module Gev.Gumbel
(
GumbelDistribution
, gumbelDist
, gumbelDistMaybe
, location
, scale
) where
import qualified Gev
data GumbelDistribution = Gumbel {
GumbelDistribution -> Double
location :: {-# UNPACK #-} !Double
, GumbelDistribution -> Double
scale :: {-# UNPACK #-} !Double
} deriving (GumbelDistribution -> GumbelDistribution -> Bool
(GumbelDistribution -> GumbelDistribution -> Bool)
-> (GumbelDistribution -> GumbelDistribution -> Bool)
-> Eq GumbelDistribution
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: GumbelDistribution -> GumbelDistribution -> Bool
$c/= :: GumbelDistribution -> GumbelDistribution -> Bool
== :: GumbelDistribution -> GumbelDistribution -> Bool
$c== :: GumbelDistribution -> GumbelDistribution -> Bool
Eq)
instance Show GumbelDistribution where
show :: GumbelDistribution -> String
show (Gumbel Double
loc Double
sc) = ShowS
forall a. Show a => a -> String
show String
"Gumbel Distribution; loc: " String -> ShowS
forall a. [a] -> [a] -> [a]
++ Double -> String
forall a. Show a => a -> String
show Double
loc String -> ShowS
forall a. [a] -> [a] -> [a]
++ String
" and scale: " String -> ShowS
forall a. [a] -> [a] -> [a]
++ Double -> String
forall a. Show a => a -> String
show Double
sc
gumbelErrMsg :: Double -> Double -> String
gumbelErrMsg :: Double -> Double -> String
gumbelErrMsg Double
loc Double
scale = String
"Gev.Gumbel: "
String -> ShowS
forall a. [a] -> [a] -> [a]
++ String
"loc = " String -> ShowS
forall a. [a] -> [a] -> [a]
++ Double -> String
forall a. Show a => a -> String
show Double
loc
String -> ShowS
forall a. [a] -> [a] -> [a]
++ String
" scale = " String -> ShowS
forall a. [a] -> [a] -> [a]
++ Double -> String
forall a. Show a => a -> String
show Double
scale
String -> ShowS
forall a. [a] -> [a] -> [a]
++ String
", but the scale parameter must be positive!"
gumbelDistMaybe :: Double -> Double -> Maybe GumbelDistribution
gumbelDistMaybe :: Double -> Double -> Maybe GumbelDistribution
gumbelDistMaybe Double
loc Double
sc
| Double
sc Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
> Double
0 = GumbelDistribution -> Maybe GumbelDistribution
forall a. a -> Maybe a
Just (GumbelDistribution -> Maybe GumbelDistribution)
-> GumbelDistribution -> Maybe GumbelDistribution
forall a b. (a -> b) -> a -> b
$ Double -> Double -> GumbelDistribution
Gumbel Double
loc Double
sc
| Bool
otherwise = Maybe GumbelDistribution
forall a. Maybe a
Nothing
gumbelDist :: Double -> Double -> GumbelDistribution
gumbelDist :: Double -> Double -> GumbelDistribution
gumbelDist Double
loc Double
sc = GumbelDistribution
-> (GumbelDistribution -> GumbelDistribution)
-> Maybe GumbelDistribution
-> GumbelDistribution
forall b a. b -> (a -> b) -> Maybe a -> b
maybe (String -> GumbelDistribution
forall a. HasCallStack => String -> a
error (String -> GumbelDistribution) -> String -> GumbelDistribution
forall a b. (a -> b) -> a -> b
$ Double -> Double -> String
gumbelErrMsg Double
loc Double
sc) GumbelDistribution -> GumbelDistribution
forall a. a -> a
id (Maybe GumbelDistribution -> GumbelDistribution)
-> Maybe GumbelDistribution -> GumbelDistribution
forall a b. (a -> b) -> a -> b
$ Double -> Double -> Maybe GumbelDistribution
gumbelDistMaybe Double
loc Double
sc
cdfGumbel :: GumbelDistribution -> Double -> Double
cdfGumbel :: GumbelDistribution -> Double -> Double
cdfGumbel (Gumbel Double
loc Double
sc) Double
x
| Double
x Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
<= Double
0 = Double
0
| Bool
otherwise = 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
exp Double
y)
where
y :: Double
y = - (Double
x Double -> Double -> Double
forall a. Num a => a -> a -> a
- Double
loc) Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Double
sc
pdfGumbel :: GumbelDistribution -> Double -> Double
pdfGumbel :: GumbelDistribution -> Double -> Double
pdfGumbel (Gumbel Double
loc Double
sc) Double
x =
let exp_y :: Double
exp_y = Double -> Double
forall a. Floating a => a -> a
exp (Double -> Double) -> Double -> Double
forall a b. (a -> b) -> a -> b
$ - (Double
xDouble -> Double -> Double
forall a. Num a => a -> a -> a
- Double
loc) Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Double
sc
const :: Double
const = Double
1 Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Double
sc
in Double
const Double -> Double -> Double
forall a. Num a => a -> a -> a
* Double
exp_y 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
exp_y)
quantileGumbel :: GumbelDistribution -> Double -> Double
quantileGumbel :: GumbelDistribution -> Double -> Double
quantileGumbel (Gumbel Double
loc Double
sc) Double
x
| Double
x Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
> Double
0 Bool -> Bool -> Bool
&& Double
x Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
< Double
1 = Double
loc Double -> Double -> Double
forall a. Num a => a -> a -> a
- Double
sc Double -> Double -> Double
forall a. Num a => a -> a -> a
* (Double -> Double
forall a. Floating a => a -> a
log (Double -> Double) -> Double -> Double
forall a b. (a -> b) -> a -> b
$ - Double -> Double
forall a. Floating a => a -> a
log Double
x)
| Bool
otherwise =
String -> Double
forall a. HasCallStack => String -> a
error (String -> Double) -> String -> Double
forall a b. (a -> b) -> a -> b
$ String
"Gev.GumbelDistribution.quantile: The given value must be between 0 and 1, got: " String -> ShowS
forall a. [a] -> [a] -> [a]
++ Double -> String
forall a. Show a => a -> String
show Double
x
instance Gev.Distribution GumbelDistribution where
cdf :: GumbelDistribution -> Double -> Double
cdf = GumbelDistribution -> Double -> Double
cdfGumbel
pdf :: GumbelDistribution -> Double -> Double
pdf = GumbelDistribution -> Double -> Double
pdfGumbel
quantile :: GumbelDistribution -> Double -> Double
quantile = GumbelDistribution -> Double -> Double
quantileGumbel