Tue Oct 19 17:25:41 2021 truncated_normal_test() Python version: 3.6.9 Test truncated_normal(). normal_01_cdf_values_test: Python version: 3.6.9 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_cdf_values_test: Normal end of execution. r8_mop_test r8_mop evaluates (-1.0)^I4 as an R8. I4 r8_mop(I4) 15 -1.0 80 1.0 17 -1.0 -98 1.0 25 -1.0 91 -1.0 10 1.0 79 -1.0 -14 1.0 -12 1.0 r8_mop_test Normal end of execution. r8poly_print_test Python version: 3.6.9 r8poly_print prints an R8POLY. The R8POLY: p(x) = 9 * x^5 + 0.78 * x^4 + 56 * x^2 - 3.4 * x + 12 r8poly_print_test: Normal end of execution. r8poly_value_horner_test Python version: 3.6.9 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 r8poly_value_horner_test: Normal end of execution. r8vec_linspace_test Python version: 3.6.9 r8vec_linspace returns evenly spaced values between A and B. The linspace vector: 0: 10 1: 12.5 2: 15 3: 17.5 4: 20 r8vec_linspace_test Normal end of execution. r8vec_print_test Python version: 3.6.9 r8vec_print prints an R8VEC. Here is an R8VEC: 0: 123.456 1: 5e-06 2: -1e+06 3: 3.14159 r8vec_print_test: Normal end of execution. r8vec_variance_test Python version: 3.6.9 r8vec_variance computes the variance of an R8VEC. Input vector: 0: 3.44562 1: -0.663476 2: -4.53548 3: 2.95907 4: -2.25323 5: 4.09647 6: -3.10605 7: -3.41565 8: -2.70614 9: -4.77091 Value = 11.434 r8vec_variance_test: Normal end of execution. truncated_normal_a_cdf_values_test: Python version: 3.6.9 truncated_normal_a_cdf_values stores values of the truncated_normal_a_cdf function. MU SIGMA A X F 100 25 50 90 0.3293202045481688 100 25 50 92 0.3599223134505957 100 25 50 94 0.3913175216041539 100 25 50 96 0.4233210140873113 100 25 50 98 0.4557365629792204 100 25 50 100 0.4883601253415709 100 25 50 102 0.5209836877039214 100 25 50 104 0.5533992365958303 100 25 50 106 0.5854027290789878 100 25 50 108 0.6167979372325459 100 25 50 110 0.6474000461349729 truncated_normal_a_cdf_values_test: Normal end of execution. truncated_normal_a_pdf_values_test: Python version: 3.6.9 truncated_normal_a_pdf_values stores values of the truncated_normal_a_pdf function. MU SIGMA A X F 100 25 50 90 0.01507373507401876 100 25 50 92 0.01551417047139894 100 25 50 94 0.01586560931024694 100 25 50 96 0.01612150073158793 100 25 50 98 0.01627701240029317 100 25 50 100 0.01632918226724295 100 25 50 102 0.01627701240029317 100 25 50 104 0.01612150073158793 100 25 50 106 0.01586560931024694 100 25 50 108 0.01551417047139894 100 25 50 110 0.01507373507401876 truncated_normal_a_pdf_values_test: Normal end of execution. truncated_normal_ab_cdf_values_test: Python version: 3.6.9 truncated_normal_ab_cdf_values stores values of the truncated_normal_ab_cdf function. MU SIGMA A B X F 100 25 50 150 90 0.3371694242213513 100 25 50 150 92 0.3685009225506048 100 25 50 150 94 0.4006444233448185 100 25 50 150 96 0.433410706690304 100 25 50 150 98 0.4665988676496338 100 25 50 150 100 0.5 100 25 50 150 102 0.5334011323503662 100 25 50 150 104 0.566589293309696 100 25 50 150 106 0.5993555766551815 100 25 50 150 108 0.6314990774493952 100 25 50 150 110 0.6628305757786487 truncated_normal_ab_cdf_values_test: Normal end of execution. truncated_normal_ab_pdf_values_test: Python version: 3.6.9 truncated_normal_ab_pdf_values stores values of the truncated_normal_ab_pdf function. MU SIGMA A B X F 100 25 50 150 90 0.01543301171801836 100 25 50 150 92 0.01588394472270638 100 25 50 150 94 0.01624375997031919 100 25 50 150 96 0.01650575046469259 100 25 50 150 98 0.01666496869385951 100 25 50 150 100 0.01671838200940538 100 25 50 150 102 0.01666496869385951 100 25 50 150 104 0.01650575046469259 100 25 50 150 106 0.01624375997031919 100 25 50 150 108 0.01588394472270638 100 25 50 150 110 0.01543301171801836 truncated_normal_ab_pdf_values_test: Normal end of execution. truncated_normal_b_cdf_values_test: Python version: 3.6.9 truncated_normal_b_cdf_values stores values of the truncated_normal_b_cdf function. MU SIGMA B X F 100 25 150 90 0.3525999538650271 100 25 150 92 0.383202062767454 100 25 150 94 0.4145972709210122 100 25 150 96 0.4466007634041696 100 25 150 98 0.4790163122960786 100 25 150 100 0.5116398746584291 100 25 150 102 0.5442634370207796 100 25 150 104 0.5766789859126887 100 25 150 106 0.6086824783958461 100 25 150 108 0.6400776865494043 100 25 150 110 0.6706797954518312 truncated_normal_b_cdf_values_test: Normal end of execution. truncated_normal_b_pdf_values_test: Python version: 3.6.9 truncated_normal_b_pdf_values stores values of the truncated_normal_b_pdf function. MU SIGMA B X F 100 25 150 90 0.01507373507401876 100 25 150 92 0.01551417047139894 100 25 150 94 0.01586560931024694 100 25 150 96 0.01612150073158793 100 25 150 98 0.01627701240029317 100 25 150 100 0.01632918226724295 100 25 150 102 0.01627701240029317 100 25 150 104 0.01612150073158793 100 25 150 106 0.01586560931024694 100 25 150 108 0.01551417047139894 100 25 150 110 0.01507373507401876 truncated_normal_b_pdf_values_test: Normal end of execution. normal_01_cdf_test Python version: 3.6.9 normal_01_cdf evaluates the CDF; X CDF CDF (exact) (computed) 0 0.5 0.5 0.1 0.539827837277029 0.5398278372805048 0.2 0.579259709439103 0.5792597094424672 0.3 0.6179114221889526 0.6179114221891665 0.4 0.6554217416103242 0.6554217416083834 0.5 0.6914624612740131 0.6914624612735877 0.6 0.725746882249927 0.7257468822526401 0.7 0.758036347776927 0.7580363477802913 0.8 0.7881446014166033 0.7881446014178579 0.9 0.8159398746532405 0.8159398746539517 1 0.8413447460685429 0.8413447460717163 1.5 0.9331927987311419 0.9331927987330156 2 0.9772498680518208 0.9772498680509744 2.5 0.993790334674224 0.9937903346744605 3 0.9986501019683699 0.9986501019683744 3.5 0.9997673709209645 0.9997673709209559 4 0.9999683287581669 0.9999683287581664 normal_01_cdf_test: Normal end of execution. normal_01_cdf_inv_test Python version: 3.6.9 normal_01_cdf_inv inverts the CDF; CDF X X (exact) (computed) 0.5 0 0 0.539828 0.1 0.09999999999999999 0.57926 0.2 0.1999999999999999 0.617911 0.3 0.2999999999999998 0.655422 0.4 0.4 0.691462 0.5 0.4999999999999998 0.725747 0.6 0.6000000000000016 0.758036 0.7 0.6999999999999998 0.788145 0.8 0.7999999999999998 0.81594 0.9 0.9 0.841345 1 1 0.933193 1.5 1.5 0.97725 2 2 0.99379 2.5 2.500000000000004 0.99865 3 2.999999999999997 0.999767 3.5 3.499999999999983 0.999968 4 4 normal_01_cdf_inv_test: Normal end of execution. normal_01_mean_test Python version: 3.6.9 normal_01_mean computes the Normal 01 mean; PDF mean = 0 Sample size = 1000 Sample mean = 0.00971011 Sample maximum = 3.3392 Sample minimum = -3.31381 normal_01_mean_test: Normal end of execution. normal_01_moment_test Python version: 3.6.9 normal_01_moment evaluates moments of the Normal 01 PDF; Order Moment 0 1 1 0 2 1 3 0 4 3 5 0 6 15 7 0 8 105 9 0 10 945 normal_01_moment_test: Normal end of execution. normal_01_pdf_test Python version: 3.6.9 normal_01_pdf evaluates the PDF; X PDF -2 0.05399096651318806 -1.9 0.0656158147746766 -1.8 0.07895015830089415 -1.7 0.09404907737688695 -1.6 0.1109208346794555 -1.5 0.1295175956658917 -1.4 0.1497274656357449 -1.3 0.1713685920478074 -1.2 0.194186054983213 -1.1 0.2178521770325506 -1 0.2419707245191434 -0.9 0.2660852498987548 -0.8 0.2896915527614827 -0.7 0.3122539333667613 -0.6 0.3332246028917997 -0.5 0.3520653267642995 -0.4 0.3682701403033233 -0.3 0.3813878154605241 -0.2 0.3910426939754559 -0.1 0.3969525474770118 0 0.3989422804014327 0.1 0.3969525474770118 0.2 0.3910426939754559 0.3 0.3813878154605241 0.4 0.3682701403033233 0.5 0.3520653267642995 0.6 0.3332246028917997 0.7 0.3122539333667613 0.8 0.2896915527614827 0.9 0.2660852498987548 1 0.2419707245191434 1.1 0.2178521770325506 1.2 0.194186054983213 1.3 0.1713685920478074 1.4 0.1497274656357449 1.5 0.1295175956658917 1.6 0.1109208346794555 1.7 0.09404907737688695 1.8 0.07895015830089415 1.9 0.0656158147746766 2 0.05399096651318806 normal_01_pdf_test: Normal end of execution. normal_01_variance_test Python version: 3.6.9 normal_01_variance computes the Normal 01 variance; PDF variance = 1 Sample size = 1000 Sample variance = 0.964533 normal_01_variance_test: Normal end of execution. normal_ms_cdf_test Python version: 3.6.9 normal_ms_cdf evaluates the CDF; PDF parameter MU = 100 PDF parameter SIGMA = 15 X CDF 70 0.0227501319490256 71.5 0.02871655981700335 73 0.03593031911349944 74.5 0.04456546275790788 76 0.05479929169747734 77.5 0.06680720126698436 79 0.08075665923561445 80.5 0.09680048458598516 82 0.1150696702192547 83.5 0.1356660609430844 85 0.1586552539282837 86.5 0.1840601253460483 88 0.2118553985821421 89.5 0.2419636522197087 91 0.2742531177473599 92.5 0.3085375387264123 94 0.3445782583916166 95.5 0.3820885778108335 97 0.4207402905575328 98.5 0.4601721627194953 100 0.5 101.5 0.5398278372805048 103 0.5792597094424672 104.5 0.6179114221891665 106 0.6554217416083834 107.5 0.6914624612735877 109 0.7257468822526401 110.5 0.7580363477802913 112 0.7881446014178579 113.5 0.8159398746539517 115 0.8413447460717163 116.5 0.8643339390569156 118 0.8849303297807454 119.5 0.9031995154140149 121 0.9192433407643855 122.5 0.9331927987330156 124 0.9452007083025227 125.5 0.9554345372420922 127 0.9640696808865006 128.5 0.9712834401829966 130 0.9772498680509744 normal_ms_cdf_test: Normal end of execution. normal_ms_cdf_inv_test Python version: 3.6.9 normal_ms_cdf_inv inverts the CDF of the Normal MS distribution. PDF parameter MU = 100 PDF parameter SIGMA = 15 X CDF CDF_inv 70 0.0227501 70 71.5 0.0287166 71.5 73 0.0359303 73 74.5 0.0445655 74.5 76 0.0547993 76 77.5 0.0668072 77.5 79 0.0807567 79 80.5 0.0968005 80.5 82 0.11507 82 83.5 0.135666 83.5 85 0.158655 85 86.5 0.18406 86.5 88 0.211855 88 89.5 0.241964 89.5 91 0.274253 91 92.5 0.308538 92.5 94 0.344578 94 95.5 0.382089 95.5 97 0.42074 97 98.5 0.460172 98.5 100 0.5 100 101.5 0.539828 101.5 103 0.57926 103 104.5 0.617911 104.5 106 0.655422 106 107.5 0.691462 107.5 109 0.725747 109 110.5 0.758036 110.5 112 0.788145 112 113.5 0.81594 113.5 115 0.841345 115 116.5 0.864334 116.5 118 0.88493 118 119.5 0.9032 119.5 121 0.919243 121 122.5 0.933193 122.5 124 0.945201 124 125.5 0.955435 125.5 127 0.96407 127 128.5 0.971283 128.5 130 0.97725 130 normal_ms_cdf_inv_test: Normal end of execution. normal_ms_mean_test Python version: 3.6.9 normal_ms_mean computes the mean of the Normal MS distribution. PDF parameter MU = 100 PDF parameter SIGMA = 15 PDF mean = 100 Sample size = 1000 Sample mean = 99.387 Sample maximum = 147.14 Sample minimum = 54.4726 normal_ms_mean_test: Normal end of execution. normal_ms_moment_test Python version: 3.6.9 normal_ms_moment evaluates moments of the Normal MS distribution. Mu = 0, Sigma = 1 Order Moment 0 1 1 1 0 0 2 1 1 3 0 0 4 3 3 5 0 0 6 15 15 7 0 0 8 105 105 Mu = 2, Sigma = 1 Order Moment 0 1 1 1 2 2 2 5 5 3 14 14 4 43 43 5 142 142 6 499 499 7 1850 1850 8 7193 7193 Mu = 10, Sigma = 2 Order Moment 0 1 1 1 10 10 2 104 104 3 1120 1120 4 12448 12448 5 142400 142400 6 1.67296e+06 1.67296e+06 7 2.01472e+07 2.01472e+07 8 2.48315e+08 2.48315e+08 Mu = 0, Sigma = 2 Order Moment 0 1 1 1 0 0 2 4 4 3 0 0 4 48 48 5 0 0 6 960 960 7 0 0 8 26880 26880 normal_ms_moment_test: Normal end of execution. normal_ms_moment_central_test Python version: 3.6.9 normal_ms_moment_central evaluates central moments of the Normal MS distribution. Mu = 0, Sigma = 1 Order Moment 0 1 1 1 0 0 2 1 1 3 0 0 4 3 3 5 0 0 6 15 15 7 0 0 8 105 105 Mu = 2, Sigma = 1 Order Moment 0 1 1 1 0 0 2 1 1 3 0 0 4 3 3 5 0 0 6 15 15 7 0 0 8 105 105 Mu = 10, Sigma = 2 Order Moment 0 1 1 1 0 0 2 4 4 3 0 0 4 48 48 5 0 0 6 960 960 7 0 0 8 26880 26880 Mu = 0, Sigma = 2 Order Moment 0 1 1 1 0 0 2 4 4 3 0 0 4 48 48 5 0 0 6 960 960 7 0 0 8 26880 26880 normal_ms_moment_central_test: Normal end of execution. normal_ms_pdf_test Python version: 3.6.9 normal_ms_pdf evaluates the PDF for the Normal MS distribution. PDF parameter MU = 100 PDF parameter SIGMA = 15 X PDF 70 0.00359939776754587 71.5 0.004374387651645106 73 0.005263343886726277 74.5 0.006269938491792463 76 0.007394722311963703 77.5 0.008634506377726116 79 0.009981831042382991 80.5 0.01142457280318716 82 0.01294573699888086 83.5 0.0145234784688367 85 0.01613138163460956 86.5 0.01773901665991699 88 0.01931277018409885 89.5 0.02081692889111742 91 0.02221497352611998 92.5 0.02347102178428663 94 0.02455134268688822 95.5 0.02542585436403494 97 0.02606951293169706 98.5 0.02646350316513412 100 0.02659615202676218 101.5 0.02646350316513412 103 0.02606951293169706 104.5 0.02542585436403494 106 0.02455134268688822 107.5 0.02347102178428663 109 0.02221497352611998 110.5 0.02081692889111742 112 0.01931277018409885 113.5 0.01773901665991699 115 0.01613138163460956 116.5 0.0145234784688367 118 0.01294573699888086 119.5 0.01142457280318716 121 0.009981831042382991 122.5 0.008634506377726116 124 0.007394722311963703 125.5 0.006269938491792463 127 0.005263343886726277 128.5 0.004374387651645106 130 0.00359939776754587 normal_ms_pdf_test: Normal end of execution. normal_ms_sample_test Python version: 3.6.9 normal_ms_sample samples the Normal MS distribution. PDF parameter MU = 100 PDF parameter SIGMA = 15 0 88.1132 1 109.054 2 93.2194 3 107.038 4 133.535 5 88.073 6 81.2885 7 127.918 8 108.13 9 109.771 normal_ms_sample_test Normal end of execution. normal_ms_variance_test Python version: 3.6.9 normal_ms_variance computes the variance of the Normal MS distribution. PDF parameter MU = 100 PDF parameter SIGMA = 15 PDF variance = 225 Sample size = 1000 Sample variance = 224.063 normal_ms_variance_test: Normal end of execution. truncated_normal_a_cdf_test Python version: 3.6.9 truncated_normal_a_cdf evaluates the CDF of the lower Truncated Normal distribution. The "parent" normal distribution has mean = mu standard deviation = sigma The parent distribution is truncated to the interval [a,+oo) Stored Computed X Mu S A CDF CDF 90.0 100.0 25.0 50.0 0.32932 0.32932 92.0 100.0 25.0 50.0 0.359922 0.359922 94.0 100.0 25.0 50.0 0.391318 0.391318 96.0 100.0 25.0 50.0 0.423321 0.423321 98.0 100.0 25.0 50.0 0.455737 0.455737 100.0 100.0 25.0 50.0 0.48836 0.48836 102.0 100.0 25.0 50.0 0.520984 0.520984 104.0 100.0 25.0 50.0 0.553399 0.553399 106.0 100.0 25.0 50.0 0.585403 0.585403 108.0 100.0 25.0 50.0 0.616798 0.616798 110.0 100.0 25.0 50.0 0.6474 0.6474 truncated_normal_a_cdf_test: Normal end of execution. truncated_normal_a_cdf_inv_test Python version: 3.6.9 truncated_normal_a_cdf_inv inverts the CDF of the lower Truncated Normal distribution. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,+oo) X CDF CDF_inv 109.583 0.64109 109.583 113.939 0.704711 113.939 100.905 0.503137 100.905 80.2896 0.196957 80.2896 98.5571 0.464812 98.5571 99.4181 0.478859 99.4181 91.716 0.355524 91.716 102.476 0.528731 102.476 106.18 0.588256 106.18 116.155 0.734899 116.155 truncated_normal_a_cdf_inv_test Normal end of execution. truncated_normal_a_mean_test Python version: 3.6.9 truncated_normal_a_mean computes the mean of the Truncated Normal distribution. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,+oo) PDF mean = 101.381 Sample size = 1000 Sample mean = 101.365 Sample maximum = 188.79 Sample minimum = 51.3482 truncated_normal_a_mean_test: Normal end of execution. truncated_normal_a_moment_test Python version: 3.6.9 truncated_normal_a_moment evaluates moments of the lower Truncated Normal distribution. Test = 0, Mu = 0, Sigma = 1, A = 0 Order Moment 0 1 1 0.797885 2 1 3 1.59577 4 3 5 6.38308 6 15 7 38.2985 8 105 Test = 1, Mu = 0, Sigma = 1, A = -10 Order Moment 0 1 1 7.6946e-23 2 1 3 7.84849e-21 4 3 5 8.00854e-19 6 15 7 8.17511e-17 8 105 Test = 2, Mu = 0, Sigma = 1, A = 10 Order Moment 0 1 1 10.0981 2 101.981 3 1030.01 4 10404 5 105101 6 1.06183e+06 7 1.07287e+07 8 1.08414e+08 Test = 3, Mu = 0, Sigma = 2, A = -10 Order Moment 0 1 1 2.97344e-06 2 3.99997 3 0.000321132 4 47.9967 5 0.0348725 6 959.636 7 3.81038 8 26840.1 Test = 4, Mu = 0, Sigma = 2, A = 10 Order Moment 0 1 1 10.373 2 107.73 3 1120.28 4 11665.8 5 121655 6 1.27062e+06 7 1.32927e+07 8 1.39307e+08 Test = 5, Mu = -5, Sigma = 1, A = -10 Order Moment 0 1 1 -5 2 26 3 -140 4 777.997 5 -4449.97 6 26139.7 7 -157397 8 969947 truncated_normal_a_moment_test: Normal end of execution. truncated_normal_a_pdf_test Python version: 3.6.9 truncated_normal_a_pdf evaluates the PDF of the lower Truncated Normal distribution. The "parent" normal distribution has mean = mu standard deviation = sigma The parent distribution is truncated to the interval [a,+oo) Stored Computed X Mu S A PDF PDF 90.0 100.0 25.0 50.0 0.0150737 0.0150737 92.0 100.0 25.0 50.0 0.0155142 0.0155142 94.0 100.0 25.0 50.0 0.0158656 0.0158656 96.0 100.0 25.0 50.0 0.0161215 0.0161215 98.0 100.0 25.0 50.0 0.016277 0.016277 100.0 100.0 25.0 50.0 0.0163292 0.0163292 102.0 100.0 25.0 50.0 0.016277 0.016277 104.0 100.0 25.0 50.0 0.0161215 0.0161215 106.0 100.0 25.0 50.0 0.0158656 0.0158656 108.0 100.0 25.0 50.0 0.0155142 0.0155142 110.0 100.0 25.0 50.0 0.0150737 0.0150737 truncated_normal_a_pdf_test: Normal end of execution. truncated_normal_a_sample_test Python version: 3.6.9 truncated_normal_a_sample samples the lower Truncated Normal distribution. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,+oo) 0 98.5337 1 93.3181 2 137.786 3 74.322 4 72.5364 5 101.818 6 124.535 7 111.109 8 90.0948 9 85.7074 truncated_normal_a_sample_test Normal end of execution. truncated_normal_a_variance_test Python version: 3.6.9 truncated_normal_a_variance computes the variance of the Truncated Normal distribution. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,+oo) PDF variance = 554.032 Sample size = 1000 Sample variance = 530.982 truncated_normal_a_variance_test: Normal end of execution. truncated_normal_ab_cdf_test Python version: 3.6.9 truncated_normal_ab_cdf evaluates the CDF of the Truncated Normal distribution. The "parent" normal distribution has mean = mu standard deviation = sigma The parent distribution is truncated to the interval [a,b] Stored Computed X Mu S A B CDF CDF 90.0 100.0 25.0 50.0 150.0 0.337169 0.337169 92.0 100.0 25.0 50.0 150.0 0.368501 0.368501 94.0 100.0 25.0 50.0 150.0 0.400644 0.400644 96.0 100.0 25.0 50.0 150.0 0.433411 0.433411 98.0 100.0 25.0 50.0 150.0 0.466599 0.466599 100.0 100.0 25.0 50.0 150.0 0.5 0.5 102.0 100.0 25.0 50.0 150.0 0.533401 0.533401 104.0 100.0 25.0 50.0 150.0 0.566589 0.566589 106.0 100.0 25.0 50.0 150.0 0.599356 0.599356 108.0 100.0 25.0 50.0 150.0 0.631499 0.631499 110.0 100.0 25.0 50.0 150.0 0.662831 0.662831 truncated_normal_ab_cdf_test: Normal end of execution. truncated_normal_ab_cdf_inv_test Python version: 3.6.9 truncated_normal_ab_cdf_inv inverts the CDF of the Truncated Normal distribution. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,150] X CDF CDF_inv 85.5009 0.270529 85.5009 78.9389 0.185459 78.9389 112.053 0.693971 112.053 61.6347 0.0415813 61.6347 135.465 0.942107 135.465 126.735 0.874602 126.735 138.675 0.959997 138.675 121.87 0.823899 121.87 100.601 0.510055 100.601 114.897 0.735064 114.897 truncated_normal_ab_cdf_inv_test Normal end of execution. truncated_normal_ab_mean_test Python version: 3.6.9 truncated_normal_ab_mean computes the mean of the Truncated Normal distribution. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,150] PDF mean = 100 Sample size = 1000 Sample mean = 99.5374 Sample maximum = 149.83 Sample minimum = 50.4613 truncated_normal_ab_mean_test: Normal end of execution. truncated_normal_ab_moment_test Python version: 3.6.9 truncated_normal_ab_moment evaluates moments of the Truncated Normal distribution. Test = 0, Mu = 0, Sigma = 1, A = -1, B = 1 Order Moment 0 1 1 0 2 0.291125 3 0 4 0.1645 5 0 6 0.113627 7 0 8 0.086514 Test = 1, Mu = 0, Sigma = 1, A = 0, B = 1 Order Moment 0 1 1 0.459862 2 0.291125 3 0.21085 4 0.1645 5 0.134523 6 0.113627 7 0.0982649 8 0.086514 Test = 2, Mu = 0, Sigma = 1, A = -1, B = 0 Order Moment 0 1 1 -0.459862 2 0.291125 3 -0.21085 4 0.1645 5 -0.134523 6 0.113627 7 -0.0982649 8 0.086514 Test = 3, Mu = 0, Sigma = 2, A = -1, B = 1 Order Moment 0 1 1 0 2 0.322357 3 0 4 0.190636 5 0 6 0.135077 7 0 8 0.104524 Test = 4, Mu = 1, Sigma = 1, A = 0, B = 2 Order Moment 0 1 1 1 2 1.29113 3 1.87338 4 2.91125 5 4.73375 6 7.94801 7 13.6665 8 23.9346 Test = 5, Mu = 0, Sigma = 1, A = 0.5, B = 2 Order Moment 0 1 1 1.04299 2 1.23812 3 1.63828 4 2.35698 5 3.60741 6 5.77795 7 9.57285 8 16.2735 Test = 6, Mu = 0, Sigma = 1, A = -2, B = 2 Order Moment 0 1 1 0 2 0.773741 3 0 4 1.41619 5 0 6 3.46081 7 0 8 9.74509 Test = 7, Mu = 0, Sigma = 1, A = -4, B = 4 Order Moment 0 1 1 0 2 0.998929 3 0 4 2.97966 5 0 6 14.6242 7 0 8 97.9836 Test = 8, Mu = 5, Sigma = 0.5, A = 4, B = 7 Order Moment 0 1 1 5.02756 2 25.4978 3 130.441 4 673.075 5 3502.72 6 18382.1 7 97269.7 8 518913 truncated_normal_ab_moment_test: Normal end of execution. truncated_normal_ab_pdf_test Python version: 3.6.9 truncated_normal_ab_pdf evaluates the PDF of the Truncated Normal distribution. The "parent" normal distribution has mean = mu standard deviation = sigma The parent distribution is truncated to the interval [a,b] Stored Computed X Mu S A B PDF PDF 90.0 100.0 25.0 50.0 150.0 0.015433 0.015433 92.0 100.0 25.0 50.0 150.0 0.0158839 0.0158839 94.0 100.0 25.0 50.0 150.0 0.0162438 0.0162438 96.0 100.0 25.0 50.0 150.0 0.0165058 0.0165058 98.0 100.0 25.0 50.0 150.0 0.016665 0.016665 100.0 100.0 25.0 50.0 150.0 0.0167184 0.0167184 102.0 100.0 25.0 50.0 150.0 0.016665 0.016665 104.0 100.0 25.0 50.0 150.0 0.0165058 0.0165058 106.0 100.0 25.0 50.0 150.0 0.0162438 0.0162438 108.0 100.0 25.0 50.0 150.0 0.0158839 0.0158839 110.0 100.0 25.0 50.0 150.0 0.015433 0.015433 truncated_normal_ab_pdf_test: Normal end of execution. truncated_normal_ab_sample_test Python version: 3.6.9 truncated_normal_ab_sample samples the Truncated Normal distribution. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,150] 0 119.585 1 108.546 2 96.1564 3 52.4428 4 109.691 5 116.82 6 130.175 7 81.1572 8 83.4609 9 122.505 truncated_normal_ab_sample_test Normal end of execution. truncated_normal_ab_variance_test Python version: 3.6.9 truncated_normal_ab_variance computes the variance of the Truncated Normal distribution. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,150] PDF variance = 483.588 Sample size = 1000 Sample variance = 494.851 truncated_normal_ab_variance_test: Normal end of execution. truncated_normal_b_cdf_test Python version: 3.6.9 truncated_normal_ab_cdf evaluates the CDF of the upper Truncated Normal distribution. The "parent" normal distribution has mean = mu standard deviation = sigma The parent distribution is truncated to the interval (-oo,b] Stored Computed X Mu S B CDF CDF 90.0 100.0 25.0 150.0 0.3526 0.3526 92.0 100.0 25.0 150.0 0.383202 0.383202 94.0 100.0 25.0 150.0 0.414597 0.414597 96.0 100.0 25.0 150.0 0.446601 0.446601 98.0 100.0 25.0 150.0 0.479016 0.479016 100.0 100.0 25.0 150.0 0.51164 0.51164 102.0 100.0 25.0 150.0 0.544263 0.544263 104.0 100.0 25.0 150.0 0.576679 0.576679 106.0 100.0 25.0 150.0 0.608682 0.608682 108.0 100.0 25.0 150.0 0.640078 0.640078 110.0 100.0 25.0 150.0 0.67068 0.67068 truncated_normal_b_cdf_test: Normal end of execution. truncated_normal_b_cdf_inv_test Python version: 3.6.9 truncated_normal_b_cdf_inv inverts the CDF of the Truncated Normal distribution. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval (-oo,150] X CDF CDF_inv 94.0785 0.415844 94.0785 102.264 0.548555 102.264 97.7161 0.474398 97.7161 107.544 0.632982 107.544 88.705 0.333289 88.705 121.035 0.818555 121.035 101.391 0.534342 101.391 110.523 0.678535 110.523 74.9937 0.162286 74.9937 88.044 0.323601 88.044 truncated_normal_b_cdf_inv_test Normal end of execution. truncated_normal_b_mean_test Python version: 3.6.9 truncated_normal_b_mean computes the mean of the Truncated Normal distribution. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval (-oo,150] PDF mean = 98.6188 Sample size = 1000 Sample mean = 98.725 Sample maximum = 149.6 Sample minimum = 21.4247 truncated_normal_b_mean_test: Normal end of execution. truncated_normal_b_moment_test Python version: 3.6.9 truncated_normal_b_moment evaluates moments of the upper Truncated Normal distribution. Test = 0, Mu = 0, Sigma = 1, B = 0 Order Moment 0 1 1 -0.797885 2 1 3 -1.59577 4 3 5 -6.38308 6 15 7 -38.2985 8 105 Test = 1, Mu = 0, Sigma = 1, B = 10 Order Moment 0 1 1 -7.6946e-23 2 1 3 -7.84849e-21 4 3 5 -8.00854e-19 6 15 7 -8.17511e-17 8 105 Test = 2, Mu = 0, Sigma = 1, B = -10 Order Moment 0 1 1 -10.0981 2 101.981 3 -1030.01 4 10404 5 -105101 6 1.06183e+06 7 -1.07287e+07 8 1.08414e+08 Test = 3, Mu = 0, Sigma = 2, B = 10 Order Moment 0 1 1 -2.97344e-06 2 3.99997 3 -0.000321132 4 47.9967 5 -0.0348725 6 959.636 7 -3.81038 8 26840.1 Test = 4, Mu = 0, Sigma = 2, B = -10 Order Moment 0 1 1 -10.373 2 107.73 3 -1120.28 4 11665.8 5 -121655 6 1.27062e+06 7 -1.32927e+07 8 1.39307e+08 Test = 5, Mu = 5, Sigma = 1, B = 10 Order Moment 0 1 1 5 2 26 3 140 4 777.997 5 4449.97 6 26139.7 7 157397 8 969947 truncated_normal_b_moment_test: Normal end of execution. truncated_normal_b_pdf_test Python version: 3.6.9 truncated_normal_b_pdf evaluates the PDF of the upper Truncated Normal distribution. The "parent" normal distribution has mean = mu standard deviation = sigma The parent distribution is truncated to the interval (-oo,b] Stored Computed X Mu S B PDF PDF 90.0 100.0 25.0 150.0 0.0150737 0.0150737 92.0 100.0 25.0 150.0 0.0155142 0.0155142 94.0 100.0 25.0 150.0 0.0158656 0.0158656 96.0 100.0 25.0 150.0 0.0161215 0.0161215 98.0 100.0 25.0 150.0 0.016277 0.016277 100.0 100.0 25.0 150.0 0.0163292 0.0163292 102.0 100.0 25.0 150.0 0.016277 0.016277 104.0 100.0 25.0 150.0 0.0161215 0.0161215 106.0 100.0 25.0 150.0 0.0158656 0.0158656 108.0 100.0 25.0 150.0 0.0155142 0.0155142 110.0 100.0 25.0 150.0 0.0150737 0.0150737 truncated_normal_ab_pdf_test: Normal end of execution. truncated_normal_b_sample_test Python version: 3.6.9 truncated_normal_b_sample samples the upper Truncated Normal distribution. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval (-oo,150] 0 78.7047 1 76.5973 2 114.607 3 122.789 4 78.4138 5 109.34 6 90.0985 7 118.794 8 77.7038 9 145.246 truncated_normal_b_sample_test Normal end of execution. truncated_normal_b_variance_test Python version: 3.6.9 truncated_normal_b_variance computes the variance of the Truncated Normal distribution. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval (-oo,150] PDF variance = 554.032 Sample size = 1000 Sample variance = 572.51 truncated_normal_b_variance_test: Normal end of execution. truncated_normal_test(): Normal end of execution. Tue Oct 19 17:25:41 2021