Wed Oct 8 08:25:19 2025 log_normal_test(): python version: 3.10.12 numpy version: 1.26.4 Test log_normal(). log_normal_cdf_test(): log_normal_cdf evaluates the Log Normal CDF log_normal_cdf_inv inverts the Log Normal CDF. log_normal_pdf evaluates the Log Normal PDF PDF parameter MU = 1 PDF parameter SIGMA = 0.5 X PDF CDF CDF_inv 0.950682 0.0923071 0.0178138 0.950682 2.48583 0.315884 0.429054 2.48583 2.1977 0.331678 0.335353 2.1977 2.46727 0.317373 0.423175 2.46727 3.57093 0.192533 0.707348 3.57093 1.28415 0.201775 0.066832 1.28415 0.866543 0.067437 0.0111129 0.866543 2.7351 0.291699 0.50492 2.7351 4.41543 0.112867 0.834029 4.41543 8.08051 0.00919525 0.985331 8.08051 log_normal_sample_test(): log_normal_mean() computes the Log Normal mean log_normal_sample() samples the Log Normal distribution log_normal_variance() computes the Log Normal variance. PDF parameter MU = 1 PDF parameter SIGMA = 0.5 PDF mean = 3.08022 PDF variance = 2.69476 Sample size = 1000 Sample mean = 3.12236 Sample variance = 2.61575 Sample maximum = 10.4378 Sample minimum = 0.615236 normal_01_cdf_test(): normal_01_cdf() evaluates the Normal 01 CDF normal_01_cdf_inv() inverts the Normal 01 CDF. normal_01_pdf() evaluates the Normal 01 PDF X PDF CDF CDF_inv -0.716283 0.308674 0.236908 -0.716283 0.209485 0.390284 0.582965 0.209485 -0.866087 0.274174 0.193221 -0.866087 -1.36413 0.157337 0.0862628 -1.36413 3.3154 0.00163705 0.999542 3.3154 -0.792215 0.291493 0.214118 -0.792215 -0.265679 0.385108 0.395243 -0.265679 0.604384 0.332346 0.727206 0.604384 0.57887 0.337401 0.718661 0.57887 0.117013 0.39622 0.546575 0.117013 normal_01_cdf_values_test(): Python version: 3.10.12 normal_01_cdf_values() stores values of the unit normal CDF. X normal_01_cdf(X) 0.000000 0.5000000000000000 0.100000 0.5398278372770290 0.200000 0.5792597094391030 0.300000 0.6179114221889526 0.400000 0.6554217416103242 0.500000 0.6914624612740131 0.600000 0.7257468822499270 0.700000 0.7580363477769270 0.800000 0.7881446014166033 0.900000 0.8159398746532405 1.000000 0.8413447460685429 1.500000 0.9331927987311419 2.000000 0.9772498680518208 2.500000 0.9937903346742240 3.000000 0.9986501019683699 3.500000 0.9997673709209645 4.000000 0.9999683287581669 normal_01_sample_test() normal_01_mean() computes the Normal 01 mean normal_01_sample() samples the Normal 01 distribution normal_01_variance() returns the Normal 01 variance. PDF mean = 0 PDF variance = 1 Sample size = 1000 Sample mean = 0.0234039 Sample variance = 1.09277 Sample maximum = 3.71165 Sample minimum = -3.57747 normal_cdf_test(): normal_cdf() evaluates the Normal CDF normal_cdf_inv() inverts the Normal CDF. normal_pdf() evaluates the Normal PDF PDF parameter A = 100 PDF parameter B = 15 X PDF CDF CDF_inv 70.4817 0.00383617 0.0245405 70.4817 108.547 0.022611 0.715589 108.547 103.547 0.0258627 0.593477 103.547 128.867 0.00417467 0.97285 128.867 94.9704 0.0251423 0.368697 94.9704 116.786 0.0142193 0.868446 116.786 115.479 0.0156166 0.848946 115.479 128.149 0.004572 0.969714 128.149 70.812 0.00400507 0.0258352 70.812 96.1307 0.0257259 0.398222 96.1307 normal_sample_test(): normal_mean() computes the Normal mean normal_sample() samples the Normal distribution normal_variance() returns the Normal variance. PDF parameter A = 100 PDF parameter B = 15 PDF mean = 100 PDF variance = 225 Sample size = 1000 Sample mean = 101.438 Sample variance = 226.549 Sample maximum = 140.99 Sample minimum = 51.5458 r8poly_print_test Python version: 3.10.12 r8poly_print prints an R8POLY. The R8POLY: p(x) = 9 * x^5 + 0.78 * x^4 + 56 * x^2 - 3.4 * x + 12 r8poly_value_horner_test(): Python version: 3.10.12 r8poly_value_horner() evaluates a polynomial at a point using Horners method. The polynomial coefficients: p(x) = 1 * x^4 - 10 * x^3 + 35 * x^2 - 50 * x + 24 I X P(X) 0 0.0000 24 1 0.3333 10.8642 2 0.6667 3.45679 3 1.0000 0 4 1.3333 -0.987654 5 1.6667 -0.691358 6 2.0000 0 7 2.3333 0.493827 8 2.6667 0.493827 9 3.0000 0 10 3.3333 -0.691358 11 3.6667 -0.987654 12 4.0000 0 13 4.3333 3.45679 14 4.6667 10.8642 15 5.0000 24 log_normal_test(): Normal end of execution. Wed Oct 8 08:25:19 2025