module Gev.Frechet
(
FrechetDistribution
, frechetDist
, frechetDistMaybe
, location
, scale
, shape
) where
import qualified Gev
data FrechetDistribution = Frechet {
FrechetDistribution -> Double
location :: {-# UNPACK #-} !Double
, FrechetDistribution -> Double
scale :: {-# UNPACK #-} !Double
, FrechetDistribution -> Double
shape :: {-# UNPACK #-} !Double
} deriving (FrechetDistribution -> FrechetDistribution -> Bool
(FrechetDistribution -> FrechetDistribution -> Bool)
-> (FrechetDistribution -> FrechetDistribution -> Bool)
-> Eq FrechetDistribution
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: FrechetDistribution -> FrechetDistribution -> Bool
$c/= :: FrechetDistribution -> FrechetDistribution -> Bool
== :: FrechetDistribution -> FrechetDistribution -> Bool
$c== :: FrechetDistribution -> FrechetDistribution -> Bool
Eq)
instance Show FrechetDistribution where
show :: FrechetDistribution -> String
show (Frechet Double
loc Double
sc Double
sh) = ShowS
forall a. Show a => a -> String
show String
"Frechet 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
", scale: " String -> ShowS
forall a. [a] -> [a] -> [a]
++ Double -> String
forall a. Show a => a -> String
show Double
sc String -> ShowS
forall a. [a] -> [a] -> [a]
++ String
" and shape: " String -> ShowS
forall a. [a] -> [a] -> [a]
++ Double -> String
forall a. Show a => a -> String
show Double
sh
frechetErrMsg :: Double -> Double -> Double -> String
frechetErrMsg :: Double -> Double -> Double -> String
frechetErrMsg Double
loc Double
scale Double
sh = String
"Gev.Frechet: "
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
" schape = " String -> ShowS
forall a. [a] -> [a] -> [a]
++ Double -> String
forall a. Show a => a -> String
show Double
sh
String -> ShowS
forall a. [a] -> [a] -> [a]
++ String
", but both the scale and shape parameters must be positive!"
frechetDistMaybe :: Double -> Double -> Double -> Maybe FrechetDistribution
frechetDistMaybe :: Double -> Double -> Double -> Maybe FrechetDistribution
frechetDistMaybe Double
loc Double
sc Double
sh
| Double
sc Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
> Double
0 Bool -> Bool -> Bool
&& Double
sh Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
> Double
0 = FrechetDistribution -> Maybe FrechetDistribution
forall a. a -> Maybe a
Just (FrechetDistribution -> Maybe FrechetDistribution)
-> FrechetDistribution -> Maybe FrechetDistribution
forall a b. (a -> b) -> a -> b
$ Double -> Double -> Double -> FrechetDistribution
Frechet Double
loc Double
sc Double
sh
| Bool
otherwise = Maybe FrechetDistribution
forall a. Maybe a
Nothing
frechetDist :: Double -> Double -> Double -> FrechetDistribution
frechetDist :: Double -> Double -> Double -> FrechetDistribution
frechetDist Double
loc Double
sc Double
sh = FrechetDistribution
-> (FrechetDistribution -> FrechetDistribution)
-> Maybe FrechetDistribution
-> FrechetDistribution
forall b a. b -> (a -> b) -> Maybe a -> b
maybe (String -> FrechetDistribution
forall a. HasCallStack => String -> a
error (String -> FrechetDistribution) -> String -> FrechetDistribution
forall a b. (a -> b) -> a -> b
$ Double -> Double -> Double -> String
frechetErrMsg Double
loc Double
sc Double
sh) FrechetDistribution -> FrechetDistribution
forall a. a -> a
id (Maybe FrechetDistribution -> FrechetDistribution)
-> Maybe FrechetDistribution -> FrechetDistribution
forall a b. (a -> b) -> a -> b
$ Double -> Double -> Double -> Maybe FrechetDistribution
frechetDistMaybe Double
loc Double
sc Double
sh
cdfFrechet :: FrechetDistribution -> Double -> Double
cdfFrechet :: FrechetDistribution -> Double -> Double
cdfFrechet (Frechet Double
loc Double
sc Double
sh) 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
y Double -> Double -> Double
forall a. Floating a => a -> a -> a
** Double
pow)
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
pow :: Double
pow = - Double
sh
pdfFrechet :: FrechetDistribution -> Double -> Double
pdfFrechet :: FrechetDistribution -> Double -> Double
pdfFrechet (Frechet Double
loc Double
sc Double
sh) Double
x =
let 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
const :: Double
const = Double
sh Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Double
sc
expterm :: Double
expterm = Double -> Double
forall a. Floating a => a -> a
exp (Double -> Double) -> Double -> Double
forall a b. (a -> b) -> a -> b
$ - (Double
y Double -> Double -> Double
forall a. Floating a => a -> a -> a
** (- Double
sh))
middle :: Double
middle = Double
y Double -> Double -> Double
forall a. Floating a => a -> a -> a
** (-Double
1 Double -> Double -> Double
forall a. Num a => a -> a -> a
- Double
sh)
in Double
const Double -> Double -> Double
forall a. Num a => a -> a -> a
* Double
middle Double -> Double -> Double
forall a. Num a => a -> a -> a
* Double
expterm
quantileFrechet :: FrechetDistribution -> Double -> Double
quantileFrechet :: FrechetDistribution -> Double -> Double
quantileFrechet (Frechet Double
loc Double
sc Double
sh) 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
logexp Double -> Double -> Double
forall a. Floating a => a -> a -> a
** Double
pow)
| Bool
otherwise =
String -> Double
forall a. HasCallStack => String -> a
error (String -> Double) -> String -> Double
forall a b. (a -> b) -> a -> b
$ String
"Gev.FrechetDistribution.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
where
logexp :: Double
logexp = - Double -> Double
forall a. Floating a => a -> a
log Double
x
pow :: Double
pow = - Double
1 Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Double
sh
instance Gev.Distribution FrechetDistribution where
cdf :: FrechetDistribution -> Double -> Double
cdf = FrechetDistribution -> Double -> Double
cdfFrechet
pdf :: FrechetDistribution -> Double -> Double
pdf = FrechetDistribution -> Double -> Double
pdfFrechet
quantile :: FrechetDistribution -> Double -> Double
quantile = FrechetDistribution -> Double -> Double
quantileFrechet