Finding tax filing probability parameters: The solution converged.
After 55 function evaluations:  fconst=-22.78771  fslope=0.59746
pop_filer_number_fraction= 0.10000
pop_filer_income_fraction= 0.50000
==> pop:
              income         fprob      filer     weight
count  1.000000e+06  1.000000e+06  1000000.0  1000000.0
mean   1.771876e+04  1.000455e-01        0.1        1.0
std    5.411221e+04  2.893777e-01        0.3        0.0
min    3.000000e+00  1.271168e-10        0.0        1.0
1%     4.350000e+02  1.645488e-10        0.0        1.0
5%     1.090000e+03  2.433598e-10        0.0        1.0
10%    1.729000e+03  3.564932e-10        0.0        1.0
25%    3.627000e+03  1.107972e-09        0.0        1.0
50%    8.091000e+03  1.595184e-08        0.0        1.0
75%    1.809800e+04  6.300023e-06        0.0        1.0
90%    3.788400e+04  4.616531e-01        0.1        1.0
95%    5.989205e+04  9.999977e-01        1.0        1.0
99%    1.493770e+05  1.000000e+00        1.0        1.0
max    2.059592e+07  1.000000e+00        1.0        1.0
          income     fprob     filer  weight
income  1.000000  0.452669  0.436593     NaN
fprob   0.452669  1.000000  0.964643     NaN
filer   0.436593  0.964643  1.000000     NaN
weight       NaN       NaN       NaN     NaN
==> sur:
              income         fprob         filer        weight
count  2.000000e+04  2.000000e+04  20000.000000  2.000000e+04
mean   1.772286e+04  9.988641e-02      0.100350  4.956777e+01
std    5.171526e+04  2.886590e-01      0.300474  5.904758e-12
min    7.000000e+00  1.274210e-10      0.000000  4.956777e+01
1%     4.080000e+02  1.619157e-10      0.000000  4.956777e+01
5%     1.104950e+03  2.455432e-10      0.000000  4.956777e+01
10%    1.746900e+03  3.603262e-10      0.000000  4.956777e+01
25%    3.631000e+03  1.110623e-09      0.000000  4.956777e+01
50%    8.203000e+03  1.705578e-08      0.000000  4.956777e+01
75%    1.821800e+04  6.768284e-06      0.000000  4.956777e+01
90%    3.790940e+04  4.654273e-01      1.000000  4.956777e+01
95%    5.888390e+04  9.999959e-01      1.000000  4.956777e+01
99%    1.446705e+05  1.000000e+00      1.000000  4.956777e+01
max    4.377438e+06  1.000000e+00      1.000000  4.956777e+01
          income     fprob     filer  weight
income  1.000000  0.469670  0.451887     NaN
fprob   0.469670  1.000000  0.964255     NaN
filer   0.451887  0.964255  1.000000     NaN
weight       NaN       NaN       NaN     NaN
agg_number_filers= 100000
agg_income_filers= 8.859 billion
Optimization terminated successfully.
         Current function value: 0.000124
         Iterations: 23
         Function evaluations: 68
xvar= [-34.22370605   0.90687195]
func(xvar)= 0.00012426261956575705
imputed_aggregate_filer_income= 8.768 billion
==> imp:
              income         fprob         filer        weight
count  2.000000e+04  2.000000e+04  20000.000000  2.000000e+04
mean   1.772286e+04  9.988641e-02      0.101300  4.956777e+01
std    5.171526e+04  2.886590e-01      0.301733  5.904758e-12
min    7.000000e+00  1.274210e-10      0.000000  4.956777e+01
1%     4.080000e+02  1.619157e-10      0.000000  4.956777e+01
5%     1.104950e+03  2.455432e-10      0.000000  4.956777e+01
10%    1.746900e+03  3.603262e-10      0.000000  4.956777e+01
25%    3.631000e+03  1.110623e-09      0.000000  4.956777e+01
50%    8.203000e+03  1.705578e-08      0.000000  4.956777e+01
75%    1.821800e+04  6.768284e-06      0.000000  4.956777e+01
90%    3.790940e+04  4.654273e-01      1.000000  4.956777e+01
95%    5.888390e+04  9.999959e-01      1.000000  4.956777e+01
99%    1.446705e+05  1.000000e+00      1.000000  4.956777e+01
max    4.377438e+06  1.000000e+00      1.000000  4.956777e+01
          income     fprob     filer  weight
income  1.000000  0.469670  0.451772     NaN
fprob   0.469670  1.000000  0.973434     NaN
filer   0.451772  0.973434  1.000000     NaN
weight       NaN       NaN       NaN     NaN
filer variable crosstab:
survey:      0     1    All
impute                     
0        17868   106  17974
1          125  1901   2026
All      17993  2007  20000
