M/Ph ~DdZddlZddlZddlZejejZ dZ GddZ Gdde Z Gdd e Z Gd d e ZGd d e ZGdde ZGdde ZGdde ZGdde ZGdde ZGddeZGddeZGdde ZGdde ZGd d!e ZGd"d#e ZGd$d%eZGd&d'eZGd(d)eZGd*d+eZGd,d-eZGd.d/eZ Gd0d1eZ!Gd2d3eZ"Gd4d5eZ#Gd6d7eZ$Gd8d9eZ%dS):zB Defines the link functions to be used with GLM and GEE families. Nc Ntjd|d|d|dtdS)NzThe z link alias is deprecated. Use z instead. The z5 link alias will be removed after the 0.15.0 release.)warningswarn FutureWarning)oldnews a/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/genmod/families/links.py_link_deprecation_warningr sY M @s @ @3 @ @c @ @ @c6eZdZdZdZdZdZdZdZdZ dS) Linkz A generic link function for one-parameter exponential family. `Link` does nothing, but lays out the methods expected of any subclass. ctS)a Return the value of the link function. This is just a placeholder. Parameters ---------- p : array_like Probabilities Returns ------- g(p) : array_like The value of the link function g(p) = z NotImplementedErrorselfps r __call__z Link.__call__s #"r ctS)a~ Inverse of the link function. Just a placeholder. Parameters ---------- z : array_like `z` is usually the linear predictor of the transformed variable in the IRLS algorithm for GLM. Returns ------- g^(-1)(z) : ndarray The value of the inverse of the link function g^(-1)(z) = p rrzs r inversez Link.inverse,s #"r ctS)a Derivative of the link function g'(p). Just a placeholder. Parameters ---------- p : array_like Returns ------- g'(p) : ndarray The value of the derivative of the link function g'(p) rrs r derivz Link.deriv=s #"r c0ddlm}|||jS)zmSecond derivative of the link function g''(p) implemented through numerical differentiation r)_approx_fprime_cs_scalar)statsmodels.tools.numdiffrr)rrrs r deriv2z Link.deriv2Ls, GFFFFF''4:666r cXd|||z S)a Derivative of the inverse link function g^(-1)(z). Parameters ---------- z : array_like `z` is usually the linear predictor for a GLM or GEE model. Returns ------- g'^(-1)(z) : ndarray The value of the derivative of the inverse of the link function Notes ----- This reference implementation gives the correct result but is inefficient, so it can be overridden in subclasses. )rrrs r inverse_derivzLink.inverse_derivTs%&4::dll1oo....r c||}|| ||dzz S)a  Second derivative of the inverse link function g^(-1)(z). Parameters ---------- z : array_like `z` is usually the linear predictor for a GLM or GEE model. Returns ------- g'^(-1)(z) : ndarray The value of the second derivative of the inverse of the link function Notes ----- This reference implementation gives the correct result but is inefficient, so it can be overridden in subclasses. )rrr)rrizs r inverse_deriv2zLink.inverse_deriv2is:(\\!__ B$**R..A"555r N __name__ __module__ __qualname____doc__rrrrr!r%r r r r sx ### ###" # # #777///*66666r r c6eZdZdZdZdZdZdZdZdZ dS) Logitz The logit transform Notes ----- call and derivative use a private method _clean to make trim p by machine epsilon so that p is in (0,1) Alias of Logit: logit = Logit() cHtj|tdtz S)z Clip logistic values to range (eps, 1-eps) Parameters ---------- p : array_like Probabilities Returns ------- pclip : ndarray Clipped probabilities ?npclip FLOAT_EPSrs r _cleanz Logit._cleanswq)R)^444r c`||}tj|d|z z S)a The logit transform Parameters ---------- p : array_like Probabilities Returns ------- z : ndarray Logit transform of `p` Notes ----- g(p) = log(p / (1 - p)) r/r4r1logrs r rzLogit.__call__s+$ KKNNva26l###r cdtj|}tj| }dd|zz S)a4 Inverse of the logit transform Parameters ---------- z : array_like The value of the logit transform at `p` Returns ------- p : ndarray Probabilities Notes ----- g^(-1)(z) = exp(z)/(1+exp(z)) r/)r1asarrayexprrts r rz Logit.inverses.$ JqMM FA2JJR!V}r cB||}d|d|z zz S)au Derivative of the logit transform Parameters ---------- p : array_like Probabilities Returns ------- g'(p) : ndarray Value of the derivative of logit transform at `p` Notes ----- g'(p) = 1 / (p * (1 - p)) Alias for `Logit`: logit = Logit() r/r r4rs r rz Logit.derivs&* KKNNQ!a%[!!r c@tj|}|d|zdzz S)aS Derivative of the inverse of the logit transform Parameters ---------- z : array_like `z` is usually the linear predictor for a GLM or GEE model. Returns ------- g'^(-1)(z) : ndarray The value of the derivative of the inverse of the logit function r r1r:r;s r r!zLogit.inverse_derivs$ F1IIAEa<r c.|d|z z}d|zdz |dzz S)a Second derivative of the logit function. Parameters ---------- p : array_like probabilities Returns ------- g''(z) : ndarray The value of the second derivative of the logit function r r@r+)rrvs r rz Logit.deriv2s( QKA Q!V##r N) r'r(r)r*r4rrrr!rr+r r r-r-sx  555 $$$*,"""0   "$$$$$r r-c>eZdZdZd dZdZdZdZdZdZ d Z d S) Powera# The power transform Parameters ---------- power : float The exponent of the power transform Notes ----- Aliases of Power: Inverse = Power(power=-1) Sqrt = Power(power=.5) InverseSquared = Power(power=-2.) Identity = Power(power=1.) r/c||_dSNpower)rrIs r __init__zPower.__init__  r cP|jdkr|Stj||jS)a Power transform link function Parameters ---------- p : array_like Mean parameters Returns ------- z : array_like Power transform of x Notes ----- g(p) = x**self.power r rIr1rs r rzPower.__call__s($ :??H8Atz** *r cV|jdkr|Stj|d|jz S)aP Inverse of the power transform link function Parameters ---------- `z` : array_like Value of the transformed mean parameters at `p` Returns ------- `p` : ndarray Mean parameters Notes ----- g^(-1)(z`) = `z`**(1/`power`) r r/rMrs r rz Power.inverse0s,$ :??H8ArDJ// /r c|jdkrtj|S|jtj||jdz zS)aC Derivative of the power transform Parameters ---------- p : array_like Mean parameters Returns ------- g'(p) : ndarray Derivative of power transform of `p` Notes ----- g'(`p`) = `power` * `p`**(`power` - 1) r rIr1 ones_likers r rz Power.derivGs<$ :??<?? ":DJN ; ;; ;r c|jdkrtj|S|j|jdz ztj||jdz zS)ag Second derivative of the power transform Parameters ---------- p : array_like Mean parameters Returns ------- g''(p) : ndarray Second derivative of the power transform of `p` Notes ----- g''(`p`) = `power` * (`power` - 1) * `p`**(`power` - 2) r r@rIr1 zeros_likers r rz Power.deriv2^sI$ :??=## #:a028AtzA~3N3NN Nr c|jdkrtj|Stj|d|jz |jz |jz S)ae Derivative of the inverse of the power transform Parameters ---------- z : array_like `z` is usually the linear predictor for a GLM or GEE model. Returns ------- g^(-1)'(z) : ndarray The value of the derivative of the inverse of the power transform function r rPrs r r!zPower.inverse_derivusC :??<?? "8ADJ$*<== J Jr c|jdkrtj|Sd|jz tj|dd|jzz |jz z|jdzz S)al Second derivative of the inverse of the power transform Parameters ---------- z : array_like `z` is usually the linear predictor for a GLM or GEE model. Returns ------- g^(-1)'(z) : ndarray The value of the derivative of the inverse of the power transform function r r@rSrs r r%zPower.inverse_deriv2sc :??=## #^HQQtz\!14: =>>?AEQO Pr Nr/) r'r(r)r*rJrrrrr!r%r+r r rErEs"+++.000.<<<.OOO.KKK(PPPPPr rEc"eZdZdZfdZxZS) InversePowerz{ The inverse transform Notes ----- g(p) = 1/p Alias of statsmodels.family.links.Power(power=-1.) cLtddS)NrHsuperrJr __class__s r rJzInversePower.__init__$ s#####r r'r(r)r*rJ __classcell__r_s@r rYrYB$$$$$$$$$r rYc"eZdZdZfdZxZS)Sqrtz The square-root transform Notes ----- g(`p`) = sqrt(`p`) Alias of statsmodels.family.links.Power(power=.5) cLtddS)N?rHr\r^s r rJz Sqrt.__init__$ r"""""r rarcs@r rfrfB#########r rfc"eZdZdZfdZxZS)InverseSquaredz The inverse squared transform Notes ----- g(`p`) = 1/(`p`\*\*2) Alias of statsmodels.family.links.Power(power=2.) cLtddS)NgrHr\r^s r rJzInverseSquared.__init__r`r rarcs@r rlrlrdr rlc"eZdZdZfdZxZS)Identityz} The identity transform Notes ----- g(`p`) = `p` Alias of statsmodels.family.links.Power(power=1.) cLtddS)Nr/rHr\r^s r rJzIdentity.__init__rir rarcs@r rororjr roc6eZdZdZdZdZdZdZdZdZ dS) Logz The log transform Notes ----- call and derivative call a private method _clean to trim the data by machine epsilon so that p is in (0,1). log is an alias of Log. cLtj|ttjSrGr1r2r3infrxs r r4z Log._cleanwq)RV,,,r c T||}tj|S)a Log transform link function Parameters ---------- x : array_like Mean parameters Returns ------- z : ndarray log(x) Notes ----- g(p) = log(p) r6rrextrarws r rz Log.__call__s!$ KKNNvayyr c*tj|S)aZ Inverse of log transform link function Parameters ---------- z : ndarray The inverse of the link function at `p` Returns ------- p : ndarray The mean probabilities given the value of the inverse `z` Notes ----- g^{-1}(z) = exp(z) rArs r rz Log.inverses$vayyr c6||}d|z S)a, Derivative of log transform link function Parameters ---------- p : array_like Mean parameters Returns ------- g'(p) : ndarray derivative of log transform of x Notes ----- g'(x) = 1/x r/r>rs r rz Log.derivs$ KKNNAv r c<||}d|dzz S)aC Second derivative of the log transform link function Parameters ---------- p : array_like Mean parameters Returns ------- g''(p) : ndarray Second derivative of log transform of x Notes ----- g''(x) = -1/x^2 r[r@r>rs r rz Log.deriv2&s!$ KKNNQ!V|r c*tj|S)al Derivative of the inverse of the log transform link function Parameters ---------- z : ndarray The inverse of the link function at `p` Returns ------- g^(-1)'(z) : ndarray The value of the derivative of the inverse of the log function, the exponential function rArs r r!zLog.inverse_deriv;svayyr N) r'r(r)r*r4rrrrr!r+r r rrrrsx---*(**r rrc<eZdZdZdZdZdZdZdZdZ dZ d S) LogCz The log-complement transform Notes ----- call and derivative call a private method _clean to trim the data by machine epsilon so that p is in (0,1). logc is an alias of LogC. cHtj|tdtz S)Nr/r0rvs r r4z LogC._cleanWswq)R)^444r c Z||}tjd|z S)a Log-complement transform link function Parameters ---------- x : array_like Mean parameters Returns ------- z : ndarray log(1 - x) Notes ----- g(p) = log(1-p) r r6rzs r rz LogC.__call__Zs%$ KKNNva!e}}r c0dtj|z S)ai Inverse of log-complement transform link function Parameters ---------- z : ndarray The inverse of the link function at `p` Returns ------- p : ndarray The mean probabilities given the value of the inverse `z` Notes ----- g^{-1}(z) = 1 - exp(z) r rArs r rz LogC.inverseos$26!99}r c<||}dd|z z S)aI Derivative of log-complement transform link function Parameters ---------- p : array_like Mean parameters Returns ------- g'(p) : ndarray derivative of log-complement transform of x Notes ----- g'(x) = -1/(1 - x) r[r/r>rs r rz LogC.derivs!$ KKNNb1f~r ch||}dtjdd|z z dzS)ab Second derivative of the log-complement transform link function Parameters ---------- p : array_like Mean parameters Returns ------- g''(p) : ndarray Second derivative of log-complement transform of x Notes ----- g''(x) = -(-1/(1 - x))^2 r[r/r@)r4r1rIrs r rz LogC.deriv2s2$ KKNNBHSBF^Q////r c,tj| S)aq Derivative of the inverse of the log-complement transform link function Parameters ---------- z : ndarray The inverse of the link function at `p` Returns ------- g^(-1)'(z) : ndarray The value of the derivative of the inverse of the log-complement function. rArs r r!zLogC.inverse_derivs q zr c,tj| S)af Second derivative of the inverse link function g^(-1)(z). Parameters ---------- z : array_like The inverse of the link function at `p` Returns ------- g^(-1)''(z) : ndarray The value of the second derivative of the inverse of the log-complement function. rArs r r%zLogC.inverse_deriv2sq zr N) r'r(r)r*r4rrrrr!r%r+r r rrMs555*(*000*$r rcZeZdZdZejjfdZdZdZ dZ dZ dZ dZ d Zd S) CDFLinka? The use the CDF of a scipy.stats distribution CDFLink is a subclass of logit in order to use its _clean method for the link and its derivative. Parameters ---------- dbn : scipy.stats distribution Default is dbn=scipy.stats.norm Notes ----- The CDF link is untested. c||_dSrGdbn)rrs r rJzCDFLink.__init__s r c`||}|j|S)a CDF link function Parameters ---------- p : array_like Mean parameters Returns ------- z : ndarray (ppf) inverse of CDF transform of p Notes ----- g(`p`) = `dbn`.ppf(`p`) )r4rppfrs r rzCDFLink.__call__s%$ KKNNx||Ar c6|j|S)ap The inverse of the CDF link Parameters ---------- z : array_like The value of the inverse of the link function at `p` Returns ------- p : ndarray Mean probabilities. The value of the inverse of CDF link of `z` Notes ----- g^(-1)(`z`) = `dbn`.cdf(`z`) )rcdfrs r rzCDFLink.inverses$x||Ar c||}d|j|j|z S)a; Derivative of CDF link Parameters ---------- p : array_like mean parameters Returns ------- g'(p) : ndarray The derivative of CDF transform at `p` Notes ----- g'(`p`) = 1./ `dbn`.pdf(`dbn`.ppf(`p`)) r/)r4rpdfrrs r rz CDFLink.derivs8$ KKNNDHLLa1111r c||}|j|}|| |j|dzz S)v Second derivative of the link function g''(p) implemented through numerical differentiation r#)r4rrr%rrrlinpreds r rzCDFLink.deriv2$sS KKNN(,,q//$$W--- W0E0E0JJJr c\ddlm}tj|}|||jdS)rr_approx_fprime_scalarTcentered)rrr1 atleast_1dr)rrrs r deriv2_numdiffzCDFLink.deriv2_numdiff.s@ DCCCCC M!  $$Q TBBBBr c6|j|S)ac Derivative of the inverse link function Parameters ---------- z : ndarray The inverse of the link function at `p` Returns ------- g^(-1)'(z) : ndarray The value of the derivative of the inverse of the logit function. This is just the pdf in a CDFLink, rrrs r r!zCDFLink.inverse_deriv9sx||Ar c\ddlm}tj|}|||jdS)a Second derivative of the inverse link function g^(-1)(z). Parameters ---------- z : array_like `z` is usually the linear predictor for a GLM or GEE model. Returns ------- g^(-1)''(z) : ndarray The value of the second derivative of the inverse of the link function Notes ----- This method should be overwritten by subclasses. The inherited method is implemented through numerical differentiation. rrTr)rrr1rr!)rrrs r r%zCDFLink.inverse_deriv2JsC* DCCCCC M!  %$Q(:TJJJJr N)r'r(r)r*scipystatsnormrJrrrrrr!r%r+r r rrs !;+*(222*KKK C C C"KKKKKr rceZdZdZdZdZdS)Probitz The probit (standard normal CDF) transform Notes ----- g(p) = scipy.stats.norm.ppf(p) probit is an alias of CDFLink. c>| |j|zS)zy Second derivative of the inverse link function This is the derivative of the pdf in a CDFLink rrs r r%zProbit.inverse_deriv2qssTX\\!__$$r c||}|j|}||j|dzz S)z@ Second derivative of the link function g''(p) r@)r4rrrrs r rz Probit.deriv2zsB KKNN(,,q//g..!333r N)r'r(r)r*r%rr+r r rrfs<%%%44444r rc.eZdZdZfdZdZdZxZS)Cauchyz The Cauchy (standard Cauchy CDF) transform Notes ----- g(p) = scipy.stats.cauchy.ppf(p) cauchy is an alias of CDFLink with dbn=scipy.stats.cauchy cjttjjdS)Nr)r]rJrrcauchyr^s r rJzCauchy.__init__s) U[/00000r c||}tj|dz z}dtjdzztj|ztj|dzz }|S)a Second derivative of the Cauchy link function. Parameters ---------- p : array_like Probabilities Returns ------- g''(p) : ndarray Value of the second derivative of Cauchy link function at `p` rhr@r#)r4r1pisincos)rrad2s r rz Cauchy.deriv2sU KKNN EQW  !^bfQii '"&))q. 8 r c>d|ztj|dzdzdzzz S)Nr@r )r1rrs r r%zCauchy.inverse_deriv2s%Qw"%16A:!"3344r )r'r(r)r*rJrr%rbrcs@r rrs`11111&5555555r rc0eZdZdZdZdZdZdZdZdS)CLogLogz The complementary log-log transform CLogLog inherits from Logit in order to have access to its _clean method for the link and its derivative. Notes ----- CLogLog is untested. c||}tjtjd|z  S)a# C-Log-Log transform link function Parameters ---------- p : ndarray Mean parameters Returns ------- z : ndarray The CLogLog transform of `p` Notes ----- g(p) = log(-log(1-p)) r r6rs r rzCLogLog.__call__s1$ KKNNvrva!e}}n%%%r cVdtjtj| z S)a[ Inverse of C-Log-Log transform link function Parameters ---------- z : array_like The value of the inverse of the CLogLog link function at `p` Returns ------- p : ndarray Mean parameters Notes ----- g^(-1)(`z`) = 1-exp(-exp(`z`)) r rArs r rzCLogLog.inverses#&2626!99*%%%%r cl||}d|dz tjd|z zz S)aZ Derivative of C-Log-Log transform link function Parameters ---------- p : array_like Mean parameters Returns ------- g'(p) : ndarray The derivative of the CLogLog transform link function Notes ----- g'(p) = - 1 / ((p-1)*log(1-p)) r/r r6rs r rz CLogLog.derivs3$ KKNNa!eq1u .//r c||}tjd|z }dd|z dz|zz }|dd|z zz}|S)a Second derivative of the C-Log-Log ink function Parameters ---------- p : array_like Mean parameters Returns ------- g''(p) : ndarray The second derivative of the CLogLog link function r rr@r6)rrflrs r rzCLogLog.deriv2sR KKNN VAE]] AEa<"$ % a!b&j r cTtj|tj|z S)a` Derivative of the inverse of the C-Log-Log transform link function Parameters ---------- z : array_like The value of the inverse of the CLogLog link function at `p` Returns ------- g^(-1)'(z) : ndarray The derivative of the inverse of the CLogLog link function rArs r r!zCLogLog.inverse_derivs va"&))m$$$r N) r'r(r)r*rrrrr!r+r r rrsi  &&&*&&&*000*(%%%%%r rc6eZdZdZdZdZdZdZdZdZ dS) LogLogz The log-log transform LogLog inherits from Logit in order to have access to its _clean method for the link and its derivative. c|||}tjtj|  S)a Log-Log transform link function Parameters ---------- p : ndarray Mean parameters Returns ------- z : ndarray The LogLog transform of `p` Notes ----- g(p) = -log(-log(p)) r6rs r rzLogLog.__call__!s0$ KKNNq z""""r cRtjtj|  S)aW Inverse of Log-Log transform link function Parameters ---------- z : array_like The value of the inverse of the LogLog link function at `p` Returns ------- p : ndarray Mean parameters Notes ----- g^(-1)(`z`) = exp(-exp(-`z`)) rArs r rzLogLog.inverse6s &vrvqbzzk"""r c`||}d|tj|zz S)aR Derivative of Log-Log transform link function Parameters ---------- p : array_like Mean parameters Returns ------- g'(p) : ndarray The derivative of the LogLog transform link function Notes ----- g'(p) = - 1 /(p * log(p)) r[r6rs r rz LogLog.derivKs*$ KKNNa26!99o&&r c||}dtj|z|tj|zdzz }|S)a Second derivative of the Log-Log link function Parameters ---------- p : array_like Mean parameters Returns ------- g''(p) : ndarray The second derivative of the LogLog link function r r@r6)rrrs r rz LogLog.deriv2`s? KKNN"&))mRVAYYA5 5 r cXtjtj|  |z S)a\ Derivative of the inverse of the Log-Log transform link function Parameters ---------- z : array_like The value of the inverse of the LogLog link function at `p` Returns ------- g^(-1)'(z) : ndarray The derivative of the inverse of the LogLog link function rArs r r!zLogLog.inverse_derivrs$vrvqbzzkAo&&&r c^||tj| dz zS)ak Second derivative of the inverse of the Log-Log transform link function Parameters ---------- z : array_like The value of the inverse of the LogLog link function at `p` Returns ------- g^(-1)''(z) : ndarray The second derivative of the inverse of the LogLog link function r )r!r1r:rs r r%zLogLog.inverse_deriv2s+!!!$$r Q77r Nr&r+r r rrsx###*###*'''*$''' 88888r rc>eZdZdZd dZdZdZdZdZdZ d Z d S) NegativeBinomiala? The negative binomial link function Parameters ---------- alpha : float, optional Alpha is the ancillary parameter of the Negative Binomial link function. It is assumed to be nonstochastic. The default value is 1. Permissible values are usually assumed to be in (.01, 2). r/c||_dSrGalpha)rrs r rJzNegativeBinomial.__init__rKr cLtj|ttjSrGrtrvs r r4zNegativeBinomial._cleanrxr cp||}tj||d|jz zz S)a> Negative Binomial transform link function Parameters ---------- p : array_like Mean parameters Returns ------- z : ndarray The negative binomial transform of `p` Notes ----- g(p) = log(p/(p + 1/alpha)) r )r4r1r7rrs r rzNegativeBinomial.__call__s3$ KKNNva1q4:~-.///r cHd|jdtj| z zz S)aa Inverse of the negative binomial transform Parameters ---------- z : array_like The value of the inverse of the negative binomial link at `p`. Returns ------- p : ndarray Mean parameters Notes ----- g^(-1)(z) = exp(z)/(alpha*(1-exp(z))) rr )rr1r:rs r rzNegativeBinomial.inverses$$TZ1rvqbzz>233r c(d||j|dzzzz S)a[ Derivative of the negative binomial transform Parameters ---------- p : array_like Mean parameters Returns ------- g'(p) : ndarray The derivative of the negative binomial transform link function Notes ----- g'(x) = 1/(x+alpha*x^2) r r@rrs r rzNegativeBinomial.derivs$A Q!V++,,r cTdd|jz|zz }||j|dzzzdz}||z S)a Second derivative of the negative binomial link function. Parameters ---------- p : array_like Mean parameters Returns ------- g''(p) : ndarray The second derivative of the negative binomial transform link function Notes ----- g''(x) = -(1+2*alpha*x)/(x+alpha*x^2)^2 r r@r)rrnumerdenoms r rzNegativeBinomial.deriv2s@&a$*nq(()TZ!q&((Q.u}r cPtj|}||jd|z dzzz S)ak Derivative of the inverse of the negative binomial transform Parameters ---------- z : array_like Usually the linear predictor for a GLM or GEE model Returns ------- g^(-1)'(z) : ndarray The value of the derivative of the inverse of the negative binomial link r r@)r1r:rr;s r r!zNegativeBinomial.inverse_derivs+ F1IIDJ!a%A-..r NrW) r'r(r)r*rJr4rrrrr!r+r r rrs  ---000*444(---(./////r rc"eZdZdZfdZxZS)logitzN Alias of Logit .. deprecated: 0.14.0 Use Logit instead. chtddtdS)Nrr-r r]rJr^s r rJzlogit.__init__s/!'7333 r rarcs@r rr Br rc"eZdZdZfdZxZS) inverse_powerzi Deprecated alias of InversePower. .. deprecated: 0.14.0 Use InversePower instead. chtddtdS)NrrYrr^s r rJzinverse_power.__init__$s/!/>BBB r rarcs@r rrrr rc"eZdZdZfdZxZS)sqrtzY Deprecated alias of Sqrt. .. deprecated: 0.14.0 Use Sqrt instead. chtddtdS)Nrrfrr^s r rJz sqrt.__init__2/!&&111 r rarcs@r rr)rr rc"eZdZdZfdZxZS)inverse_squaredzm Deprecated alias of InverseSquared. .. deprecated: 0.14.0 Use InverseSquared instead. chtddtdS)Nrrlrr^s r rJzinverse_squared.__init__@s1!"35EFFF r rarcs@r rr7rr rc"eZdZdZfdZxZS)identityza Deprecated alias of Identity. .. deprecated: 0.14.0 Use Identity instead. chtddtdS)Nrrorr^s r rJzidentity.__init__Ns/!*j999 r rarcs@r rrErr rc"eZdZdZfdZxZS)r7z The log transform .. deprecated: 0.14.0 Use Log instead. Notes ----- log is a an alias of Log. chtddtdS)Nr7rrrr^s r rJz log.__init__`s/!%/// r rarcs@r r7r7SB  r r7c"eZdZdZfdZxZS)logcz The log-complement transform .. deprecated: 0.14.0 Use LogC instead. Notes ----- logc is a an alias of LogC. chtddtdS)Nrrrr^s r rJz logc.__init__rrr rarcs@r rrerr rc"eZdZdZfdZxZS)probitz The probit (standard normal CDF) transform .. deprecated: 0.14.0 Use Probit instead. Notes ----- probit is an alias of Probit. chtddtdS)Nrrrr^s r rJzprobit.__init__/!(H555 r rarcs@r rrwrr rc"eZdZdZfdZxZS)rz The Cauchy (standard Cauchy CDF) transform .. deprecated: 0.14.0 Use Cauchy instead. Notes ----- cauchy is an alias of Cauchy. chtddtdS)Nrrrr^s r rJzcauchy.__init__rr rarcs@r rrrr rc"eZdZdZfdZxZS)cloglogz The CLogLog transform link function. .. deprecated: 0.14.0 Use CLogLog instead. Notes ----- g(`p`) = log(-log(1-`p`)) cloglog is an alias for CLogLog cloglog = CLogLog() chtddtdS)Nrrrr^s r rJzcloglog.__init__s/!)Y777 r rarcs@r rrB  r rc"eZdZdZfdZxZS)loglogz The LogLog transform link function. .. deprecated: 0.14.0 Use LogLog instead. Notes ----- g(`p`) = -log(-log(`p`)) loglog is an alias for LogLog loglog = LogLog() chtddtdS)Nrrrr^s r rJzloglog.__init__rr rarcs@r rrrr rc$eZdZdZdfd ZxZS)nbinomz The negative binomial link function. .. deprecated: 0.14.0 Use NegativeBinomial instead. Notes ----- g(p) = log(p/(p + 1/alpha)) nbinom is an alias of NegativeBinomial. nbinom = NegativeBinomial(alpha=1.) r/cltddt|dS)Nrrrr)rrr_s r rJznbinom.__init__s5!(,>??? u%%%%%r rWrarcs@r rrsG  &&&&&&&&&&r r)&r*numpyr1 scipy.statsrrfinfofloatepsr3r r r-rErYrfrlrorrrrrrrrrrrrrrr7rrrrrrr+r r rs, BHUOO  i6i6i6i6i6i6i6i6X@$@$@$@$@$D@$@$@$FXPXPXPXPXPDXPXPXPv $ $ $ $ $5 $ $ $ # # # # #5 # # # $ $ $ $ $U $ $ $ # # # # #u # # #ooooo$ooodAAAAA4AAAJQKQKQKQKQKeQKQKQKh44444W444<"5"5"5"5"5W"5"5"5Jm%m%m%m%m%em%m%m%`w8w8w8w8w8Uw8w8w8tv/v/v/v/v/tv/v/v/t     E        L        4        n        x   #$4$V$V$g*V*&&&&& &&&&&r