02 March 2022 10:14:13 AM TRUNCATED_NORMAL_TEST C version Test the TRUNCATED_NORMAL library. I4_UNIFORM_TEST I4_UNIFORM_AB computes pseudorandom values in an interval [A,B]. The lower endpoint A = -100 The upper endpoint B = 200 The initial seed is 123456789 1 -35 2 187 3 149 4 69 5 25 6 -81 7 -23 8 -67 9 -87 10 90 11 -82 12 35 13 20 14 127 15 139 16 -100 17 170 18 5 19 -72 20 -96 R8_CHOOSE_TEST R8_CHOOSE evaluates C(N,K). N K CNK 0 0 1 1 0 1 1 1 1 2 0 1 2 1 2 2 2 1 3 0 1 3 1 3 3 2 3 3 3 1 4 0 1 4 1 4 4 2 6 4 3 4 4 4 1 5 0 1 5 1 5 5 2 10 5 3 10 5 4 5 5 5 1 R8_FACTORIAL2_TEST R8_FACTORIAL2 evaluates the double factorial. 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) -57 -1.0 92 1.0 66 1.0 12 1.0 -17 -1.0 -87 -1.0 -49 -1.0 -78 1.0 -92 1.0 27 -1.0 R8_UNIFORM_01_TEST R8_UNIFORM_01 samples a uniform random distribution in [0,1]. distributed random numbers. Using initial random number seed = 123456789 First few values: 0 0.218418 1 0.956318 2 0.829509 3 0.561695 4 0.415307 5 0.066119 6 0.257578 7 0.109957 8 0.043829 9 0.633966 Number of samples was 1000 Minimum value was 0.001838 Maximum value was 0.997908 Average value was 0.503040 Variance was 0.082332 R8POLY_PRINT_TEST R8POLY_PRINT prints an R8POLY. The R8POLY: p(x) = 9 * x^5 +0.78 * x^4 +56 * x^2 -3.4 * x +2 R8POLY_VALUE_HORNER_TEST R8POLY_VALUE_HORNER evaluates a polynomial at one point, using Horner's 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 R8VEC_LINSPACE_NEW_TEST For a R8VEC: R8VEC_LINSPACE_NEW: evenly spaced points between A and B; r8vec_linspace ( 5, 10, 20 ) 0: 10 1: 12.5 2: 15 3: 17.5 4: 20 R8VEC_PRINT_TEST R8VEC_PRINT prints an R8VEC. The R8VEC: 0: 123.456 1: 5e-06 2: -1e+06 3: 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 Sample size = 1000 Sample mean = -0.0169444 Sample maximum = 3.32858 Sample minimum = -3.02975 NORMAL_01_MOMENT_TEST NORMAL_01_MOMENT evaluates Normal 01 moments; 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 0.05399096651318806 -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_SAMPLE_TEST NORMAL_01_SAMPLE returns samples from the normal distribution with mean 0 and standard deviation 1. 1 1.67904 2 -0.472769 3 -0.56606 4 -0.231124 5 1.21293 6 0.535037 7 1.26938 8 1.04954 9 -1.66609 10 -1.86523 NORMAL_01_VARIANCE_TEST NORMAL_01_VARIANCE computes the Normal 01 variance; PDF variance = 1 Sample size = 1000 Sample variance = 0.999622 NORMAL_MS_CDF_TEST NORMAL_MS_CDF evaluates the Normal MS CDF; Parameter MU = 100 Parameteter 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_INV_TEST NORMAL_MS_CDF_INV inverts the Normal MS CDF; Parameter MU = 100 Parameteter 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_MEAN_TEST NORMAL_MS_MEAN computes the Normal MS mean. Parameter MU = 100 Parameteter SIGMA = 15 PDF mean = 100 Sample size = 1000 Sample mean = 99.7458 Sample maximum = 149.929 Sample minimum = 54.5537 NORMAL_MS_MOMENT_TEST NORMAL_MS_MOMENT evaluates Normal MS moments; Parameter MU = 100 Parameteter SIGMA = 15 Order Moment 0 1 1 100 2 10225 3 1067500 4 113651875 5 12325937500 6 1360452109375 7 152685226562500 8 1.741123472851562e+16 9 2.015956880664062e+18 10 2.368534383916504e+20 NORMAL_MS_MOMENT_CENTRAL_TEST NORMAL_MS_MOMENT_CENTRAL evaluates Normal MS central moments; Parameter MU = 100 Parameteter SIGMA = 15 Order Moment 0 1 1 0 2 225 3 0 4 151875 5 0 6 170859375 7 0 8 269103515625 9 0 10 544934619140625 NORMAL_MS_PDF_TEST NORMAL_MS_PDF evaluates the Normal MS PDF; Parameter MU = 100 Parameteter SIGMA = 15 X PDF 70 0.002726657788170133 71.5 0.002752427569304898 73 0.002774478399303293 74.5 0.002793083095968333 76 0.002808500132044491 77.5 0.002820973374346913 79 0.002830732106402435 80.5 0.002837991264014851 82 0.002842951827175776 83.5 0.002845801323286164 85 0.002846714406107569 86.5 0.002845853482562336 88 0.002843369365741316 89.5 0.002839401937508679 91 0.002834080808130182 92.5 0.002827525963574023 94 0.002819848393692489 95.5 0.002811150696512828 97 0.002801527655449843 98.5 0.002791066787485373 100 0.002779848861309965 101.5 0.002767948385146287 103 0.002755434064517858 104.5 0.00274236923062773 106 0.002728812240299862 107.5 0.002714816848635318 109 0.002700432555665593 110.5 0.002685704928361967 112 0.002670675899395224 113.5 0.002655384044044492 115 0.002639864836635049 116.5 0.002624150887849117 118 0.002608272164205834 119.5 0.002592256190950526 121 0.002576128239532179 122.5 0.002559911500783945 124 0.002543627244856253 125.5 0.00252729496888717 127 0.002510932533330819 128.5 0.002494556287802812 130 0.002478181187242165 NORMAL_MS_SAMPLE_TEST NORMAL_MS_SAMPLE returns samples from the Normal MS PDF. Parameter MU = 100 Parameteter SIGMA = 15 1 125.186 2 92.9085 3 91.5091 4 96.5331 5 118.194 6 108.026 7 119.041 8 115.743 9 75.0087 10 72.0216 NORMAL_MS_VARIANCE_TEST NORMAL_MS_VARIANCE computes the Normal MS variance; Parameter MU = 100 Parameteter SIGMA = 15 PDF variance = 225 Sample size = 1000 Sample variance = 224.915 TRUNCATED_NORMAL_A_CDF_TEST: TRUNCATED_NORMAL_A_CDF evaluates the lower Truncated Normal Cumulative Density Function. MU S A X CDF1 CDF2 100.0 25.0 50.0 90.0 0.3293202045481688 0.3293202045495739 100.0 25.0 50.0 92.0 0.3599223134505957 0.3599223134504884 100.0 25.0 50.0 94.0 0.3913175216041539 0.3913175216012952 100.0 25.0 50.0 96.0 0.4233210140873113 0.4233210140828035 100.0 25.0 50.0 98.0 0.4557365629792204 0.4557365629756831 100.0 25.0 50.0 100.0 0.4883601253415709 0.4883601253411278 100.0 25.0 50.0 102.0 0.5209836877039214 0.5209836877065723 100.0 25.0 50.0 104.0 0.5533992365958303 0.5533992365994519 100.0 25.0 50.0 106.0 0.5854027290789878 0.5854027290809604 100.0 25.0 50.0 108.0 0.6167979372325459 0.6167979372317671 100.0 25.0 50.0 110.0 0.6474000461349729 0.6474000461326815 TRUNCATED_NORMAL_A_CDF_INV_TEST 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 82.0355 0.218418 82.0355 143.008 0.956318 143.008 124.191 0.829509 124.191 104.515 0.561695 104.515 95.5021 0.415307 95.5021 66.0709 0.0661187 66.0709 85.0161 0.257578 85.0161 71.8645 0.109957 71.8645 62.2618 0.043829 62.2618 109.115 0.633966 109.115 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 = 101.504 Sample maximum = 171.782 Sample minimum = 50.8055 TRUNCATED_NORMAL_A_MOMENT_TEST TRUNCATED_NORMAL_A_MOMENT evaluates the moments of the Lower Truncated Normal PDF: 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_PDF_TEST: TRUNCATED_NORMAL_A_PDF evaluates the lower Truncated Normal Probability Density Function. MU S A X PDF1 PDF2 100.0 25.0 50.0 90.0 0.01507373507401876 0.01507373507403181 100.0 25.0 50.0 92.0 0.01551417047139894 0.01551417047141238 100.0 25.0 50.0 94.0 0.01586560931024694 0.01586560931026069 100.0 25.0 50.0 96.0 0.01612150073158793 0.01612150073160189 100.0 25.0 50.0 98.0 0.01627701240029317 0.01627701240030727 100.0 25.0 50.0 100.0 0.01632918226724295 0.0163291822672571 100.0 25.0 50.0 102.0 0.01627701240029317 0.01627701240030727 100.0 25.0 50.0 104.0 0.01612150073158793 0.01612150073160189 100.0 25.0 50.0 106.0 0.01586560931024694 0.01586560931026069 100.0 25.0 50.0 108.0 0.01551417047139894 0.01551417047141238 100.0 25.0 50.0 110.0 0.01507373507401876 0.01507373507403181 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) 0 82.0355 1 143.008 2 124.191 3 104.515 4 95.5021 5 66.0709 6 85.0161 7 71.8645 8 62.2618 9 109.115 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 = 555.665 TRUNCATED_NORMAL_AB_CDF_TEST: TRUNCATED_NORMAL_AB_CDF evaluates the Truncated Normal Cumulative Density Function. MU S A B X CDF1 CDF2 100.0 25.0 50.0 150.0 90.0 0.3371694242213513 0.3371694242230959 100.0 25.0 50.0 150.0 92.0 0.3685009225506048 0.3685009225508293 100.0 25.0 50.0 150.0 94.0 0.4006444233448185 0.4006444233422553 100.0 25.0 50.0 150.0 96.0 0.433410706690304 0.433410706686082 100.0 25.0 50.0 150.0 98.0 0.4665988676496338 0.4665988676464356 100.0 25.0 50.0 150.0 100.0 0.5 0.5000000000000001 100.0 25.0 50.0 150.0 102.0 0.5334011323503662 0.5334011323535645 100.0 25.0 50.0 150.0 104.0 0.566589293309696 0.5665892933139179 100.0 25.0 50.0 150.0 106.0 0.5993555766551815 0.5993555766577449 100.0 25.0 50.0 150.0 108.0 0.6314990774493952 0.6314990774491708 100.0 25.0 50.0 150.0 110.0 0.6628305757786487 0.6628305757769042 TRUNCATED_NORMAL_AB_CDF_INV_TEST 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 81.63 0.218418 81.63 137.962 0.956318 137.962 122.367 0.829509 122.367 103.704 0.561695 103.704 94.899 0.415307 94.899 65.8326 0.0661187 65.8326 84.5743 0.257578 84.5743 71.5672 0.109957 71.5672 62.0654 0.043829 62.0654 108.155 0.633966 108.155 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 = 100.123 Sample maximum = 149.108 Sample minimum = 50.7873 TRUNCATED_NORMAL_AB_MOMENT_TEST TRUNCATED_NORMAL_AB_MOMENT evaluates the moments of the Truncated Normal PDF: 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_PDF_TEST: TRUNCATED_NORMAL_AB_PDF evaluates the PDF of the Truncated Normal Distribution. MU S A B X PDF1 PDF2 100.0 25.0 50.0 150.0 90.0 0.01543301171801836 0.01543301171804573 100.0 25.0 50.0 150.0 92.0 0.01588394472270638 0.01588394472273455 100.0 25.0 50.0 150.0 94.0 0.01624375997031919 0.016243759970348 100.0 25.0 50.0 150.0 96.0 0.01650575046469259 0.01650575046472186 100.0 25.0 50.0 150.0 98.0 0.01666496869385951 0.01666496869388907 100.0 25.0 50.0 150.0 100.0 0.01671838200940538 0.01671838200943504 100.0 25.0 50.0 150.0 102.0 0.01666496869385951 0.01666496869388907 100.0 25.0 50.0 150.0 104.0 0.01650575046469259 0.01650575046472186 100.0 25.0 50.0 150.0 106.0 0.01624375997031919 0.016243759970348 100.0 25.0 50.0 150.0 108.0 0.01588394472270638 0.01588394472273455 100.0 25.0 50.0 150.0 110.0 0.01543301171801836 0.01543301171804573 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] 0 81.63 1 137.962 2 122.367 3 103.704 4 94.899 5 65.8326 6 84.5743 7 71.5672 8 62.0654 9 108.155 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 = 486.064 TRUNCATED_NORMAL_B_CDF_TEST: TRUNCATED_NORMAL_B_CDF_TEST evaluates the CDF of the upper Truncated Normal Distribution. MU S B X CDF1 CDF2 100.0 25.0 150.0 90.0 0.3525999538650271 0.3525999538673185 100.0 25.0 150.0 92.0 0.383202062767454 0.3832020627682329 100.0 25.0 150.0 94.0 0.4145972709210122 0.4145972709190397 100.0 25.0 150.0 96.0 0.4466007634041696 0.446600763400548 100.0 25.0 150.0 98.0 0.4790163122960786 0.4790163122934276 100.0 25.0 150.0 100.0 0.5116398746584291 0.5116398746588723 100.0 25.0 150.0 102.0 0.5442634370207796 0.5442634370243169 100.0 25.0 150.0 104.0 0.5766789859126887 0.5766789859171965 100.0 25.0 150.0 106.0 0.6086824783958461 0.6086824783987049 100.0 25.0 150.0 108.0 0.6400776865494043 0.6400776865495117 100.0 25.0 150.0 110.0 0.6706797954518312 0.6706797954504261 TRUNCATED_NORMAL_B_CDF_INV_TEST TRUNCATED_NORMAL_B_CDF_INV inverts the CDF 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] X CDF CDF_INV 80.1372 0.218418 80.1372 137.766 0.956318 137.766 122.006 0.829509 122.006 103.073 0.561695 103.073 94.0447 0.415307 94.0447 62.0713 0.0661187 62.0713 83.2727 0.257578 83.2727 68.9956 0.109957 68.9956 57.0318 0.043829 57.0318 107.607 0.633966 107.607 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 = 98.7101 Sample maximum = 149.087 Sample minimum = 27.2041 TRUNCATED_NORMAL_B_MOMENT_TEST TRUNCATED_NORMAL_B_MOMENT evaluates the moments of the Upper Truncated Normal PDF: 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_PDF_TEST: TRUNCATED_NORMAL_B_PDF evaluates the PDF of the upper Truncated Normal Distribution. MU S B X PDF1 PDF2 100.0 25.0 150.0 90.0 0.01507373507401876 0.01507373507403181 100.0 25.0 150.0 92.0 0.01551417047139894 0.01551417047141238 100.0 25.0 150.0 94.0 0.01586560931024694 0.01586560931026069 100.0 25.0 150.0 96.0 0.01612150073158793 0.01612150073160189 100.0 25.0 150.0 98.0 0.01627701240029317 0.01627701240030727 100.0 25.0 150.0 100.0 0.01632918226724295 0.0163291822672571 100.0 25.0 150.0 102.0 0.01627701240029317 0.01627701240030727 100.0 25.0 150.0 104.0 0.01612150073158793 0.01612150073160189 100.0 25.0 150.0 106.0 0.01586560931024694 0.01586560931026069 100.0 25.0 150.0 108.0 0.01551417047139894 0.01551417047141238 100.0 25.0 150.0 110.0 0.01507373507401876 0.01507373507403181 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] 0 80.1372 1 137.766 2 122.006 3 103.073 4 94.0447 5 62.0713 6 83.2727 7 68.9956 8 57.0318 9 107.607 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 = 560.281 TRUNCATED_NORMAL_TEST Normal end of execution. 02 March 2022 10:14:13 AM