Tue May 20 22:02:43 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 4.95659 0.0782197 0.885209 4.95659 1.45767 0.251756 0.106322 1.45767 1.84005 0.319785 0.217574 1.84005 3.00603 0.260108 0.579744 3.00603 3.51984 0.198342 0.697363 3.51984 3.54229 0.195777 0.701788 3.54229 3.76779 0.171106 0.743115 3.76779 1.58325 0.280944 0.139838 1.58325 1.82282 0.318045 0.212077 1.82282 2.19847 0.331661 0.335608 2.19847 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 = 3.0633 Sample variance = 2.55176 Sample maximum = 11.8022 Sample minimum = 0.562896 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 0.26038 0.385645 0.602715 0.26038 0.374052 0.371987 0.645817 0.374052 -0.807905 0.287856 0.209573 -0.807905 0.588515 0.335507 0.721907 0.588515 -0.143711 0.394844 0.442864 -0.143711 1.66963 0.0989859 0.952504 1.66963 -0.570923 0.338946 0.284026 -0.570923 1.09497 0.219057 0.863236 1.09497 -0.0153216 0.398895 0.493888 -0.0153216 -2.61719 0.0129873 0.00443285 -2.61719 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 = 0.0166975 Sample variance = 1.0386 Sample maximum = 3.56045 Sample minimum = -3.56871 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 92.2947 0.0233088 0.303735 92.2947 97.2387 0.0261493 0.426974 97.2387 95.0411 0.0251818 0.370476 95.0411 98.6395 0.026487 0.463866 98.6395 75.8712 0.00729358 0.0538536 75.8712 99.8621 0.026595 0.496332 99.8621 90.0043 0.0213006 0.252585 90.0043 85.2446 0.0163945 0.162634 85.2446 117.539 0.0134259 0.87885 117.539 105.651 0.0247741 0.646819 105.651 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 = 99.3115 Sample variance = 219.94 Sample maximum = 144.159 Sample minimum = 53.625 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. Tue May 20 22:02:43 2025