module Gev.GevDist
(
GevDistribution
, gevDist
, gevDistMaybe
, location
, scale
, shape
) where
import qualified Gev
data GevDistribution = GEV {
GevDistribution -> Double
location :: {-# UNPACK #-} !Double
, GevDistribution -> Double
scale :: {-# UNPACK #-} !Double
, GevDistribution -> Double
shape :: {-# UNPACK #-} !Double
} deriving (GevDistribution -> GevDistribution -> Bool
(GevDistribution -> GevDistribution -> Bool)
-> (GevDistribution -> GevDistribution -> Bool)
-> Eq GevDistribution
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: GevDistribution -> GevDistribution -> Bool
$c/= :: GevDistribution -> GevDistribution -> Bool
== :: GevDistribution -> GevDistribution -> Bool
$c== :: GevDistribution -> GevDistribution -> Bool
Eq)
instance Show GevDistribution where
show :: GevDistribution -> String
show (GEV Double
loc Double
sc Double
sh) = ShowS
forall a. Show a => a -> String
show String
"GEV 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
gevErrMsg :: Double -> Double -> Double -> String
gevErrMsg :: Double -> Double -> Double -> String
gevErrMsg Double
loc Double
scale Double
sh = String
"Gev.GevDist: "
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 the scale parameter must be positive!"
gevDistMaybe :: Double -> Double -> Double -> Maybe GevDistribution
gevDistMaybe :: Double -> Double -> Double -> Maybe GevDistribution
gevDistMaybe Double
loc Double
sc Double
sh
| Double
sc Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
> Double
0 = GevDistribution -> Maybe GevDistribution
forall a. a -> Maybe a
Just (GevDistribution -> Maybe GevDistribution)
-> GevDistribution -> Maybe GevDistribution
forall a b. (a -> b) -> a -> b
$ Double -> Double -> Double -> GevDistribution
GEV Double
loc Double
sc Double
sh
| Bool
otherwise = Maybe GevDistribution
forall a. Maybe a
Nothing
gevDist :: Double -> Double -> Double -> GevDistribution
gevDist :: Double -> Double -> Double -> GevDistribution
gevDist Double
loc Double
sc Double
sh = GevDistribution
-> (GevDistribution -> GevDistribution)
-> Maybe GevDistribution
-> GevDistribution
forall b a. b -> (a -> b) -> Maybe a -> b
maybe (String -> GevDistribution
forall a. HasCallStack => String -> a
error (String -> GevDistribution) -> String -> GevDistribution
forall a b. (a -> b) -> a -> b
$ Double -> Double -> Double -> String
gevErrMsg Double
loc Double
sc Double
sh) GevDistribution -> GevDistribution
forall a. a -> a
id (Maybe GevDistribution -> GevDistribution)
-> Maybe GevDistribution -> GevDistribution
forall a b. (a -> b) -> a -> b
$ Double -> Double -> Double -> Maybe GevDistribution
gevDistMaybe Double
loc Double
sh Double
sc
gevDomainCheck :: GevDistribution -> Double -> Bool
gevDomainCheck :: GevDistribution -> Double -> Bool
gevDomainCheck (GEV Double
loc Double
sc Double
sh) Double
x =
if Double
1 Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double
sh Double -> Double -> Double
forall a. Num a => a -> a -> a
* (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) Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
> Double
0 then Bool
True else Bool
False
gevArg :: Double -> Double -> Double -> Double -> Double
gevArg :: Double -> Double -> Double -> Double -> Double
gevArg Double
loc Double
sc Double
sh Double
x =
if Double
sh Double -> Double -> Bool
forall a. Eq a => a -> a -> Bool
== Double
0 then Double
one else Double
two
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
one :: Double
one = Double -> Double
forall a. Floating a => a -> a
exp (Double -> Double) -> Double -> Double
forall a b. (a -> b) -> a -> b
$ - Double
y
two :: Double
two = (Double
1 Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double
sh Double -> Double -> Double
forall a. Num a => a -> a -> a
* Double
y) Double -> Double -> Double
forall a. Floating a => a -> a -> a
** (- Double
1 Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Double
sh)
cdfGEV :: GevDistribution -> Double -> Double
cdfGEV :: GevDistribution -> Double -> Double
cdfGEV (GEV Double
loc Double
sc Double
sh) Double
x
| Double
x Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
<= Double
0 = Double
0
| Double
1 Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double
sh Double -> Double -> Double
forall a. Num a => a -> a -> a
* (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) Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
> Double
0 = Double -> Double
forall a. Floating a => a -> a
exp (Double -> Double) -> Double -> Double
forall a b. (a -> b) -> a -> b
$ - Double
tVal
| Bool
otherwise =
String -> Double
forall a. HasCallStack => String -> a
error (String -> Double) -> String -> Double
forall a b. (a -> b) -> a -> b
$ String
"Gev.GevDist.cdf: The given x value is not in the support of the Distribution: " String -> ShowS
forall a. [a] -> [a] -> [a]
++ Double -> String
forall a. Show a => a -> String
show Double
x
where
tVal :: Double
tVal = Double -> Double -> Double -> Double -> Double
gevArg Double
loc Double
sc Double
sh Double
x
pdfGEV :: GevDistribution -> Double -> Double
pdfGEV :: GevDistribution -> Double -> Double
pdfGEV (GEV Double
loc Double
sc Double
sh) Double
x
| Double
1 Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double
sh Double -> Double -> Double
forall a. Num a => a -> a -> a
* (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) Double -> Double -> Bool
forall a. Ord a => a -> a -> Bool
> Double
0 = 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 -> Double
forall a. Floating a => a -> a
exp ( - Double
tVal)
| Bool
otherwise =
String -> Double
forall a. HasCallStack => String -> a
error (String -> Double) -> String -> Double
forall a b. (a -> b) -> a -> b
$ String
"Gev.GevDist.pdf: The given x value is not in the support of the Distribution: " String -> ShowS
forall a. [a] -> [a] -> [a]
++ Double -> String
forall a. Show a => a -> String
show Double
x
where
tVal :: Double
tVal = Double -> Double -> Double -> Double -> Double
gevArg Double
loc Double
sc Double
sh Double
x
const :: Double
const = Double
1 Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Double
sc
middle :: Double
middle = Double
tVal Double -> Double -> Double
forall a. Floating a => a -> a -> a
** (Double
sh Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double
1)
quantileGEV :: GevDistribution -> Double -> Double
quantileGEV :: GevDistribution -> Double -> Double
quantileGEV (GEV 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 = if Double
sh Double -> Double -> Bool
forall a. Eq a => a -> a -> Bool
== Double
0 then Double
one else Double
two
| Bool
otherwise =
String -> Double
forall a. HasCallStack => String -> a
error (String -> Double) -> String -> Double
forall a b. (a -> b) -> a -> b
$ String
"Gev.GEVDist.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
logx :: Double
logx = - Double -> Double
forall a. Floating a => a -> a
log Double
x
one :: Double
one = - Double
sc Double -> Double -> Double
forall a. Num a => a -> a -> a
* Double -> Double
forall a. Floating a => a -> a
log Double
logx Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double
loc
const :: Double
const = Double
sc Double -> Double -> Double
forall a. Fractional a => a -> a -> a
/ Double
sh
two :: Double
two = Double
const Double -> Double -> Double
forall a. Num a => a -> a -> a
* (Double
logx Double -> Double -> Double
forall a. Floating a => a -> a -> a
** (- Double
sh)) Double -> Double -> Double
forall a. Num a => a -> a -> a
- Double
const Double -> Double -> Double
forall a. Num a => a -> a -> a
+ Double
loc
instance Gev.Distribution GevDistribution where
cdf :: GevDistribution -> Double -> Double
cdf = GevDistribution -> Double -> Double
cdfGEV
pdf :: GevDistribution -> Double -> Double
pdf = GevDistribution -> Double -> Double
pdfGEV
quantile :: GevDistribution -> Double -> Double
quantile = GevDistribution -> Double -> Double
quantileGEV