{|j3 U g d Z ddlZddlZddlZddlZddlmZ ddlmZ ddl m
Z
m Z m Z ddl
mZmZ ddlmZmZmZmZmZmZmZmZmZ ddlmZ dd lm Z dd
l m Z m Z m Z ed Z! G d d
e" Z#d Z$dBdZ%d Z&d Z'd Z(d Z)dCdZ*dddddde+e, fdZ-de.d e.de.fd Z/d ej` jb z d z Z2e.e3d < de.d e.de,fd!Z4de.d e.defd"Z5d# Z6dBd$Z7d% Z8dBd&Z9d' Z:d( Z;d) Zd, Z?d-d.d/d0Z@dBd1ZAdBd2ZBdBd3ZCdBd4ZDd5 ZEd6 ZFd7d8d9ZG e d:d; ZHdd<d=ZId> ZJ dd?lKmJZJ G d@ dA ZMy# eL$ r Y w xY w)E)
NormalDistStatisticsError correlation
covariancefmeangeometric_mean
harmonic_meanlinear_regressionmeanmedianmedian_grouped median_high
median_lowmode multimodepstdev pvariance quantilesstdevvariance NFraction)Decimal)countgroupbyrepeat) bisect_left bisect_right) hypotsqrtfabsexperftaulogfsumsumprod)reduce)
itemgetter)Counter
namedtuple defaultdict @c e Zd Zy)r N)__name__
__module__ __qualname__ #/usr/lib64/python3.12/statistics.pyr r s r3 r c p d}t }|j }i }|j }t | t D ]9 \ }} || t t | D ] \ }} |dz
} || d |z || < ; d |v r|d }
n t d |j D }
t t |t } | |
|fS )Nr c 3 : K | ] \ }}t || y wNr .0dns r4 z_sum.. s @/?tq!HQN/? ) setaddgetr typemap _exact_ratiosumitemsr( _coerceint) datar types types_addpartials partials_gettypvaluesr< r; totalTs r4 _sumrR s >
E EE IH<. s . s @,?DAq!Q ,?r> c 3 @ K | ] \ }}t |||z y wr8 r r9 s r4 r= z_ss.. s" D/Ctq!(1ac"/Cs )rR r? r@ r, rH r rB rC rD r rE rF r( rG )rI rV rQ ssdr rJ rK sx_partials sxx_partialsrN rO r< sxsxxr; s ` @r4 _ssr^ sV } B?Bc # D K | D ] }|dk r t | | y w)Nr )r )rO errmsgrU s r4 _fail_negrx _ s* A
q5!&) ) s Faverager6 )keyreversetiesstartreturnc V |dk7 rt d| | t || } t t | t | }|dz
}dgt | z }t
|t d D ]: \ }} t | }
t |
} || dz dz z } |
D ]
\ }
}| ||< || z
}< |S )Nry z Unknown tie resolution method: )r{ r6 r )rz ) ro rC sortedzipr lenr r) list)rI rz r{ r| r} val_posiresult_ggroupsizerankrt orig_poss r4 _rankr g s H y:4(CDD
3~Suw'9G
AS3w<
FZ]31Q5zD1H>! $OE8 #F8 % T
4 Mr3 r< mc P t j | |z }|||z |z | k7 z S r8 )rb isqrt)r< r as r4 _integer_sqrt_of_frac_rtor s. P
16A !A
r3 r _sqrt_bit_widthc | j |j z
t z
dz }|dk\ r t | |d|z z |z }d}||z S t | d|z z | }d| z }||z S )Nr r r6 )
bit_lengthr r )r< r qrp rq s r4 _float_sqrt_of_fracr s ;
!,,. (? :q@AAv-aa!e<A { "" .a26k1= A2g { ""r3 c | dk r| s t d S | | }} t | t | z j }|j \ }}|j }|j \ }}d| z ||z dz z |||z ||z z dz z kD r|S |j }|j \ } }
d| z ||
z dz z ||| z |
|z z dz z k r|S |S )Nr z0.0 r )r r rm next_plus
next_minus) r< r rootnrdrplusnpdpminusnmdms r4 _decimal_sqrt_of_fracr s = Av5> !rA21 AJ # ) ) +D
"
"
$FB >> D
"
"
$FB1u2zABB 2 22 OO E
#
#
%FB1u2zABB 2 22 Kr3 c ` t | \ }}}|dk r t d t ||z | S )Nr6 z%mean requires at least one data point)rR r ru )rI rQ rP r< s r4 r
r
s< t*KAua1u EFF EAIq !!r3 c ^ |) t | t | }s t d |z S t |t
t f s t | } t | | }t | }|s t d ||z S # t $ r dfd} || } Y w xY w# t $ r t d w xY w)Nr c 3 @ K t | d D ] \ }| y w)Nr6 r} ) enumerate)iterablerU r< s r4 r zfmean..count s! %ha 8DAqG 9s z&fmean requires at least one data pointz(data and weights must be the same lengthz sum of weights must be non-zero) r ri r& r
isinstancer tupler' ro )rI weightsr rP numdenr< s @r4 r r s D A T
!"JK Kqy ge} -w-JdG$ w-C ?@@ 9+ A
;D J HIIJs A9 B 9BBB,c | t t t t | S # t $ r
t d d w xY w)NzGgeometric mean requires a non-empty dataset containing positive numbers)r" r rC r% ro r )rI s r4 r r sJ
G5S$ ()) G < =BF GGs !% ;c z t | | u r t | } d}t | }|dk r t d |dk( rD|B| d }t |t
j t f r|dk r t | |S t d |t d| }|}nQt | |u r t | }t | |k7 r t d t d t || D \ }}} t | | } t d t || D \ }}} |dk r t d t ||z | S # t $ r Y yw xY w)
Nz.harmonic mean does not support negative valuesr6 z.harmonic_mean requires at least one data pointr zunsupported typez*Number of weights does not match data sizec 3 K | ] }| y wr8 r2 )r: ws r4 r= z harmonic_mean..N s G,Fq,Fs c 3 4 K | ] \ }}|r||z nd yw)r Nr2 )r: r rU s r4 r= z harmonic_mean..Q s" P=OTQq1uq 0=Os z Weighted sum must be positive)iterr r r r numbersRealr ri r rR rx r ZeroDivisionErrorru )
rI r rw r< rU sum_weightsr rQ rP r s
r4 r r ! sR , DzTDz
=F D A1u NOO
aGO G a',,0 11u%f--H ./ /A, =G #7mG w<1 !"NO O GIgv,F G G;v& PS$=O PP5%
z =>> K%' ++ s #,D. . D:9D:c t | } t | }|dk( r t d |dz dk( r| |dz S |dz }| |dz
| | z dz S Nr no median for empty datar r6 r r r )rI r< r s r4 r r Y sl $@@As A> >Bc t t | j d } |d d S # t $ r
t d d w xY w)Nr6 r zno mode for empty data)r* r most_common
IndexErrorr )rI pairss r4 r r sU ,
DJ + +A .EBQx{ B 67TABs . Ac t t | }|sg S t |j }|j D cg c]
\ }}||k( s | c}}S c c}}w r8 )r* r maxrO rF )rI countsmaxcountrt r s r4 r r sX T$Z
F 6==?#H&,lln JnleU8IEn JJ Js
A A r exclusive)r< methodc * |dk r t d t | } t | }|dk r t d |dk( rW|dz
}g }t d| D ]? }t ||z | \ }}| | ||z
z | |dz |z z |z } |j | A |S |dk( rn|dz }g }t d| D ]V }||z |z }|dk rdn||dz
kD r|dz
n|}||z ||z z
}| |dz
||z
z | | |z z |z } |j | X |S t
d| )Nr6 zn must be at least 1r z"must have at least two data points inclusiver Unknown method: )r r r rangedivmodappendro )
rI r< r ldr r r r delta interpolateds
r4 r r 9 sf 1u 455 $>r3 c t | | \ }}}}|dk r t d ||z }t |t r t |j
|j S t |j
|j S )Nr6 z'pstdev requires at least one data pointr )rI r rQ r rV r< r s r4 r r sl dB-KAr1a1u GHH
q&C!W $S]]COODD s}}coo >>r3 c t | \ }}}}|dk r t d ||dz
z } t | t |j |j
fS # t $ r% t | t | t | z fcY S w xY wr )r^ r rh r rp rq ra )rI rQ r r r< r s r4 _mean_stdevr s PYNAr41u GHH
A,C4T{ /
s OOO 4T{E$K%) 3334s *A +BBc t | }t | |k7 r t d |dk r t d t | |z t | |z t fd| D fd|D }||dz
z S )NzDcovariance requires that both inputs have same number of data pointsr z,covariance requires at least two data pointsc 3 ( K | ] }|z
y wr8 r2 )r: xir s r4 r= z covariance.. s )q29q c 3 ( K | ] }|z
y wr8 r2 r: yiybars r4 r= z covariance.. s +B"BIr r6 )r r r& r' )rU yr< sxyr r s @@r4 r r s} AA
1v{ dee1u LMM 7Q;D 7Q;D
)q)+B+B
CC !a%=r3 linear)r c t | }t | |k7 r t d |dk r t d |dvrt d| |dk( r#|dz
dz }t | | } t || }n@t | |z }t | |z }| D cg c] }||z
} }|D cg c] }||z
}}t | | } t | | }
t || } | t
|
| z z S c c}w c c}w # t $ r t d
w xY w) NzEcorrelation requires that both inputs have same number of data pointsr z-correlation requires at least two data points> r rankedr r r6 r r z&at least one of the inputs is constant)r r ro r r& r' r r ) rU r r r< r} r r r r r r] syys r4 r r s0 , AA
1v{ eff1u MNN
))+F:677
Q" !5 ! !5 !Aw{Aw{!" #2R$Y #!" #2R$Y #
!Q-C
!Q-C
!Q-CHT#)_$$
$ # H FGGHs C&" C+C0 0DLinearRegressionslope intercept) proportionalc
t | }t | |k7 r t d |dk r t d |s9t | |z }t | |z
| D cg c] }||z
} }
fd|D }t | | dz }t | | } ||z }|rdn
|z z
} t || S c c}w # t $ r t d w xY w)NzKlinear regression requires that both inputs have same number of data pointsr z3linear regression requires at least two data pointsc 3 ( K | ] }|z
y wr8 r2 r s r4 r= z$linear_regression..u s #2R$Yr z
x is constantr )r r r& r' r r ) rU r r r< r r r r] r r r s @r4 r r F s $J AA
1v{ kll1u STT Aw{Aw{!" #2R$Y # # #
!Q-#
C
!Q-C/c $ )l@g N@g"]Ξ@gnC`@gu @giK~j@gv|E@gd|1@gfRr@gu.2@g~y@gn8(E@ ?r g @g?g鬷ZaI?ggElD?g7\?guSS?g=.
@gj%b@gHw@gjRe?g9dh?
>g('߿A?g~z ?g@3?gɅ3?g3fRx?gIFl @gt>g*Yn>gESB\T?gN;A+?gUR1?gE F?gPn@g&>@gigtcI,\>gŝI?g*F2v?gC4?gO1?)r! r r% )pr sigmar rr r rU s r4 _normal_dist_inv_cdfr s
CA Aw% q1u 0140145601456 11 566 1 1 56 6
1 1
56 6 1
1 56
6 11 566 1140145601456 11 566 1 1 56 6
1 1
56 6 1
1 56
6
#IQY
#X37A c!fW
ACx
G1A51256712567 22 677 2 2 67 7
2 2
67 7 2
2 67
7 22 2A51256712567 22 677 2 2 67 7
2 2
67 7 2
2 67
7
G1A51256712567 22 677 2 2 67 7
2 2
67 7 2
2 67
7 22 3Q61256712567 22 677 2 2 67 7
2 2
67 7 2
2 67
7 c A3w
B
U r3 )r c e Zd Z dddZd dZed ZdddZd Zd
Z d Z
d!d Z d
Z d Z
ed Zed Zed Zed Zed Zd Zd Zd Zd Zd Zd ZeZd ZeZ d Z d Z d Z d Z d Z!y)"r z(Arithmetic mean of a normal distributionz+Standard deviation of a normal distribution_mu_sigmac f |dk r t d t | | _ t | | _ y )Nr zsigma must be non-negative)r rh r r )selfr r s r4 __init__zNormalDist.__init__ s. N 3;!">? ?9El r3 c | t | S r8 )r )clsrI s r4 from_sampleszNormalDist.from_samples s ?K%&&r3 N)seedc |t j n t j | j }| j | j }}t d | D cg c] } |||
c}S c c}w r8 )randomgaussRandomr r r )r r< r r r r r s r4 sampleszNormalDist.samples sY G $ &--2E2K2KHHdkkE*0q/:/Qb% /:::s A,c | j | j z }|s t d || j z
}t ||z d|z z t t
|z z S )Nz$pdf() not defined when sigma is zerog )r r r r" r r$ )r rU r diffs r4 pdfzNormalDist.pdf sY >;;,!"HI I488|4$;$/23d3>6JJJr3 c | j s t d ddt || j z
| j t z z z z S )Nz$cdf() not defined when sigma is zeror r )r r r# r _SQRT2r rU s r4 cdfzNormalDist.cdf sC 6{{!"HI IcCTXX $++2F G HHIIr3 c p |dk s|dk\ r t d t || j | j S )Nr r z$p must be in the range 0.0 < p < 1.0)r r r r )r r s r4 inv_cdfzNormalDist.inv_cdf s9
8qCx!"HI I#Atxx==r3 c f t d| D cg c] }| j ||z c}S c c}w rs )r r! )r r< r s r4 r zNormalDist.quantiles s4 .31a[9[ QU#[999s .c t |t s t d | |}}|j |j f|j |j fk r||}}|j
|j
}}|r|s t
d ||z
}t |j |j z
}|s%dt |d|j z t z z z
S |j |z |j |z z
}|j |j z t ||z |t ||z z z z } || z |z }
|| z
|z } dt |j |
|j |
z
t |j | |j | z
z z
S )Nz$Expected another NormalDist instancez(overlap() not defined when sigma is zeror r- )
r r ri r r r r r! r# r r r% r ) r otherXYX_varY_vardvr r bx1x2s r4 overlapzNormalDist.overlap sd
%, BC CU1
HHaee !%% 0 0aqAzz1::uE!"LM M
U]
!%%!%%-
R3>F#: ;<< <
EEEMAEEEM )
HHqxx $rBwc%%-6H1H'H"I I!er\!er\d1559quuRy01DrQUU2Y9N4OOPPr3 c j | j s t d || j z
| j z S )Nz'zscore() not defined when sigma is zero)r r r r s r4 zscorezNormalDist.zscore9 s3 {{!"KL LDHH ++r3 c | j S r8 r r s r4 r
zNormalDist.meanD s 5xxr3 c | j S r8 r1 r2 s r4 r zNormalDist.medianI s 6xxr3 c | j S r8 r1 r2 s r4 r zNormalDist.modeN s
xxr3 c | j S r8 r r2 s r4 r zNormalDist.stdevW s 8{{r3 c 6 | j | j z S r8 r6 r2 s r4 r zNormalDist.variance\ s +{{T[[((r3 c t |t rAt | j |j z t | j |j S t | j |z | j S r8 r r r r r r+ r, s r4 __add__zNormalDist.__add__a T b* % bffrvvouRYY /JK K"&&2+ryy11r3 c t |t rAt | j |j z
t | j |j S t | j |z
| j S r8 r9 r: s r4 __sub__zNormalDist.__sub__o r< r3 c b t | j |z | j t | z S r8 r r r r! r: s r4 __mul__zNormalDist.__mul__} +
"&&2+ryy48';< rA rD rH rJ __radd__rL __rmul__rO rR rU rW rZ r2 r3 r4 r r s .
:?I
# ' ' "& ; KJ > : QD , ) ) 2 2 ==-. H H; -P%&r3 r r8 )znegative value)r )N__all__rb r r sys fractionsr decimalr itertoolsr r r bisectr r r r r! r" r# r$ r% r& r' functoolsr( operatorr) collectionsr* r+ r, r ro r rR r^ rd rG rD ru rx r rh r rH r
float_infomant_digr __annotations__r r r
r r r r r r
r r r r r r r r r r r r r r _statistics ImportErrorr r2 r3 r4 rn s hT .
, , , E E E 8 8
c j 3 l& R 4>+ \$ IQ 34PU; 3l 3>>222Q6 6
#3
#3
#5
#S S W <",!HG&5,p+0 ,&E+PB<Kr ; (4b)%X& R?$?$
4(8 $, -H` 02HI 05 7>zG V 0
Z& Z& s /E EE