiscreteGen d, StatefulGen g m) =>
d -> g -> m Int
forall g (m :: * -> *).
StatefulGen g m =>
GeometricDistribution0 -> g -> m Int
D.genDiscreteVar GeometricDistribution0
d g
g -- | Create geometric distribution.geometric0 ::Double-- ^ Success rate->GeometricDistribution0 geometric0 :: Double -> GeometricDistribution0
geometric0 Double
x =GeometricDistribution0
-> (GeometricDistribution0 -> GeometricDistribution0)
-> Maybe GeometricDistribution0
-> GeometricDistribution0
forall b a. b -> (a -> b) -> Maybe a -> b
maybe([Char] -> GeometricDistribution0
forall a. HasCallStack => [Char] -> a
error([Char] -> GeometricDistribution0)
-> [Char] -> GeometricDistribution0
forall a b. (a -> b) -> a -> b
$Double -> [Char]
errMsg0 Double
x )GeometricDistribution0 -> GeometricDistribution0
forall a. a -> a
id(Maybe GeometricDistribution0 -> GeometricDistribution0)
-> Maybe GeometricDistribution0 -> GeometricDistribution0
forall a b. (a -> b) -> a -> b
$Double -> Maybe GeometricDistribution0
geometric0E Double
x -- | Create geometric distribution.geometric0E ::Double-- ^ Success rate->MaybeGeometricDistribution0 geometric0E :: Double -> Maybe GeometricDistribution0
geometric0E Double
x |Double
x Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
>Double
0Bool -> Bool -> Bool
&&Double
x Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
<=Double
1=GeometricDistribution0 -> Maybe GeometricDistribution0
forall a. a -> Maybe a
Just(Double -> GeometricDistribution0
GD0 Double
x )|Bool
otherwise=Maybe GeometricDistribution0
forall a. Maybe a
NothingerrMsg0 ::Double->StringerrMsg0 :: Double -> [Char]
errMsg0 Double
x =[Char]
"Statistics.Distribution.Geometric.geometric0: probability must be in (0,1] range. Got "[Char] -> ShowS
forall a. [a] -> [a] -> [a]
++Double -> [Char]
forall a. Show a => a -> [Char]
showDouble
x