#! /usr/bin/env python
#
def negative_binomial_cdf_values ( n_data ):

#*****************************************************************************80
#
## NEGATIVE_BINOMIAL_CDF_VALUES returns values of the negative binomial CDF.
#
#  Discussion:
#
#    Assume that a coin has a probability P of coming up heads on
#    any one trial.  Suppose that we plan to flip the coin until we
#    achieve a total of S heads.  If we let F represent the number of
#    tails that occur in this process, then the value of F satisfies
#    a negative binomial PDF:
#
#      PDF(F,S,P) = Choose ( F from F+S-1 ) * P^S * (1-P)^F
#
#    The negative binomial CDF is the probability that there are F or
#    fewer failures upon the attainment of the S-th success.  Thus,
#
#      CDF(F,S,P) = sum ( 0 <= G <= F ) PDF(G,S,P)
#
#    In Mathematica, the function can be evaluated by:
#
#      Needs["Statistics`DiscreteDistributions`]
#      dist = NegativeBinomialDistribution [ s, p ]
#      CDF [ dist, f ]
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    20 February 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    F C Powell,
#    Statistical Tables for Sociology, Biology and Physical Sciences,
#    Cambridge University Press, 1982.
#
#    Stephen Wolfram,
#    The Mathematica Book,
#    Fourth Edition,
#    Wolfram Media / Cambridge University Press, 1999.
#
#  Parameters:
#
#    Input/output, integer N_DATA.  The user sets N_DATA to 0 before the
#    first call.  On each call, the routine increments N_DATA by 1, and
#    returns the corresponding data; when there is no more data, the
#    output value of N_DATA will be 0 again.
#
#    Output, integer F, the maximum number of failures.
#
#    Output, integer S, the number of successes.
#
#    Output, real P, the probability of a success on one trial.
#
#    Output, real CDF, the probability of at most F failures 
#    before the S-th success.
#
  import numpy as np

  n_max = 27

  cdf_vec = np.array ( ( \
     0.6367187500000000E+00, \
     0.3632812500000000E+00, \
     0.1445312500000000E+00, \
     0.5000000000000000E+00, \
     0.2265625000000000E+00, \
     0.6250000000000000E-01, \
     0.3437500000000000E+00, \
     0.1093750000000000E+00, \
     0.1562500000000000E-01, \
     0.1792000000000000E+00, \
     0.4096000000000000E-01, \
     0.4096000000000000E-02, \
     0.7047000000000000E-01, \
     0.1093500000000000E-01, \
     0.7290000000000000E-03, \
     0.9861587127990000E+00, \
     0.9149749500510000E+00, \
     0.7471846521450000E+00, \
     0.8499053647030009E+00, \
     0.5497160941090026E+00, \
     0.2662040052146710E+00, \
     0.6513215599000000E+00, \
     0.2639010709000000E+00, \
     0.7019082640000000E-01, \
     0.1000000000000000E+01, \
     0.1990000000000000E-01, \
     0.1000000000000000E-03 ))

  f_vec = np.array ( ( \
     4,  3,  2, \
     3,  2,  1, \
     2,  1,  0, \
     2,  1,  0, \
     2,  1,  0, \
    11, 10,  9, \
    17, 16, 15, \
     9,  8,  7, \
     2,  1,  0 ))

  p_vec = np.array ( ( \
     0.50E+00, \
     0.50E+00, \
     0.50E+00, \
     0.50E+00, \
     0.50E+00, \
     0.50E+00, \
     0.50E+00, \
     0.50E+00, \
     0.50E+00, \
     0.40E+00, \
     0.40E+00, \
     0.40E+00, \
     0.30E+00, \
     0.30E+00, \
     0.30E+00, \
     0.30E+00, \
     0.30E+00, \
     0.30E+00, \
     0.10E+00, \
     0.10E+00, \
     0.10E+00, \
     0.10E+00, \
     0.10E+00, \
     0.10E+00, \
     0.10E-01, \
     0.10E-01, \
     0.10E-01 ))

  s_vec = np.array ( ( \
    4, 5, 6, \
    4, 5, 6, \
    4, 5, 6, \
    4, 5, 6, \
    4, 5, 6, \
    1, 2, 3, \
    1, 2, 3, \
    1, 2, 3, \
    0, 1, 2 ))

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    f = 0
    s = 0
    p = 0.0
    cdf = 0.0
  else:
    f = f_vec[n_data]
    s = s_vec[n_data]
    p = p_vec[n_data]
    cdf = cdf_vec[n_data]
    n_data = n_data + 1

  return n_data, f, s, p, cdf

def negative_binomial_cdf_values_test ( ):

#*****************************************************************************80
#
## NEGATIVE_BINOMIAL_CDF_VALUES_TEST demonstrates the use of NEGATIVE_BINOMIAL_CDF_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    20 February 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'NEGATIVE_BINOMIAL_CDF_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  NEGATIVE_BINOMIAL_CDF_VALUES stores values of the unit normal CDF.' )
  print ( '' )
  print ( '       F       S        P            CDF()' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, f, s, p, cdf = negative_binomial_cdf_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %6d  %6d  %12f  %24.16f' % ( f, s, p, cdf ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'NEGATIVE_BINOMIAL_CDF_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  negative_binomial_cdf_values_test ( )
  timestamp ( )