"""
Defines the link functions to be used with GLM and GEE families.
"""

import numpy as np
import scipy.stats
import warnings
from glum import Link

FLOAT_EPS = np.finfo(float).eps


def _link_deprecation_warning(old, new):
    warnings.warn(
        f"The {old} link alias is deprecated. Use {new} instead. The {old} "
        f"link alias will be removed after the 0.15.0 release.",
        FutureWarning
    )
    # raise




class Logit(Link):
    """
    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()
    """

    def _clean(self, p):
        """
        Clip logistic values to range (eps, 1-eps)

        Parameters
        ----------
        p : array_like
            Probabilities

        Returns
        -------
        pclip : ndarray
            Clipped probabilities
        """
        return np.clip(p, FLOAT_EPS, 1. - FLOAT_EPS)

    def link(self, p):
        """
        The logit transform

        Parameters
        ----------
        p : array_like
            Probabilities

        Returns
        -------
        z : ndarray
            Logit transform of `p`

        Notes
        -----
        g(p) = log(p / (1 - p))
        """
        p = self._clean(p)
        return np.log(p / (1. - p))



    def inverse(self, z):
        """
        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))
        """
        z = np.asarray(z)
        t = np.exp(-z)
        return 1. / (1. + t)




    def derivative(self, p):
        """
        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()
        """
        p = self._clean(p)
        return 1. / (p * (1 - p))




    def inverse_derivative(self, z):
        """
        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
        """
        t = np.exp(z)
        return t / (1 + t) ** 2




    def derivative2(self, p):
        """
        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
        """
        v = p * (1 - p)
        return (2 * p - 1) / v ** 2





class Power(Link):
    """
    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.)
    """

    def __init__(self, power=1.):
        self.power = power

    def link(self, p):
        """
        Power transform link function

        Parameters
        ----------
        p : array_like
            Mean parameters

        Returns
        -------
        z : array_like
            Power transform of x

        Notes
        -----
        g(p) = x**self.power
        """
        if self.power == 1:
            return p
        else:
            return np.power(p, self.power)



    def inverse(self, z):
        """
        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`)
        """
        if self.power == 1:
            return z
        else:
            return np.power(z, 1. / self.power)




    def derivative(self, p):
        """
        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)
        """
        if self.power == 1:
            return np.ones_like(p)
        else:
            return self.power * np.power(p, self.power - 1)




    def derivative2(self, p):
        """
        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)
        """
        if self.power == 1:
            return np.zeros_like(p)
        else:
            return self.power * (self.power - 1) * np.power(p, self.power - 2)




    def inverse_derivative(self, z):
        """
        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
        """
        if self.power == 1:
            return np.ones_like(z)
        else:
            return np.power(z, (1 - self.power) / self.power) / self.power




    def inverse_derivative2(self, z):
        """
        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
        """
        if self.power == 1:
            return np.zeros_like(z)
        else:
            return ((1 - self.power) *
                    np.power(z, (1 - 2*self.power)/self.power) / self.power**2)





class InversePower(Power):
    """
    The inverse transform

    Notes
    -----
    g(p) = 1/p

    Alias of statsmodels.family.links.Power(power=-1.)
    """

    def __init__(self):
        super().__init__(power=-1.)



class Sqrt(Power):
    """
    The square-root transform

    Notes
    -----
    g(`p`) = sqrt(`p`)

    Alias of statsmodels.family.links.Power(power=.5)
    """

    def __init__(self):
        super().__init__(power=.5)




class InverseSquared(Power):
    r"""
    The inverse squared transform

    Notes
    -----
    g(`p`) = 1/(`p`\*\*2)

    Alias of statsmodels.family.links.Power(power=2.)
    """

    def __init__(self):
        super().__init__(power=-2.)





class Identity(Power):
    """
    The identity transform

    Notes
    -----
    g(`p`) = `p`

    Alias of statsmodels.family.links.Power(power=1.)
    """

    def __init__(self):
        super().__init__(power=1.)





class Log(Link):
    """
    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.
    """

    def _clean(self, x):
        return np.clip(x, FLOAT_EPS, np.inf)

    def link(self, p, **extra):
        """
        Log transform link function

        Parameters
        ----------
        x : array_like
            Mean parameters

        Returns
        -------
        z : ndarray
            log(x)

        Notes
        -----
        g(p) = log(p)
        """
        x = self._clean(p)
        return np.log(x)



    def inverse(self, z):
        """
        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)
        """
        return np.exp(z)




    def derivative(self, p):
        """
        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
        """
        p = self._clean(p)
        return 1. / p




    def derivative2(self, p):
        """
        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
        """
        p = self._clean(p)
        return -1. / p ** 2




    def inverse_derivative(self, z):
        """
        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
        """
        return np.exp(z)





class LogC(Link):
    """
    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.
    """

    def _clean(self, x):
        return np.clip(x, FLOAT_EPS, 1. - FLOAT_EPS)

    def link(self, p, **extra):
        """
        Log-complement transform link function

        Parameters
        ----------
        x : array_like
            Mean parameters

        Returns
        -------
        z : ndarray
            log(1 - x)

        Notes
        -----
        g(p) = log(1-p)
        """
        x = self._clean(p)
        return np.log(1 - x)



    def inverse(self, z):
        """
        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)
        """
        return 1 - np.exp(z)




    def derivative(self, p):
        """
        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)
        """
        p = self._clean(p)
        return -1. / (1. - p)




    def derivative2(self, p):
        """
        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
        """
        p = self._clean(p)
        return -1 * np.power(-1. / (1. - p), 2)




    def inverse_derivative(self, z):
        """
        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.
        """
        return -np.exp(z)




    def inverse_derivative2(self, z):
        """
        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.
        """
        return -np.exp(z)



# TODO: the CDFLink is untested


class CDFLink(Logit):
    """
    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.
    """

    def __init__(self, dbn=scipy.stats.norm):
        self.dbn = dbn

    def link(self, p):
        """
        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`)
        """
        p = self._clean(p)
        return self.dbn.ppf(p)



    def inverse(self, z):
        """
        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`)
        """
        return self.dbn.cdf(z)




    def derivative(self, p):
        """
        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`))
        """
        p = self._clean(p)
        return 1. / self.dbn.pdf(self.dbn.ppf(p))




    def derivative2(self, p):
        """
        Second derivative of the link function g''(p)

        implemented through numerical differentiation
        """
        p = self._clean(p)
        linpred = self.dbn.ppf(p)
        return - self.inverse_derivative2(linpred) / self.dbn.pdf(linpred) ** 3




    def derivative2_numdiff(self, p):
        """
        Second derivative of the link function g''(p)

        implemented through numerical differentiation
        """
        from statsmodels.tools.numdiff import _approx_fprime_scalar
        p = np.atleast_1d(p)
        # Note: special function for norm.ppf does not support complex
        return _approx_fprime_scalar(p, self.deriv, centered=True)




    def inverse_derivative(self, z):
        """
        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,
        """
        return self.dbn.pdf(z)




    def inverse_derivative2(self, z):
        """
        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.
        """
        from statsmodels.tools.numdiff import _approx_fprime_scalar
        z = np.atleast_1d(z)

        # Note: special function for norm.ppf does not support complex
        return _approx_fprime_scalar(z, self.inverse_deriv, centered=True)





class Probit(CDFLink):
    """
    The probit (standard normal CDF) transform

    Notes
    -----
    g(p) = scipy.stats.norm.ppf(p)

    probit is an alias of CDFLink.
    """



    def inverse_derivative2(self, z):
        """
        Second derivative of the inverse link function

        This is the derivative of the pdf in a CDFLink

        """
        return - z * self.dbn.pdf(z)




    def derivative2(self, p):
        """
        Second derivative of the link function g''(p)

        """
        p = self._clean(p)
        linpred = self.dbn.ppf(p)
        return linpred / self.dbn.pdf(linpred) ** 2





class Cauchy(CDFLink):
    """
    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
    """

    def __init__(self):
        super().__init__(dbn=scipy.stats.cauchy)



    def derivative2(self, p):
        """
        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`
        """
        p = self._clean(p)
        a = np.pi * (p - 0.5)
        d2 = 2 * np.pi ** 2 * np.sin(a) / np.cos(a) ** 3
        return d2




    def inverse_derivative2(self, z):
        return - 2 * z / (np.pi * (z ** 2 + 1) ** 2)





class CLogLog(Logit):
    """
    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.
    """

    def link(self, p):
        """
        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))
        """
        p = self._clean(p)
        return np.log(-np.log(1 - p))



    def inverse(self, z):
        """
        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`))
        """
        return 1 - np.exp(-np.exp(z))




    def derivative(self, p):
        """
        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))
        """
        p = self._clean(p)
        return 1. / ((p - 1) * (np.log(1 - p)))




    def derivative2(self, p):
        """
        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
        """
        p = self._clean(p)
        fl = np.log(1 - p)
        d2 = -1 / ((1 - p) ** 2 * fl)
        d2 *= 1 + 1 / fl
        return d2




    def inverse_derivative(self, z):
        """
        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
        """
        return np.exp(z - np.exp(z))





class LogLog(Logit):
    """
    The log-log transform

    LogLog inherits from Logit in order to have access to its _clean method
    for the link and its derivative.
    """

    def link(self, p):
        """
        Log-Log transform link function

        Parameters
        ----------
        p : ndarray
            Mean parameters

        Returns
        -------
        z : ndarray
            The LogLog transform of `p`

        Notes
        -----
        g(p) = -log(-log(p))
        """
        p = self._clean(p)
        return -np.log(-np.log(p))



    def inverse(self, z):
        """
        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`))
        """
        return np.exp(-np.exp(-z))




    def derivative(self, p):
        """
        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))
        """
        p = self._clean(p)
        return -1. / (p * (np.log(p)))




    def derivative2(self, p):
        """
        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
        """
        p = self._clean(p)
        d2 = (1 + np.log(p)) / (p * (np.log(p))) ** 2
        return d2




    def inverse_derivative(self, z):
        """
        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
        """
        return np.exp(-np.exp(-z) - z)




    def inverse_derivative2(self, z):
        """
        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
        """
        return self.inverse_derivative(z) * (np.exp(-z) - 1)





class NegativeBinomial(Link):
    """
    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).
    """

    def __init__(self, alpha=1.):
        self.alpha = alpha

    def _clean(self, x):
        return np.clip(x, FLOAT_EPS, np.inf)

    def link(self, p):
        """
        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))
        """
        p = self._clean(p)
        return np.log(p / (p + 1 / self.alpha))



    def inverse(self, z):
        """
        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)))
        """
        return -1 / (self.alpha * (1 - np.exp(-z)))




    def derivative(self, p):
        """
        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)
        """
        return 1 / (p + self.alpha * p ** 2)




    def derivative2(self, p):
        """
        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
        """
        numer = -(1 + 2 * self.alpha * p)
        denom = (p + self.alpha * p ** 2) ** 2
        return numer / denom




    def inverse_derivative(self, z):
        """
        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
        """
        t = np.exp(z)
        return t / (self.alpha * (1 - t) ** 2)



# TODO: Deprecated aliases, remove after 0.15
class logit(Logit):
    """
    Alias of Logit

    .. deprecated: 0.14.0

       Use Logit instead.
    """

    def __init__(self):
        _link_deprecation_warning('logit', 'Logit')
        super().__init__()


class inverse_power(InversePower):
    """
    Deprecated alias of InversePower.

    .. deprecated: 0.14.0

        Use InversePower instead.
    """

    def __init__(self):
        _link_deprecation_warning('inverse_power', 'InversePower')
        super().__init__()


class sqrt(Sqrt):
    """
    Deprecated alias of Sqrt.

    .. deprecated: 0.14.0

        Use Sqrt instead.
    """

    def __init__(self):
        _link_deprecation_warning('sqrt', 'Sqrt')
        super().__init__()


class inverse_squared(InverseSquared):
    """
    Deprecated alias of InverseSquared.

    .. deprecated: 0.14.0

        Use InverseSquared instead.
    """

    def __init__(self):
        _link_deprecation_warning('inverse_squared', 'InverseSquared')
        super().__init__()


class identity(Identity):
    """
    Deprecated alias of Identity.

    .. deprecated: 0.14.0

        Use Identity instead.
    """

    def __init__(self):
        _link_deprecation_warning('identity', 'Identity')
        super().__init__()


class log(Log):
    """
    The log transform

    .. deprecated: 0.14.0

       Use Log instead.

    Notes
    -----
    log is a an alias of Log.
    """

    def __init__(self):
        _link_deprecation_warning('log', 'Log')
        super().__init__()


class logc(LogC):
    """
    The log-complement transform

    .. deprecated: 0.14.0

       Use LogC instead.

    Notes
    -----
    logc is a an alias of LogC.
    """

    def __init__(self):
        _link_deprecation_warning('logc', 'LogC')
        super().__init__()


class probit(Probit):
    """
    The probit (standard normal CDF) transform

    .. deprecated: 0.14.0

       Use Probit instead.

    Notes
    -----
    probit is an alias of Probit.
    """

    def __init__(self):
        _link_deprecation_warning('probit', 'Probit')
        super().__init__()


class cauchy(Cauchy):
    """
    The Cauchy (standard Cauchy CDF) transform

    .. deprecated: 0.14.0

       Use Cauchy instead.

    Notes
    -----
    cauchy is an alias of Cauchy.
    """

    def __init__(self):
        _link_deprecation_warning('cauchy', 'Cauchy')
        super().__init__()


class cloglog(CLogLog):
    """
    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()
    """

    def __init__(self):
        _link_deprecation_warning('cloglog', 'CLogLog')
        super().__init__()


class loglog(LogLog):
    """
    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()
    """

    def __init__(self):
        _link_deprecation_warning('loglog', 'LogLog')
        super().__init__()


class nbinom(NegativeBinomial):
    """
    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.)
    """

    def __init__(self, alpha=1.):
        _link_deprecation_warning('nbinom', 'NegativeBinomial')
        super().__init__(alpha=alpha)
