08-Oct-2025 22:54:09 truncated_normal_test(): MATLAB/Octave version 6.4.0 Test truncated_normal() r8_factorial2_test(): r8_factorial2() evaluates the double factorial function. N Exact Computed 0 1 1 1 1 1 2 2 2 3 3 3 4 8 8 5 15 15 6 48 48 7 105 105 8 384 384 9 945 945 10 3840 3840 11 10395 10395 12 46080 46080 13 135135 135135 14 645120 645120 15 2027025 2027025 r8_mop_test(): r8_mop() evaluates (-1.0)^I4 as an R8. I4 R8_MOP(I4) -8 1.0 -27 -1.0 42 1.0 52 1.0 37 -1.0 51 -1.0 -49 -1.0 -12 1.0 46 1.0 -67 -1.0 r8poly_print_test() r8poly_print() prints an R8POLY. The R8POLY: = +9.000000 * x^5 +0.780000 * x^4 +56.000000 * x^2 -3.400000 * x +12.000000 r8poly_value_horner_test(): r8poly_value_horner() evaluates a polynomial at one point, using Horner's method. The polynomial: = +1.000000 * x^4 -10.000000 * x^3 +35.000000 * x^2 -50.000000 * x +24.000000 I X P(X) 1 0.0000 24 2 0.3333 10.8642 3 0.6667 3.45679 4 1.0000 0 5 1.3333 -0.987654 6 1.6667 -0.691358 7 2.0000 0 8 2.3333 0.493827 9 2.6667 0.493827 10 3.0000 0 11 3.3333 -0.691358 12 3.6667 -0.987654 13 4.0000 0 14 4.3333 3.45679 15 4.6667 10.8642 16 5.0000 24 r8vec_print_test(): r8vec_print() prints an R8VEC. The R8VEC: 1: 123.456 2: 5e-06 3: -1e+06 4: 3.14159 normal_01_cdf_test(): normal_01_cdf() evaluates the Normal 01 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_inv_test(): normal_01_cdf_inv() inverts the Normal 01 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_mean_test(): normal_01_mean() computes the Normal 01 mean; PDF mean = 0.000000 Sample size = 1000 Sample mean = 0.005988 Sample maximum = 3.216870 Sample minimum = -3.539309 normal_01_moment_test(): 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_pdf_test(): normal_01_pdf() evaluates the Normal 01 PDF; X PDF -2 0.053991 -1.9 0.0656158 -1.8 0.0789502 -1.7 0.0940491 -1.6 0.110921 -1.5 0.129518 -1.4 0.149727 -1.3 0.171369 -1.2 0.194186 -1.1 0.217852 -1 0.241971 -0.9 0.266085 -0.8 0.289692 -0.7 0.312254 -0.6 0.333225 -0.5 0.352065 -0.4 0.36827 -0.3 0.381388 -0.2 0.391043 -0.1 0.396953 0 0.398942 0.1 0.396953 0.2 0.391043 0.3 0.381388 0.4 0.36827 0.5 0.352065 0.6 0.333225 0.7 0.312254 0.8 0.289692 0.9 0.266085 1 0.241971 1.1 0.217852 1.2 0.194186 1.3 0.171369 1.4 0.149727 1.5 0.129518 1.6 0.110921 1.7 0.0940491 1.8 0.0789502 1.9 0.0656158 2 0.053991 normal_01_sample_test(): normal_01_sample() returns samples from the normal distribution with mean 0 and standard deviation 1. 1 1.73409 2 -1.4886 3 0.180602 4 -0.49747 5 0.367582 6 -0.215369 7 -0.584397 8 0.112178 9 1.7023 10 -0.779008 normal_01_variance_test(): normal_01_variance() returns the Normal 01 variance. PDF variance = 1.000000 Sample size = 1000 Sample variance = 0.990534 normal_ms_cdf_test(): normal_ms_cdf() evaluates the CDF for the Normal MS distribution. PDF parameter MU = 100.000000 PDF parameter SIGMA = 15.000000 X CDF 70 0.0227501 71.5 0.0287166 73 0.0359303 74.5 0.0445655 76 0.0547993 77.5 0.0668072 79 0.0807567 80.5 0.0968005 82 0.11507 83.5 0.135666 85 0.158655 86.5 0.18406 88 0.211855 89.5 0.241964 91 0.274253 92.5 0.308538 94 0.344578 95.5 0.382089 97 0.42074 98.5 0.460172 100 0.5 101.5 0.539828 103 0.57926 104.5 0.617911 106 0.655422 107.5 0.691462 109 0.725747 110.5 0.758036 112 0.788145 113.5 0.81594 115 0.841345 116.5 0.864334 118 0.88493 119.5 0.9032 121 0.919243 122.5 0.933193 124 0.945201 125.5 0.955435 127 0.96407 128.5 0.971283 130 0.97725 normal_ms_cdf_inv_test(): normal_ms_cdf_inv() inverts the CDF for the Normal MS distribution. PDF parameter MU = 100.000000 PDF parameter SIGMA = 15.000000 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_mean_test(): normal_ms_mean() computes the mean of the Normal MS distribution. PDF parameter MU = 100.000000 PDF parameter SIGMA = 15.000000 PDF mean = 100.000000 Sample size = 1000 Sample mean = 99.729786 Sample maximum = 151.641798 Sample minimum = 58.398393 normal_ms_moment_test(): normal_ms_moment() evaluates the 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_central_test(): normal_ms_moment_central() evaluates the 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_pdf_test() normal_ms_pdf() evaluates the PDF for the Normal MS distribution. PDF parameter MU = 100.000000 PDF parameter SIGMA = 15.000000 X PDF 70 0.0035994 71.5 0.00437439 73 0.00526334 74.5 0.00626994 76 0.00739472 77.5 0.00863451 79 0.00998183 80.5 0.0114246 82 0.0129457 83.5 0.0145235 85 0.0161314 86.5 0.017739 88 0.0193128 89.5 0.0208169 91 0.022215 92.5 0.023471 94 0.0245513 95.5 0.0254259 97 0.0260695 98.5 0.0264635 100 0.0265962 101.5 0.0264635 103 0.0260695 104.5 0.0254259 106 0.0245513 107.5 0.023471 109 0.022215 110.5 0.0208169 112 0.0193128 113.5 0.017739 115 0.0161314 116.5 0.0145235 118 0.0129457 119.5 0.0114246 121 0.00998183 122.5 0.00863451 124 0.00739472 125.5 0.00626994 127 0.00526334 128.5 0.00437439 130 0.0035994 normal_ms_sample_test(): normal_ms_sample() samples the Normal MS distribution. PDF parameter MU = 100.000000 PDF parameter SIGMA = 15.000000 1 115.918 2 108.565 3 96.1721 4 103.272 5 113.329 6 100.149 7 107.44 8 112.149 9 113.24 10 102.122 normal_ms_variance_test(): normal_ms_variance() returns the variance of the Normal MS distribution. PDF parameter MU = 100.000000 PDF parameter SIGMA = 15.000000 PDF variance = 225.000000 Sample size = 1000 Sample variance = 223.512724 truncated_normal_a_cdf_test(): truncated_normal_a_cdf() evaluates the lower Truncated Normal CDF. 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_inv_test(): truncated_normal_a_cdf_inv() inverts the CDF for the lower Truncated Normal Distribution. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,+00) X CDF CDF_INV 130.682 0.887581 130.682 103.598 0.546905 103.598 105.495 0.577375 105.495 101.745 0.51683 101.745 71.7363 0.108849 71.7363 100.973 0.504238 100.973 117.033 0.746395 117.033 78.5702 0.176945 78.5702 77.5546 0.16566 77.5546 95.9091 0.421856 95.9091 truncated_normal_a_mean_test(): truncated_normal_a_mean() computes the mean 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) PDF mean = 101.381 Sample size = 1000 Sample mean = 101.345 Sample maximum = 173.985 Sample minimum = 51.4628 truncated_normal_a_moment_test(): truncated_normal_a_moment() evaluates the moments of the Lower Truncated Normal PDF: Test = 1, 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 = 2, 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 = 3, 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 = 4, 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 = 5, 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 = 6, 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_pdf_test(): truncated_normal_a_pdf() evaluates the lower Truncated Normal PDF. 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_sample_test(): 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) 1 112.994 2 101.364 3 111.755 4 122.365 5 107.798 6 88.5976 7 157.59 8 107.198 9 107.759 10 94.7914 truncated_normal_a_variance_test(): truncated_normal_a_variance() computes the variance. 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) PDF variance = 554.032 Sample size = 1000 Sample variance = 547.397 truncated_normal_ab_cdf_test(): truncated_normal_ab_cdf() evaluates the Truncated Normal CDF. 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_inv_test(): truncated_normal_ab_cdf_inv() inverts the CDF for 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 51.8833 0.00459435 51.8833 113.567 0.716157 113.567 81.287 0.214063 81.287 95.6391 0.427461 95.6391 72.2826 0.116323 72.2826 142.34 0.976509 142.34 118.355 0.781386 118.355 144.51 0.984541 144.51 98.3954 0.473192 98.3954 74.4222 0.136592 74.4222 truncated_normal_ab_mean_test(): 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 = 100.415 Sample maximum = 148.796 Sample minimum = 50.0131 truncated_normal_ab_moment_test(): truncated_normal_ab_moment() evaluates the moments of the Truncated Normal PDF: Test = 1, 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 = 2, 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 = 3, 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 = 4, 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 = 5, 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 = 6, 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 = 7, 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 = 8, 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 = 9, 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_pdf_test(): truncated_normal_ab_pdf() evaluates the Truncated Normal PDF. 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_sample_test() 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] 1 119.83 2 97.0758 3 137.454 4 57.7436 5 135.318 6 110.27 7 79.495 8 97.2527 9 105.643 10 134.906 truncated_normal_ab_variance_test(): 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 = 473.895 truncated_normal_b_cdf_test(): truncated_normal_b_cdf() evaluates the upper Truncated Normal CDF. 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_inv_test(): truncated_normal_b_cdf_inv() inverts the CDF for 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] X CDF CDF_INV 109.053 0.656302 109.053 112.048 0.701013 112.048 89.9934 0.352501 89.9934 84.2103 0.26997 84.2103 94.6375 0.424742 94.6375 86.6908 0.304155 86.6908 115.452 0.748768 115.452 101.466 0.53557 101.466 96.6351 0.45686 96.6351 131.87 0.919737 131.87 truncated_normal_b_mean_test(): truncated_normal_b_mean() computes the mean of 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] PDF mean = 98.6188 Sample size = 1000 Sample mean = 98.9281 Sample maximum = 149.72 Sample minimum = 23.9491 truncated_normal_b_moment_test(): truncated_normal_b_moment() evaluates the moments of the Upper Truncated Normal PDF: Test = 1, Mu = 0, Sigma = 1, B = 0 Order Moment 0 1 1 -0.7978845608 2 1 3 -1.595769122 4 3 5 -6.383076486 6 15 7 -38.29845892 8 105 Test = 2, Mu = 0, Sigma = 1, B = 10 Order Moment 0 1 1 -7.694598627e-23 2 1 3 -7.848490599e-21 4 3 5 -8.008538251e-19 6 15 7 -8.175110922e-17 8 105 Test = 3, Mu = 0, Sigma = 1, B = -10 Order Moment 0 1 1 -10.09809323 2 101.9809323 3 -1030.00551 4 10404.03603 5 -105100.9544 6 1061829.504 7 -10728698.96 8 108413738.9 Test = 4, Mu = 0, Sigma = 2, B = 10 Order Moment 0 1 1 -2.973439882e-06 2 3.999970266 3 -0.0003211315072 4 47.99666975 5 -0.03487250293 6 959.636051 7 -3.810379952 8 26840.07503 Test = 5, Mu = 0, Sigma = 2, B = -10 Order Moment 0 1 1 -10.37300793 2 107.7300793 3 -1120.284857 4 11665.76889 5 -121654.6371 6 1270616.171 7 -13292719.22 8 139307332.1 Test = 6, Mu = 5, Sigma = 1, B = 10 Order Moment 0 1 1 4.999998513 2 25.9999777 3 139.9997369 4 777.9971306 5 4449.969733 6 26139.68565 7 157396.7599 8 969946.7319 truncated_normal_b_pdf_test(): truncated_normal_b_pdf() evaluates the Upper Truncated Normal PDF. 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_b_sample_test(): 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] 1 71.503 2 136.456 3 106.049 4 83.4597 5 125.007 6 85.7977 7 95.0228 8 97.2048 9 131.318 10 120.699 truncated_normal_b_variance_test(): truncated_normal_b_variance() computes the variance. of 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] PDF variance = 554.032 Sample size = 1000 Sample variance = 572.515 truncated_normal_test(): Normal end of execution. 08-Oct-2025 22:54:10