class_docstr: This class implements an Log Normal model for univariate data. The model has parameterized
  form:
  
  .. math::  S(t) = 1 - \Phi\left(\frac{\log(t) - \mu}{\sigma}\right),  \;\; \sigma >0
  
  where :math:`\Phi` is the CDF of a standard normal random variable.
  This implies the cumulative hazard rate is
  
  .. math::  H(t) = -\log\left(1 - \Phi\left(\frac{\log(t) - \mu}{\sigma}\right)\right)
  
  For inference, our null hypothesis is that mu=0.0, and sigma=1.0.
  
  After calling the ``.fit`` method, you have access to properties like: ``survival_function_``, ``mu_``, ``sigma_``.
  A summary of the fit is available with the method ``print_summary()``
  
  Parameters
  -----------
  alpha: float, optional (default=0.05)
      the level in the confidence intervals.
  
  
  Attributes
  ----------
  cumulative_hazard_ : DataFrame
      The estimated cumulative hazard (with custom timeline if provided)
  hazard_ : DataFrame
      The estimated hazard (with custom timeline if provided)
  survival_function_ : DataFrame
      The estimated survival function (with custom timeline if provided)
  cumulative_density_ : DataFrame
      The estimated cumulative density function (with custom timeline if provided)
  density_: DataFrame
      The estimated density function (PDF) (with custom timeline if provided)
  
  variance_matrix_ : DataFrame
      The variance matrix of the coefficients
  median_survival_time_: float
      The median time to event
  mu_: float
      The fitted parameter in the model
  sigma_: float
      The fitted parameter in the model
  durations: array
      The durations provided
  event_observed: array
      The event_observed variable provided
  timeline: array
      The time line to use for plotting and indexing
  entry: array or None
      The entry array provided, or None
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code: def _log_hazard(self, params, times):
      mu_, sigma_ = params
      Z = (np.log(times) - mu_) / sigma_
      return (
          norm.logpdf(Z, loc=0, scale=1)
          - np.log(sigma_)
          - np.log(times)
          - norm.logsf(Z)
      )
  
file_path: lifelines/lifelines/fitters/log_normal_fitter.py
imports: from scipy.special import erfinv
  import autograd.numpy
  from autograd.scipy.stats import norm
  from lifelines.fitters import KnownModelParametricUnivariateFitter
  from lifelines.utils import CensoringType
label_desc: Use image node_id 5 for calling the LogNormalFitter obj's underlying member method code with example usage: obj._log_hazard(params, times) and returns: unknown