Your IP : 18.217.8.237


Current Path : /opt/alt/python313/lib64/python3.13/__pycache__/
Upload File :
Current File : //opt/alt/python313/lib64/python3.13/__pycache__/statistics.cpython-313.opt-2.pyc

�

*}g���
���%/SQrSSKrSSKrSSKrSSKrSSKJr SSKJr SSK	J
r
JrJr SSK
JrJr SSKJrJrJrJrJrJrJrJrJr SSKJrJrJrJrJrJrJrJ r J!r!J"r" SS	K#J$r$ SS
K%J&r& SSK'J(r(J)r)J*r* \"S5r+\r,"S
S\-5r.Sr/SaSjr0Sr1Sr2Sr3Sr4SbSjr5SSSSS.S\6\74Sjjr8S\9S\9S\94Sjr:S\RvRx-S -r=\9\>S!'S\9S\9S\74S"jr?S\9S\9S\4S#jr@S$rASaS%jrBS&rCSaS'jrDS(rES)rFS*rGScS+jrHS,rIS-rJSdSS/.S0jjrKS1S2S3.S4jrLSaS5jrMSaS6jrNSaS7jrOSaS8jrPS9rQS:\7S;\7S\74S<jrRS=rSS>S?.S@jrT\)"SASB5rUSSC.SDjrVSErWSSFKXJWrW "SGSH5rZSeSIjr[SJr\\["\\SKSLSM9r]SNr^\["\^SOSPSM9r_\Z"5R�SQSRSSST\]\_SUSVSW.	ra\aS.\aSX'\aSY\aSZ'\aS[\aS\'\aS]\aS^'SdSS_.S`jjrbg!\Ya N|f=f)f)�
NormalDist�StatisticsError�correlation�
covariance�fmean�geometric_mean�
harmonic_mean�kde�
kde_random�linear_regression�mean�median�median_grouped�median_high�
median_low�mode�	multimode�pstdev�	pvariance�	quantiles�stdev�variance�N��Fraction)�Decimal)�count�groupby�repeat)�bisect_left�bisect_right)	�hypot�sqrt�fabs�exp�erf�tau�log�fsum�sumprod)
�isfinite�isinf�pi�cos�sin�tan�cosh�asin�atan�acos)�reduce)�
itemgetter)�Counter�
namedtuple�defaultdict�@c��\rSrSrSrg)r��N)�__name__�
__module__�__qualname__�__firstlineno__�__static_attributes__r<��1/opt/alt/python313/lib64/python3.13/statistics.pyrr�s��rBrc�r�Sn[5nURn0nURn[U[5H9upgU"U5 [[U5Hup�US-
nU"U	S5U-XI'M M; SU;aUSn
O [SUR555n
[[U[5nX�U4$)Nr�c3�<# �UHup[X!5v� M g7f�Nr��.0�d�ns   rC�	<genexpr>�_sum.<locals>.<genexpr>�s���@�/?�t�q�H�Q�N�N�/?���)�set�add�getr�type�map�_exact_ratio�sum�itemsr4�_coerce�int)�datar�types�	types_add�partials�partials_get�typ�valuesrKrJ�total�Ts            rC�_sumrb�s���@
�E��E�E��	�	�I��H��<�<�L��t�T�*����#����f�-�D�A��Q�J�E�&�q�!�,�q�0�H�K�.�+�
�x�������@�x�~�~�/?�@�@���w��s�#�A�
�e��rBc�^^�Tb[UU4SjU55up#nX#TU4$Sn[5nURn[[5n[[5n[U[5HHup�U"U	5 [[U
5H'unmUS-
nUT==U-
ss'UT==X�--
ss'M) MJ U(d[S5=nmO^SU;aUS=nmOP[SUR555n[SUR555n
XM-X�--
U-nX�-m[[U[5nX#TU4$)Nc3�6># �UHoT-
=mT-v� M g7frGr<)rI�x�crJs  ��rCrL�_ss.<locals>.<genexpr>�s����<�t�!�q�5�j�a�A�-�t�s�rrEc3�<# �UHup[X!5v� M g7frGrrHs   rCrLrg�s���@�,?�D�A��!���,?�rNc3�B# �UHup[X!U-5v� M g7frGrrHs   rCrLrg�s ���D�/C�t�q�(�1��c�"�"�/C�s�)rbrOrPr8rXrrRrSrTrrUrVr4rW)rYrfra�ssdrrZr[�sx_partials�sxx_partialsr^r_rK�sx�sxxrJs `            @rC�_ssro�sA���	�}��<�t�<�<�
�����5�!�!�
�E��E�E��	�	�I��c�"�K��s�#�L��t�T�*����#����f�-�D�A�q��Q�J�E���N�a��N���O�q�u�$�O�.�+���1�+���a�	
��	��d�#�#��a��@�K�,=�,=�,?�@�
@���D�|�/A�/A�/C�D�D���{�R�W�$��-���J���w��s�#�A�
�A�u��rBc�p�UR5$![a [R"U5s$f=frG)�	is_finite�AttributeError�mathr*)res rC�	_isfinitert�s1�� ��{�{�}���� ��}�}�Q��� �s�� 5�5c���XLaU$U[Ld	U[LaU$U[LaU$[X5(aU$[X5(aU$[U[5(aU$[U[5(aU$[U[5(a[U[5(aU$[U[5(a[U[5(aU$Sn[X RUR4-5e)Nz"don't know how to coerce %s and %s)rX�bool�
issubclassr�float�	TypeErrorr=)ra�S�msgs   rCrWrWs���	�v�q���C�x�1��9�a�x��C�x��(��!����(��!����(��!�S���1�H��!�S���1�H��!�X���:�a��#7�#7����!�U���
�1�h� 7� 7���
.�C�
�C�:�:�q�z�z�2�2�
3�3rBc��UR5$![a O[[4a US4s$f=fURUR
4$![a% S[
U5RS3n[U5ef=f)Nzcan't convert type 'z' to numerator/denominator)	�as_integer_ratiorr�
OverflowError�
ValueError�	numerator�denominatorrRr=ry)rer{s  rCrTrT#s���<��!�!�#�#���
���:�&���4�y��������Q�]�]�+�+����$�T�!�W�%5�%5�$6�6P�Q����n���s��
4�4�4�A�/A?c� �[U5ULaU$[U[5(aURS:wa[nU"U5$![
a> [U[5(a'U"UR5U"UR5-s$ef=f�NrE)rRrwrXr�rxryrr�)�valueras  rC�_convertr�Qs����E�{�a�����!�S���e�/�/�1�4������x������a��!�!��U�_�_�%��%�*;�*;�(<�<�<��	�s�A�AB
�B
c#�H# �UHnUS:a[U5eUv� M g7f)Nr)r)r_�errmsgres   rC�	_fail_negr�cs&���
���q�5�!�&�)�)����s� "F�averagerE)�key�reverse�ties�start�returnc�J�US:wa[SU<35eUb[X5n[[U[	55US9nUS-
nS/[U5-n[
U[S5S9H8up�[U	5n
[U
5nXkS-S--nU
H	up�X�U'M Xk-
nM: U$)Nr�zUnknown tie resolution method: )r�rEr)r��)	rrS�sorted�zipr�lenrr5�list)rYr�r�r�r��val_pos�i�result�_�g�group�size�rankr��orig_poss               rC�_rankr�ks���J�y���:�4�(�C�D�D�
���3�~���S��u�w�'��9�G�
��	�A��S�3�w�<�
�F���Z��]�3����Q����5�z���1�H��>�!��$�O�E�#�8�� %�	�	��
4��MrBrK�mc�L�[R"X-5nX"U-U-U:g-$rG)rs�isqrt)rKr��as   rC�_integer_sqrt_of_frac_rtor��s)��	
�
�
�1�6��A��!��A���
��rBr���_sqrt_bit_widthc���UR5UR5-
[-
S-nUS:�a[XSU--5U-nSnX4-$[USU--U5nSU*-nX4-$)Nr�rrE���)�
bit_lengthr�r�)rKr��qr�r�s     rC�_float_sqrt_of_fracr��s|��
����!�,�,�.�	(�?�	:�q�@�A��A�v�-�a�a�!�e��<��A�	����"�"�.�a�2��6�k�1�=�	��A�2�g���"�"rBc��US::aU(d[S5$U*U*p[U5[U5-R5nUR5up4UR5nUR5upgSU-XG-S--XU-Xs--S--:�aU$UR	5nUR5up�SU-XJ-S--XU	-X�--S--:aU$U$)Nrz0.0�r�)rr"r}�	next_plus�
next_minus)rKr��root�nr�dr�plus�np�dp�minus�nm�dms           rC�_decimal_sqrt_of_fracr��s���
	�A�v���5�>�!��r�A�2�1��A�J����#�)�)�+�D�
�
"�
"�
$�F�B��>�>��D�
�
"�
"�
$�F�B��1�u����z��A�B������ 2�2�2����O�O��E�
�
#�
#�
%�F�B��1�u����z��A�B������ 2�2�2����KrBc�\�[U5upnUS:a[S5e[X#-U5$)NrEz%mean requires at least one data point)rbrr�)rYrar`rKs    rCrr�s3�� �t�*�K�A�a��1�u��E�F�F��E�I�q�!�!rBc�~^�Uc.[U5m[U5nT(d[S5eUT-$[	U[
[45(d[U5n[X5n[U5nU(d[S5eXE-$![a SmU4SjnU"U5nN�f=f![a [S5ef=f)Nrc3�>># �[USS9H
umnUv� M g7f)NrE�r�)�	enumerate)�iterablererKs  �rCr�fmean.<locals>.count�s ����%�h�a�8�D�A�q��G�9�s�z&fmean requires at least one data pointz(data and weights must be the same lengthzsum of weights must be non-zero)	r�ryr(r�
isinstancer��tupler)r)rY�weightsrr`�num�denrKs      @rCrr�s������		��D�	�A��T�
���!�"J�K�K��q�y���g��e�}�-�-��w�-��J��d�$���w�-�C���?�@�@��9���+�	��A�
���;�D�	�� �J��H�I�I�J�s�B�B&�B#�"B#�&B<c�J^^�SmSmUU4Sjn[[[U"U555nT(d[S5e[R
"U5(a[R$T(a&U[R:Xa[R$S$[UT-5$)NrFc3�># �[USS9HAumnUS:�d[R"U5(aUv� M-US:XaSmM7[SU5e g7f)NrEr��TzNo negative inputs allowed)r�rs�isnanr)r�re�
found_zerorKs  ��rC�count_positive�&geometric_mean.<locals>.count_positive"sM�����h�a�0�D�A�q��3�w�$�*�*�Q�-�-����c��!�
�%�&B�A�F�F�
1�s�AAzMust have a non-empty datasetr�)	r(rSr'rrsr��nan�infr$)rYr�r`r�rKs   @@rCrrs���	
�A��J�G�
��S�.��.�/�0�E���=�>�>��z�z�%����x�x��� �D�H�H�,�t�x�x�5�#�5��u�q�y�>�rBc��[U5ULa[U5nSn[U5nUS:a[S5eUS:XaKUcHUSn[	U[
R[45(aUS:a[U5eU$[S5eUc[SU5nUnOQ[U5ULa[U5n[U5U:wa[S5e[S[X555upen[X5n[S[X555upxn	US::a[S	5e[XX-U5$![a gf=f)
Nz.harmonic mean does not support negative valuesrEz.harmonic_mean requires at least one data pointrzunsupported typez*Number of weights does not match data sizec3�$# �UHov� M g7frGr<)rI�ws  rCrL� harmonic_mean.<locals>.<genexpr>bs��� G�,F�q��,F�s�c3�@# �UHupU(aX-OSv� M g7f)rNr<)rIr�res   rCrLr�es���P�=O�T�Q��q�u�q�0�=O�s�zWeighted sum must be positive)�iterr�r�rr��numbers�Realrryrrbr�r��ZeroDivisionErrorr�)
rYr�r�rKre�sum_weightsr�rar`rs
          rCrr5sD��.�D�z�T���D�z��
=�F��D�	�A��1�u��N�O�O�	
�a��G�O���G���a�'�,�,��0�1�1��1�u�%�f�-�-��H��.�/�/�����A�,������=�G�#��7�m�G��w�<�1��!�"N�O�O� � G�I�g�,F� G�G�������&���P�S��=O�P�P���%�
��z��=�>�>��K�'��+�+��	����s�-)D5�5
E�Ec��[U5n[U5nUS:Xa[S5eUS-S:XaXS-$US-nXS-
X-S-$�Nr�no median for empty datar�rE�r�r�r)rYrKr�s   rCr
r
msa���$�<�D��D�	�A��A�v��8�9�9��1�u��z���F�|��
��F����U��d�g�%��*�*rBc��[U5n[U5nUS:Xa[S5eUS-S:XaXS-$XS-S-
$r�r��rYrKs  rCrr�sQ���$�<�D��D�	�A��A�v��8�9�9��1�u��z���F�|����F�Q�J��rBc�^�[U5n[U5nUS:Xa[S5eXS-$)Nrr�r�r�r�s  rCrr�s5���$�<�D��D�	�A��A�v��8�9�9��Q��<�rBc�$�[U5n[U5nU(d[S5eXS-n[X5n[	XUS9n[U5n[U5nX1S--
nUnXT-
nXaUS-U-
-U--$![a [S5ef=f)Nr�r�)�loz$Value cannot be converted to a floatr9)r�r�rrr rxrry)	rY�intervalrKrer��j�L�cf�fs	         rCrr�s���V�$�<�D��D�	�A���8�9�9�	
�!�V��A�	�D��A��T��#�A�A���?���!�H��	
�s�N��A�	
�B�	��A��1�q�5�2�:�&��*�*�*���A��>�@�@�A�s�A9�9Bc��[[U55RS5nUSS$![a
 [	S5Sef=f)NrErzno mode for empty data)r6r��most_common�
IndexErrorr)rY�pairss  rCrr�sP��.
�D��J��+�+�A�.�E�B��Q�x��{����B��6�7�T�A�B�s	�-�Ac���[[U55nU(d/$[UR55nUR	5VVs/sHup4XB:XdMUPM snn$s snnfrG)r6r��maxr_rV)rY�counts�maxcountr�rs     rCrrsO���T�$�Z�
 �F���	��6�=�=�?�#�H�&,�l�l�n�J�n�l�e��8I�E�n�J�J��Js�
A#�A#�normal)�
cumulativec��^^^^^	^
^^^
^^�[T5mT(d[S5e[TS[[45(d[S5eTS::a[ST<35eU==S:XaO	=S:XaO O.  [
S[-5m[
S5mU4S	jmU4S
jmSnO�=S:Xa
 SmS
mSnO�=S:Xa" S[-m
S[-mU
4SjmU4SjmSnO�==S:XaO	=S:XaO O  SmSmSnO�=S:Xa
 SmSmSnO==S:XaO	=S:XaO O  SmSmSnOc==S:XaO	=S:XaO O  S mS!mSnOG=S":Xa
 S#mS$mSnO7S%:Xa"[S&-m
[S-mU
U4S'jmU4S(jmSnO[S)U<35eUcUUU4S*jnUUU4S+jnO&[T5m
TU-m	UU	UUUU
4S,jnUU	UUUU
4S-jnU(aS.T<S/U<3Ul	U$S0T<S/U<3Ul	U$)1N�Empty data sequencer�)Data sequence must contain ints or floatsr��$Bandwidth h must be positive, not h=r��gaussr�c�,>�[SU-U-5T-$)N�࿩r$)�t�sqrt2pis �rC�<lambda>�kde.<locals>.<lambda>�s���#�d�Q�h��l�+�g�5rBc�,>�SS[UT-5--$�N��?��?)r%)r��sqrt2s �rCr�r��s���#��s�1�u�9�~�!5�6rB�logisticc�$�SS[U5--$r��r0�r�s rCr�r��s��#��t�A�w��/rBc�*�SS[U5S---
$�Nr�r�rs rCr�r��s��#��s�1�v��|� 4�4rB�sigmoidrEc� >�T[U5-$rGr)r��c1s �rCr�r��s
���"�t�A�w�,rBc�2>�T[[U55-$rG)r2r$�r��c2s �rCr�r��s���"�t�C��F�|�+rB�rectangular�uniformc��g�Nr�r<rs rCr�r��s��#rBc��SU-S-$rr<rs rCr�r��s��#��'�C�-rBr��
triangularc��S[U5-
$r��absrs rCr�r��s��#��A��,rBc�,�X-US:aSOS-U-S-$)Nr�r�r�r<rs rCr�r��s��!�#��C���T�:�Q�>��DrB�	parabolic�epanechnikovc��SSX--
-$)N��?r�r<rs rCr�r��s��#��q�u��-rBc�$�SUS--SU--S-$)Ngпr�rr�r<rs rCr�r��s��$��A��+��a��/�#�5rB�quartic�biweightc��SSX--
S--$�N��?r�r�r<rs rCr�r�����%�3���;�1�"4�4rBc�6�SUS--SUS---
SU--S-$�Ng�?�g�?r�r r�r<rs rCr�r��s'��$��A��+��a��d�
�2�U�Q�Y�>��DrB�	triweightc��SSX--
S--$�N���?r�r�r<rs rCr�r��r!rBc�B�SSUS--SUS---US--
U--S-$�Nr(g�$I�$I¿�g333333�?r$r�r�r<rs rCr�r��s1��%�4��1��9�s�1�a�4�x�#7�!�Q�$�#>��#B�C�c�IrB�cosiner�c�&>�T[TU-5-$rG)r-)r�r	rs ��rCr�r��s���"�s�2��6�{�*rBc�,>�S[TU-5-S-$r�r.rs �rCr�r��s���#��B��F��+�c�1rB�Unknown kernel name: c�V>^�[T5n[UUU4SjT55UT--$)Nc3�@># �UHnT"TU-
T-5v� M g7frGr<�rI�x_i�K�hres  ���rCrL�#kde.<locals>.pdf.<locals>.<genexpr>��!����8�4�C�q�!�c�'�Q��'�'�4����r�rU)rerKr5rYr6s` ���rC�pdf�kde.<locals>.pdf�s&����D�	�A��8�4�8�8�A��E�B�BrBc�P>^�[T5n[UUU4SjT55U-$)Nc3�@># �UHnT"TU-
T-5v� M g7frGr<�rIr4�Wr6res  ���rCrL�#kde.<locals>.cdf.<locals>.<genexpr>�r8r9r:)rerKr@rYr6s` ���rC�cdf�kde.<locals>.cdf�s"����D�	�A��8�4�8�8�1�<�<rBc��>^�[T5T:wa[T5m	[T5m[T	TT-
5n[T	TT-5nT	Xn[	UUU4SjU55TT--$)Nc3�@># �UHnT"TU-
T-5v� M g7frGr<r3s  ���rCrLr7�s!����=�9�C�q�!�c�'�Q��'�'�9�r9�r�r�rr rU)
rer�r��	supportedr5�	bandwidthrYr6rK�samples
`   ������rCr;r<�sc����4�y�A�~�������I���F�A�	�M�2�A��V�Q��]�3�A��q�
�I��=�9�=�=��Q��G�GrBc��>^�[T5T:wa[T5m	[T5m[T	TT-
5n[T	TT-5nT	Xn[	UUU4SjU5U5T-$)Nc3�@># �UHnT"TU-
T-5v� M g7frGr<r?s  ���rCrLrA�s!����>�I�S��1�s�7�a�-�(�(�I�r9rF)
rer�r�rGr@rHrYr6rKrIs
`   ������rCrBrC�sa����4�y�A�~�������I���F�A�	�M�2�A��V�Q��]�3�A��q�
�I��>�I�>��B�Q�F�FrBzCDF estimate with h=� and kernel=zPDF estimate with h=)
r�rr�rXrxryr"r,r��__doc__)rYr6�kernelr��supportr;rBr5r@rHr	rrKrIrr�s``     @@@@@@@@@rCr	r	(s�����H	�D�	�A���3�4�4��d�1�g��U�|�,�,��C�D�D��C�x�� E�1�&�I�J�J�
�
�X��
��1�r�6�l�G���G�E�5�A�6�A��G�
�/�A�4�A��G�
��R��B��R��B�&�A�+�A��G�
&�]�Y�
&��A�'�A��G�
�&�A�D�A��G�
)�[�>�
)�-�A�5�A��G�
#�Y��
#�4�A�D�A��G�
�4�A�I�A��G�
��a��B��a��B�*�A�1�A��G�
�!�$9�&��"D�E�E���	C�	=�	=�������K�	�	H�	H�	G�	G��-�1�&�
�f�[�A����
�.�1�&�
�f�[�A����
rBr��	exclusive)rK�methodc�@�US:a[S5e[U5n[U5nUS:aUS:XaXS-
-$[S5eUS:XaTUS-
n/n[SU5H;n[	Xd-U5upxXX-
-XS-U--U-n	URU	5 M= U$US:XakUS-n/n[SU5HRnXd-U-nUS:aSOXsS-
:�aUS-
OUnXd-Xq--
nXS-
X-
-XU--U-n	URU	5 MT U$[
SU<35e)NrEzn must be at least 1r�z!must have at least one data point�	inclusiverP�Unknown method: )rr�r��range�divmod�appendr)
rYrKrQ�ldr�r�r�r��delta�interpolateds
          rCrr!s\�� 	�1�u��4�5�5��$�<�D�	�T��B�	�A�v�
��7��q�5�>�!��A�B�B�
�����F�����q�!��A��a�e�Q�'�H�A� �G�q�y�1�D�Q��K�%�4G�G�1�L�L��M�M�,�'���
�
�����F�����q�!��A����
�A���U���q�D���1��a�A��C�!�#�I�E� �Q��K�1�9�5���%��G�1�L�L��M�M�,�'���
�
�'��z�2�
3�3rBc�b�[X5up#pEUS:a[S5e[X5S-
-U5$)Nr�z*variance requires at least two data pointsrE�rorr�)rY�xbarra�ssrfrKs      rCrrWs8��L�d�/�K�A�1��1�u��J�K�K��B�a�%�L�!�$�$rBc�\�[X5up#pEUS:a[S5e[X5-U5$)NrEz*pvariance requires at least one data pointr\)rY�murar^rfrKs      rCrr�s4��F�d�-�K�A�1��1�u��J�K�K��B�F�A��rBc��[X5up#pEUS:a[S5eX5S-
-n[U[5(a [	UR
UR5$[UR
UR5$�Nr�z'stdev requires at least two data pointsrE�rorrwrr�r�r�r�)rYr]rar^rfrK�msss       rCrr�sf���d�/�K�A�1��1�u��G�H�H�
�A��,�C��!�W���$�S�]�]�C�O�O�D�D��s�}�}�c�o�o�>�>rBc���[X5up#pEUS:a[S5eX5-n[U[5(a [	UR
UR5$[UR
UR5$)NrEz'pstdev requires at least one data pointrc)rYr`rar^rfrKrds       rCrr�sb���d�-�K�A�1��1�u��G�H�H�
�&�C��!�W���$�S�]�]�C�O�O�D�D��s�}�}�c�o�o�>�>rBc�
�[U5upp4US:a[S5eX$S-
-n[U5[URUR
54$![a% [U5[U5[U5-4s$f=frb)rorrxr�r�r�rr)rYrar^r]rKrds      rC�_mean_stdevrg�s|����Y�N�A�4��1�u��G�H�H�
�A��,�C�4��T�{�/��
�
�s���O�O�O���4��T�{�E�$�K�%��)�3�3�3�4�s�*A�,B�Bre�yc�T�[X-5n[U5(dG[U5(a5[U5(d%[U5(dSn[X0-X1-5U-$U$U(d%U(aU(aSn[X0-X1-5U-$U$[	X4X*45nX$SU---$)Ng�g�ar9)r"r*r+�	_sqrtprodr))rerhr6�scalerJs     rCrjrj�s����Q�U��A��A�;�;���8�8�E�!�H�H�U�1�X�X��E��U�Y��	�2�U�:�:�������E��U�Y��	�2�U�:�:���	����B�� �A��C�!�G�}��rBc�^^�[U5n[U5U:wa[S5eUS:a[S5e[U5U-m[U5U-m[U4SjU5U4SjU55nX2S-
-$)NzDcovariance requires that both inputs have same number of data pointsr�z,covariance requires at least two data pointsc3�,># �UH	oT-
v� M g7frGr<)rI�xir]s  �rCrL�covariance.<locals>.<genexpr>s����)�q���9�q���c3�,># �UH	oT-
v� M g7frGr<�rI�yi�ybars  �rCrLros����+B��"��I��rprE)r�rr(r))rerhrK�sxyr]rts    @@rCrr�sv���"	�A��A�
�1�v��{��d�e�e��1�u��L�M�M���7�Q�;�D���7�Q�;�D�
�)�q�)�+B��+B�
C�C��a�%�=�rB�linear)rQc��[U5n[U5U:wa[S5eUS:a[S5eUS;a[SU<35eUS:XaUS-
S-n[XS	9n[XS	9nOD[	U5U-n[	U5U-nUVs/sHowU-
PM	 nnUVs/sHo�U-
PM	 nn[X5n	[X5n
[X5nU	[
X�5-$s snfs snf![a [S
5ef=f)NzEcorrelation requires that both inputs have same number of data pointsr�z-correlation requires at least two data points>rv�rankedrTrxrEr�r�z&at least one of the inputs is constant)r�rrr�r(r)rjr�)rerhrQrKr�r]rtrnrsrurn�syys            rCrrs��.	�A��A�
�1�v��{��e�f�f��1�u��M�N�N�
�)�)��+�F�:�6�7�7�
����Q��"����!�!���!�!���A�w��{���A�w��{��!"�#��2�$�Y���#�!"�#��2�$�Y���#�
�!�-�C�
�!�-�C�
�!�-�C�H��Y�s�(�(�(��

$��#���H��F�G�G�H�s�
C!�!C&�
C+�+D�LinearRegression��slope�	intercept)�proportionalc�^
�[U5n[U5U:wa[S5eUS:a[S5eU(d<[U5U-n[U5U-m
UVs/sHoUU-
PM	 nnU
4SjU5n[X5S-n[X5nXg-nU(aSOT
UW--
n	[X�S9$s snf![a [S5ef=f)NzKlinear regression requires that both inputs have same number of data pointsr�z3linear regression requires at least two data pointsc3�,># �UH	oT-
v� M g7frGr<rrs  �rCrL�$linear_regression.<locals>.<genexpr>ws����#��2�$�Y��rpr�z
x is constantr{)r�rr(r)r�rz)rerhr~rKr]rnrurnr|r}rts          @rCrrHs����L	�A��A�
�1�v��{��k�l�l��1�u��S�T�T���A�w��{���A�w��{��!"�#��2�$�Y���#�#��#��
�!�-�#�
�C�
�!�-�C�/��	��$������)<�I��%�=�=��
$���/��o�.�.�/�s�B3�B8�8Cc���US-
n[U5S::amSX3--
nSU-S-U-S-U-S-U-S-U-S	-U-S
-U-S-U-nSU-S
-U-S-U-S-U-S-U-S-U-S-U-S-nXV-nXU--$US::aUOSU-
n[[U5*5nUS::a^US-
nSU-S-U-S-U-S-U-S-U-S-U-S-U-S-nSU-S -U-S!-U-S"-U-S#-U-S$-U-S%-U-S-nO]US-
nS&U-S'-U-S(-U-S)-U-S*-U-S+-U-S,-U-S--nS.U-S/-U-S0-U-S1-U-S2-U-S3-U-S4-U-S-nXV-nUS:aU*nXU--$)5Nr�g333333�?g��Q��?g^�}o)��@g�E.k�R�@g ��Ul�@g*u��>l�@g�N����@g�"]Ξ@gnC���`@gu��@giK��~j�@gv��|E�@g��d�|1�@gfR��r��@g��u.2�@g���~y�@g�n8(E@r�r�g@g�������?g鬷�ZaI?gg�El�D�?g7\�����?g�uS�S�?g�=�.
@gj%b�@g���Hw�@gjR�e�?g�9dh?
>g('߿��A?g��~z �?g@�3��?gɅ3��?g3fR�x�?gI�F��l@g����t��>g*�Y��n�>gESB\T?g�N;A+�?g�UR1��?gE�F���?gP�n��@g&�>���@g����i�<g�@�F�>g�tcI,\�>g�ŝ���I?g*F2�v�?g�C4�?g��O�1�?)r#r"r')�pr`�sigmar��rr�r�res        rC�_normal_dist_inv_cdfr��s���	
�C��A��A�w�%���q�u���0�1�4�0�1�45�6�0�1�45�6�1�1�56�6�1�	1�56�	6�
1�1�
56�6�1�
1�56�
6�1�1�56�6��1�1�4�0�1�45�6�0�1�45�6�1�1�56�6�1�	1�56�	6�
1�1�
56�6�1�
1�56�
6����
�I����Y���
�#�X��3��7�A��c�!�f�W�
�A��C�x�
��G��1�A�5�1�2�56�7�1�2�56�7�2�2�67�7�2�	2�67�	7�
2�2�
67�7�2�
2�67�
7�2�2��2�A�5�1�2�56�7�1�2�56�7�2�2�67�7�2�	2�67�	7�
2�2�
67�7�2�
2�67�
7����
��G��1�A�5�1�2�56�7�1�2�56�7�2�2�67�7�2�	2�67�	7�
2�2�
67�7�2�
2�67�
7�2�2��3�Q�6�1�2�56�7�1�2�56�7�2�2�67�7�2�	2�67�	7�
2�2�
67�7�2�
2�67�
7����	�	�A��3�w�
�B��
�U���rB)r�c��\rSrSrSSS.rS!Sjr\S5rSS.S	jrS
r	Sr
SrS"S
jrSr
Sr\S5r\S5r\S5r\S5r\S5rSrSrSrSrSrSr\rSr\rSrSrSr Sr!S r"Sr#g)#ri�z(Arithmetic mean of a normal distributionz+Standard deviation of a normal distribution��_mu�_sigmac�f�US:a[S5e[U5Ul[U5Ulg)Nr�zsigma must be non-negative)rrxr�r�)�selfr`r�s   rC�__init__�NormalDist.__init__�s+���3�;�!�">�?�?���9����E�l��rBc��U"[U56$rG)rg)�clsrYs  rC�from_samples�NormalDist.from_samples�s���K��%�&�&rBN��seedc��Uc[RO[R"U5Rn[nURnURn[SU5Vs/sHot"U"5XV5PM sn$s snfrG)�random�Randomr�r�r�r)r�rKr��rnd�inv_cdfr`r�r�s        rC�samples�NormalDist.samples�s^��#�|�f�m�m����t�1D�1K�1K��&��
�X�X������39�$��?�C�?�a����r�)�?�C�C��Cs� A:c��URUR-nU(d[S5eXR-
n[X3-SU--5[	[
U-5-$)Nz$pdf() not defined when sigma is zerog�)r�rr�r$r"r&)r�rer�diffs    rCr;�NormalDist.pdf�sR���;�;����,���!�"H�I�I��8�8�|���4�;�$��/�2�3�d�3��>�6J�J�JrBc��UR(d[S5eSS[XR-
UR[--5--$)Nz$cdf() not defined when sigma is zeror�r�)r�rr%r��_SQRT2�r�res  rCrB�NormalDist.cdf�s>���{�{�!�"H�I�I��c�C��X�X��$�+�+��2F� G�H�H�I�IrBc�p�US::dUS:�a[S5e[XRUR5$)Nr�r�z$p must be in the range 0.0 < p < 1.0)rr�r�r�)r�r�s  rCr��NormalDist.inv_cdfs2��
��8�q�C�x�!�"H�I�I�#�A�x�x����=�=rBc�f�[SU5Vs/sHo RX!-5PM sn$s snfr�)rUr�)r�rKr�s   rCr�NormalDist.quantiless+��.3�1�a�[�9�[����Q�U�#�[�9�9��9s�.c	�4�[U[5(d[S5eXp2URUR4URUR4:aX2p2UR
UR
pTU(aU(d[
S5eXT-
n[URUR-
5nU(d%S[USUR-[--5-
$URU-URU--
nURUR-[Xw-U[XT-5--5-n	X�-U-n
X�-
U-nS[URU
5URU
5-
5[URU5URU5-
5--
$)Nz$Expected another NormalDist instancez(overlap() not defined when sigma is zeror�r9)
r�rryr�r�rrr#r%r�r"r'rB)r��other�X�Y�X_var�Y_var�dvr�r��b�x1�x2s            rC�overlap�NormalDist.overlapsN�� �%��,�,��B�C�C��1�
�H�H�a�e�e�����!�%�%�0�0��q��z�z�1�:�:�u��E�!�"L�M�M�
�]��
�!�%�%�!�%�%�-�
 �����R�3����>�F�#:�;�<�<�<�
�E�E�E�M�A�E�E�E�M�)��
�H�H�q�x�x��$�r�w��c�%�-�6H�1H�'H�"I�I���e�r�\���e�r�\���d�1�5�5��9�q�u�u�R�y�0�1�D����r��Q�U�U�2�Y�9N�4O�O�P�PrBc�p�UR(d[S5eXR-
UR-$)Nz'zscore() not defined when sigma is zero)r�rr�r�s  rC�zscore�NormalDist.zscore=s,���{�{�!�"K�L�L��H�H�����+�+rBc��UR$rG�r��r�s rCr�NormalDist.meanH�
���x�x�rBc��UR$rGr�r�s rCr
�NormalDist.medianMr�rBc��UR$rGr�r�s rCr�NormalDist.modeRs
���x�x�rBc��UR$rG�r�r�s rCr�NormalDist.stdev[s���{�{�rBc�4�URUR-$rGr�r�s rCr�NormalDist.variance`s���{�{�T�[�[�(�(rBc���[U[5(aA[URUR-[URUR55$[URU-UR5$rG�r�rr�r!r��r�r�s  rC�__add__�NormalDist.__add__e�R���b�*�%�%��b�f�f�r�v�v�o�u�R�Y�Y��	�	�/J�K�K��"�&�&�2�+�r�y�y�1�1rBc���[U[5(aA[URUR-
[URUR55$[URU-
UR5$rGr�r�s  rC�__sub__�NormalDist.__sub__sr�rBc�`�[URU-UR[U5-5$rG�rr�r�r#r�s  rC�__mul__�NormalDist.__mul__��&���"�&�&�2�+�r�y�y�4��8�';�<�<rBc�`�[URU-UR[U5-5$rGr�r�s  rC�__truediv__�NormalDist.__truediv__�r�rBc�B�[URUR5$rG�rr�r��r�s rC�__pos__�NormalDist.__pos__�s���"�&�&�"�)�)�,�,rBc�D�[UR*UR5$rGr�r�s rC�__neg__�NormalDist.__neg__�s���2�6�6�'�2�9�9�-�-rBc��X-
*$rGr<r�s  rC�__rsub__�NormalDist.__rsub__�s����z�rBc��[U[5(d[$URUR:H=(a URUR:H$rG)r�r�NotImplementedr�r�r�s  rC�__eq__�NormalDist.__eq__�s:���"�j�)�)�!�!��v�v�����:�B�I�I����$:�:rBc�D�[URUR45$rG)�hashr�r�r�s rC�__hash__�NormalDist.__hash__�s���T�X�X�t�{�{�+�,�,rBc�j�[U5RSUR<SUR<S3$)Nz(mu=z, sigma=�))rRr=r�r�r�s rC�__repr__�NormalDist.__repr__�s.���t�*�%�%�&�d�4�8�8�,�h�t�{�{�o�Q�O�OrBc�2�URUR4$rGr�r�s rC�__getstate__�NormalDist.__getstate__�s���x�x����$�$rBc�"�UuUlUlgrGr�)r��states  rC�__setstate__�NormalDist.__setstate__�s�� %����$�+rB)r�r�)r�)$r=r>r?r@�	__slots__r��classmethodr�r�r;rBr�rr�r��propertyrr
rrrr�r�r�r�r�r��__radd__r��__rmul__r�r�r�r�r�rAr<rBrCrr�s��:�?��I�
#��'��'�"&�D�K�J�>�	:� Q�D	,������������������)��)�2�2�=�=�-�.��H���H�;�-�P�%�&rBrc� ^^^^�UUUU4SjnU$)Nc�>�T"U5n[T"U5U-
=n5T:�a)XT"U5--n[T"U5U-
=n5T:�aM)U$rGr)rhrer�r��f_inv_estimate�f_prime�	tolerances   ����rC�f_inv�_newton_raphson.<locals>.f_inv�sY����1����!�A�$��(�"�$�#�i�/�
���
�"�"�A��!�A�$��(�"�$�#�i�/��rBr<)r�r�r�r�r�s```` rC�_newton_raphsonr��s������LrBc��US::aSU4OSSU-
4upSU-S-S-
nUSs=:�aS:aO X!-$US[S	U-S
-5--
nX!-$)Nr�r���r9g��鼹A�?g����Mbp?gV-����?gM�p�^v�?g��$2h@g_���@r/�r��signres   rC�_quartic_invcdf_estimater�sk���s�(�s�A�h��s�Q�w��G�D�	�q��_�$�s�*�A��E��E���8�O�	
�[�3�{�Q��1A�A�B�
B�B���8�OrBc�6�SUS--SUS---
SU--S-$r#r<rs rCr�r��s'��$��A��+��a��d�
�*�U�Q�Y�6��<rBc��SSX--
S--$rr<rs rCr�r�������q�u��� 2�2rB)r�r�r�c�F�US::aSU4OSSU-
4upSU-S-S-
nX!-$)Nr�r�rr9g�c���?r<rs   rC�_triweight_invcdf_estimater	�s8���s�(�s�A�h��s�Q�w��G�D�	�q��'�'�#�-�A��8�OrBc�B�SSUS--SUS---US--
U--S-$r*r<rs rCr�r��s1��%�4��1��9�s�1�a�4�x�/�!�Q�$�6��:�;�c�ArBc��SSX--
S--$r'r<rs rCr�r��rrBc�$�[USU-
-5$r�)r'�r�s rCr�r��s��#�a�1�q�5�k�*rBc�>�[[U[-S-55$)Nr�)r'r/r,r
s rCr�r��s���S��R����]�+rBc��SU-S-
$�Nr�rEr<r
s rCr�r��s��Q�q�S�1�WrBc�P�S[[SU-S-
5[-S-5-$)Nr�rEr�)r-r3r,r
s rCr�r��s$��1�s�D��1��Q��K�"�$4��#9�:�:rBc�X�US:a[SU-5S-
$S[SSU--
5-
$)Nr�r�rE)r"r
s rCr�r��s/��Q��W�D��1��I��M�K�!�d�1�q��s�7�m�:K�KrBc�8�S[SU-S-
5-[-$r)r1r,r
s rCr�r��s���D��1��q��M�)�B�.rB)	r�rrr
rrr%rr,r�r
rrrrrr�c�^^^^^	�[T5nU(d[S5e[TS[[45(d[S5eTS::a[ST<35e[RU5mTc[SU<35e[RU5nURm	URmUUUUU	4SjnST<S	U<3UlU$)
Nr�rr�r�r�r0c�6>�T"T5TT"T"55--$rGr<)�choicerYr6�
kernel_invcdfr�s�����rC�rand�kde_random.<locals>.rand
s����d�|�a�-���"9�9�9�9rBzRandom KDE selection with h=rL)
r�rr�rXrxry�_kernel_invcdfsrQ�_randomr�r�rrM)
rYr6rNr�rK�prngrrrr�s
``     @@@rCr
r
�s����$	�D�	�A���3�4�4��d�1�g��U�|�,�,��C�D�D��C�x�� E�1�&�I�J�J�#�'�'��/�M���� 5�f�Z�@�A�A��>�>�$��D�
�[�[�F�
�[�[�F�:�:�3��v�]�6�+�F�D�L��KrBrG)znegative value)r�)r�)g�-���q=)c�__all__rsr�r��sys�	fractionsr�decimalr�	itertoolsrrr�bisectrr r!r"r#r$r%r&r'r(r)r*r+r,r-r.r/r0r1r2r3�	functoolsr4�operatorr5�collectionsr6r7r8r�rrrrbrortrWrTr�r�r�rxr�rXr��
float_info�mant_digr��__annotations__r�r�rrrrr
rrrrrr	rrrrrrgrjrrrzrr��_statistics�ImportErrorrr�r�_quartic_invcdfr	�_triweight_invcdfr�rr
r<rBrC�<module>r-s���h�T��2��
�
���,�,�,�E�E�E�K�K�K���8�8�	
�c���
��	�j�	�3�l&�R �4�>+�\�$���I�Q�3�4�PU�;�3�l��������3�>�>�2�2�2�Q�6���6�
#�3�
#�3�
#�5�
#��S��S��W��<"�,!�H �F5,�p+�0 �,�&E+�PB�<K�(Q��Q�r�;�-4�l)%�X&�R?�$?�$
4����5��U��:�8$,�-H�`�0�2H�I��05�7>�zG�V	�0�
\&�\&�B��"�-�<�2�4��
�
$�/�A�2�4���l�"�"�*�+�$�:��"�K�.�
��+�8�4����,�]�;��	��"1�+�">����-�i�8��
��)��)��i�	��	�s�.G(�(G1�0G1

?>