module Gev.Weibull
    (
      WeibullDistribution
     -- * constructors
    , weibullDist
    , weibullDistMaybe
     -- * accessors
    , location
    , scale
    , shape
    ) where

import qualified Gev

data WeibullDistribution = Weibull {
      WeibullDistribution -> Double
location :: {-# UNPACK #-} !Double
    , WeibullDistribution -> Double
scale    :: {-# UNPACK #-} !Double
    , WeibullDistribution -> Double
shape    :: {-# UNPACK #-} !Double
    } deriving (WeibullDistribution -> WeibullDistribution -> Bool
(WeibullDistribution -> WeibullDistribution -> Bool)
-> (WeibullDistribution -> WeibullDistribution -> Bool)
-> Eq WeibullDistribution
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: WeibullDistribution -> WeibullDistribution -> Bool
$c/= :: WeibullDistribution -> WeibullDistribution -> Bool
== :: WeibullDistribution -> WeibullDistribution -> Bool
$c== :: WeibullDistribution -> WeibullDistribution -> Bool
Eq)

instance Show WeibullDistribution where
    show :: WeibullDistribution -> String
show (Weibull Double
loc Double
sc Double
sh) = ShowS
forall a. Show a => a -> String
show String
"Weibull 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

-- error message when initiating Weibull with scale and/or shape parameter less than 0.
weibullErrMsg :: Double -> Double -> Double -> String
weibullErrMsg :: Double -> Double -> Double -> String
weibullErrMsg Double
loc Double
scale Double
sh = String
"Gev.Weibull: " 
    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!"

weibullDistMaybe :: Double -> Double -> Double -> Maybe WeibullDistribution
weibullDistMaybe :: Double -> Double -> Double -> Maybe WeibullDistribution
weibullDistMaybe 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 = WeibullDistribution -> Maybe WeibullDistribution
forall a. a -> Maybe a
Just (WeibullDistribution -> Maybe WeibullDistribution)
-> WeibullDistribution -> Maybe WeibullDistribution
forall a b. (a -> b) -> a -> b
$ Double -> Double -> Double -> WeibullDistribution
Weibull Double
loc Double
sc Double
sh
    | Bool
otherwise = Maybe WeibullDistribution
forall a. Maybe a
Nothing

weibullDist :: Double -> Double -> Double -> WeibullDistribution
weibullDist :: Double -> Double -> Double -> WeibullDistribution
weibullDist Double
loc Double
sc Double
sh = WeibullDistribution
-> (WeibullDistribution -> WeibullDistribution)
-> Maybe WeibullDistribution
-> WeibullDistribution
forall b a. b -> (a -> b) -> Maybe a -> b
maybe (String -> WeibullDistribution
forall a. HasCallStack => String -> a
error (String -> WeibullDistribution) -> String -> WeibullDistribution
forall a b. (a -> b) -> a -> b
$ Double -> Double -> Double -> String
weibullErrMsg Double
loc Double
sc Double
sh) WeibullDistribution -> WeibullDistribution
forall a. a -> a
id (Maybe WeibullDistribution -> WeibullDistribution)
-> Maybe WeibullDistribution -> WeibullDistribution
forall a b. (a -> b) -> a -> b
$ Double -> Double -> Double -> Maybe WeibullDistribution
weibullDistMaybe Double
loc Double
sh Double
sc

-- | The CDF of the Weibull distribution
cdfWeibull :: WeibullDistribution -> Double -> Double
cdfWeibull :: WeibullDistribution -> Double -> Double
cdfWeibull (Weibull 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
sh)
        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

-- | The PDF of the Weibull distribution
pdfWeibull :: WeibullDistribution -> Double -> Double
pdfWeibull :: WeibullDistribution -> Double -> Double
pdfWeibull (Weibull 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
sh Double -> Double -> Double
forall a. Num a => a -> a -> a
- Double
1)
    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

quantileWeibull :: WeibullDistribution -> Double -> Double
quantileWeibull :: WeibullDistribution -> Double -> Double
quantileWeibull (Weibull 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.WeibullDistribution.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 WeibullDistribution where
    pdf :: WeibullDistribution -> Double -> Double
pdf      = WeibullDistribution -> Double -> Double
pdfWeibull
    cdf :: WeibullDistribution -> Double -> Double
cdf      = WeibullDistribution -> Double -> Double
cdfWeibull
    quantile :: WeibullDistribution -> Double -> Double
quantile = WeibullDistribution -> Double -> Double
quantileWeibull