class_docstr: Poisson Distribution
  ----
  This class contains methods relating to the Poisson distribution for time series.
docstr: Negative loglikelihood function
  
  Parameters
  ----------
  y : np.ndarray
      univariate time series
  
  mean : np.ndarray
      array of location parameters for the Poisson distribution
  
  scale : float
      scale parameter for the Poisson distribution
  
  shape : float
      tail thickness parameter for the Poisson distribution
  
  skewness : float
      skewness parameter for the Poisson distribution
  
  Returns
  ----------
  - Negative loglikelihood of the Poisson family
docstr_tok: ["Negative","loglikelihood","function","Parameters","--","--","--","--","--","y",":","np.ndarray","univariate","time","series","mean",":","np.ndarray","array","of","location","parameters","for","the","Poisson","distribution","scale",":","float","scale","parameter","for","the","Poisson","distribution","shape",":","float","tail","thickness","parameter","for","the","Poisson","distribution","skewness",":","float","skewness","parameter","for","the","Poisson","distribution","Returns","--","--","--","--","--","-","Negative","loglikelihood","of","the","Poisson","family"]
code: def neg_loglikelihood(y, mean, scale, shape, skewness):
      """Negative loglikelihood function
  
      Parameters
      ----------
      y : np.ndarray
          univariate time series
  
      mean : np.ndarray
          array of location parameters for the Poisson distribution
  
      scale : float
          scale parameter for the Poisson distribution
  
      shape : float
          tail thickness parameter for the Poisson distribution
  
      skewness : float
          skewness parameter for the Poisson distribution
  
      Returns
      ----------
      - Negative loglikelihood of the Poisson family
      """
      return -np.sum(-mean + np.log(mean) * y - sp.gammaln(y + 1))
  
imports: import numpy
  import scipy.stats
  import scipy.special
  from .poisson_kalman_recursions import nl_univariate_KFS, nld_univariate_KFS
  from .family import Family
  from .flat import Flat
  from .normal import Normal
  from .gas_recursions import gas_recursion_poisson_orderone, gas_recursion_poisson_ordertwo
  from .gas_recursions import gasx_recursion_poisson_orderone, gasx_recursion_poisson_ordertwo
  from .gas_recursions import gas_llev_recursion_poisson_orderone, gas_llev_recursion_poisson_ordertwo
  from .gas_recursions import gas_llt_recursion_poisson_orderone, gas_llt_recursion_poisson_ordertwo
  from .gas_recursions import gas_reg_recursion_poisson_orderone, gas_reg_recursion_poisson_ordertwo
label_desc: Use image node_id 10 for calling the Poisson obj's underlying member method code with example usage: obj.neg_loglikelihood(y, mean, scale, shape, skewness) and returns: unknown