class_docstr: This class implements an Exponential model for univariate data. The model has parameterized
  form:
  
  .. math::  S(t) = \exp\left(\frac{-t}{\lambda}\right),   \lambda >0
  
  which implies the cumulative hazard rate is
  
  .. math::  H(t) = \frac{t}{\lambda}
  
  and the hazard rate is:
  
  .. math::  h(t) = \frac{1}{\lambda}
  
  After calling the ``.fit`` method, you have access to properties like: ``survival_function_``, ``lambda_``, ``cumulative_hazard_``
  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)
  confidence_interval_cumulative_hazard_ : DataFrame
      The lower and upper confidence intervals for the cumulative hazard
  hazard_ : DataFrame
      The estimated hazard (with custom timeline if provided)
  confidence_interval_hazard_ : DataFrame
      The lower and upper confidence intervals for the hazard
  survival_function_ : DataFrame
      The estimated survival function (with custom timeline if provided)
  confidence_interval_survival_function_ : DataFrame
      The lower and upper confidence intervals for the survival function
  variance_matrix_ : DataFrame
      The variance matrix of the coefficients
  median_survival_time_: float
      The median time to event
  lambda_: 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
  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)
  
  confidence_interval_cumulative_density_ : DataFrame
      The lower and upper confidence intervals for the cumulative density
code: def _log_hazard(self, params, times):
      lambda_ = params[0]
      return -anp.log(lambda_)
  
file_path: lifelines/lifelines/fitters/exponential_fitter.py
imports: import numpy
  from autograd import numpy
  from lifelines.fitters import KnownModelParametricUnivariateFitter
label_desc: Use image node_id 3 for calling the ExponentialFitter obj's underlying member method code with example usage: obj._log_hazard(params, times) and returns: unknown