17 September 2021 11:54:35.907 PM TRUNCATED_NORMAL_TEST FORTRAN90 version: Test the TRUNCATED_NORMAL library. I4_UNIFORM_AB_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 51 2 99 3 143 4 -42 5 -50 6 -29 7 82 8 64 9 196 10 173 11 31 12 59 13 105 14 121 15 -6 16 141 17 112 18 79 19 -71 20 15 R8_CHOOSE_TEST R8_CHOOSE evaluates C(N,K). N K CNK 0 0 1.00000 1 0 1.00000 1 1 1.00000 2 0 1.00000 2 1 2.00000 2 2 1.00000 3 0 1.00000 3 1 3.00000 3 2 3.00000 3 3 1.00000 4 0 1.00000 4 1 4.00000 4 2 6.00000 4 3 4.00000 4 4 1.00000 5 0 1.00000 5 1 5.00000 5 2 10.0000 5 3 10.0000 5 4 5.00000 5 5 1.00000 R8_FACTORIAL2_TEST R8_FACTORIAL2 computes the double factorial function. N Exact Computed 0 1.000000000000000 1.000000000000000 1 1.000000000000000 1.000000000000000 2 2.000000000000000 2.000000000000000 3 3.000000000000000 3.000000000000000 4 8.000000000000000 8.000000000000000 5 15.00000000000000 15.00000000000000 6 48.00000000000000 48.00000000000000 7 105.0000000000000 105.0000000000000 8 384.0000000000000 384.0000000000000 9 945.0000000000000 945.0000000000000 10 3840.000000000000 3840.000000000000 11 10395.00000000000 10395.00000000000 12 46080.00000000000 46080.00000000000 13 135135.0000000000 135135.0000000000 14 645120.0000000000 645120.0000000000 15 2027025.000000000 2027025.000000000 R8_MOP_TEST R8_MOP evaluates (-1.0)^I4 as an R8. I4 R8_MOP(I4) 55 -1.0 -38 1.0 -67 -1.0 38 1.0 -10 1.0 -68 1.0 61 -1.0 -54 1.0 -68 1.0 -79 -1.0 R8POLY_PRINT_TEST R8POLY_PRINT prints an R8POLY. The R8POLY: p(x) = 9.00000 * x ^ 5 + 0.780000 * x ^ 4 + 56.0000 * x ^ 2 - 3.40000 * x + 12.0000 R8POLY_VALUE_HORNER_TEST R8POLY_VALUE_HORNER evaluates a polynomial at one point, using Horner's method. The polynomial coefficients: p(x) = 1.00000 * x ^ 4 - 10.0000 * x ^ 3 + 35.0000 * x ^ 2 - 50.0000 * x + 24.0000 I X P(X) 1 0.0000 24.0000 2 0.3333 10.8642 3 0.6667 3.45679 4 1.0000 0.00000 5 1.3333 -0.987654 6 1.6667 -0.691358 7 2.0000 0.00000 8 2.3333 0.493827 9 2.6667 0.493827 10 3.0000 0.00000 11 3.3333 -0.691358 12 3.6667 -0.987654 13 4.0000 0.00000 14 4.3333 3.45679 15 4.6667 10.8642 16 5.0000 24.0000 R8VEC_LINSPACE_TEST For a R8VEC: R8VEC_LINSPACE: evenly spaced points between A and B; r8vec_linspace ( 5, 10, 20 ) 1: 10.000000 2: 12.500000 3: 15.000000 4: 17.500000 5: 20.000000 R8VEC_PRINT_TEST R8VEC_PRINT prints an R8VEC. The R8VEC: 1: 123.45600 2: 0.50000000E-05 3: -1000000.0 4: 3.1415927 NORMAL_01_CDF_TEST NORMAL_01_CDF inverts the CDF; X CDF CDF (exact) (computed) 0.00000 0.5000000000000000 0.5000000000000000 0.100000 0.5398278372770290 0.5398278372805048 0.200000 0.5792597094391030 0.5792597094424672 0.300000 0.6179114221889526 0.6179114221891665 0.400000 0.6554217416103242 0.6554217416083834 0.500000 0.6914624612740131 0.6914624612735877 0.600000 0.7257468822499270 0.7257468822526401 0.700000 0.7580363477769270 0.7580363477802913 0.800000 0.7881446014166033 0.7881446014178579 0.900000 0.8159398746532405 0.8159398746539517 1.00000 0.8413447460685429 0.8413447460717163 1.50000 0.9331927987311419 0.9331927987330156 2.00000 0.9772498680518208 0.9772498680509744 2.50000 0.9937903346742240 0.9937903346744605 3.00000 0.9986501019683699 0.9986501019683744 3.50000 0.9997673709209645 0.9997673709209559 4.00000 0.9999683287581669 0.9999683287581664 NORMAL_01_CDF_INV_TEST NORMAL_01_CDF_INV evaluates the CDF; CDF X X (exact) (computed) 0.500000 0.000000000000000 0.000000000000000 0.539828 0.1000000000000000 0.9999999999999999E-01 0.579260 0.2000000000000000 0.1999999999999999 0.617911 0.3000000000000000 0.2999999999999998 0.655422 0.4000000000000000 0.4000000000000000 0.691462 0.5000000000000000 0.4999999999999998 0.725747 0.6000000000000000 0.6000000000000016 0.758036 0.7000000000000000 0.6999999999999998 0.788145 0.8000000000000000 0.7999999999999998 0.815940 0.9000000000000000 0.9000000000000000 0.841345 1.000000000000000 1.000000000000000 0.933193 1.500000000000000 1.500000000000000 0.977250 2.000000000000000 2.000000000000000 0.993790 2.500000000000000 2.500000000000004 0.998650 3.000000000000000 2.999999999999997 0.999767 3.500000000000000 3.499999999999983 0.999968 4.000000000000000 4.000000000000000 NORMAL_01_MEAN_TEST NORMAL_01_MEAN computes the mean for tne Normal 01 PDF PDF mean = 0.00000 Sample size = 1000 Sample mean = 0.368795E-01 Sample maximum = 3.31699 Sample minimum = -3.40927 NORMAL_01_MOMENT_TEST NORMAL_01_MOMENT returns the moments for tne Normal 01 PDF Order Moment 0 1.00000 1 0.00000 2 1.00000 3 0.00000 4 3.00000 5 0.00000 6 15.0000 7 0.00000 8 105.000 9 0.00000 10 945.000 NORMAL_01_PDF_TEST NORMAL_01_PDF evaluates the Normal 01 PDF. X PDF -2.00000 0.539910E-01 -1.90000 0.656158E-01 -1.80000 0.789502E-01 -1.70000 0.940491E-01 -1.60000 0.110921 -1.50000 0.129518 -1.40000 0.149727 -1.30000 0.171369 -1.20000 0.194186 -1.10000 0.217852 -1.00000 0.241971 -0.900000 0.266085 -0.800000 0.289692 -0.700000 0.312254 -0.600000 0.333225 -0.500000 0.352065 -0.400000 0.368270 -0.300000 0.381388 -0.200000 0.391043 -0.100000 0.396953 0.00000 0.398942 0.100000 0.396953 0.200000 0.391043 0.300000 0.381388 0.400000 0.368270 0.500000 0.352065 0.600000 0.333225 0.700000 0.312254 0.800000 0.289692 0.900000 0.266085 1.00000 0.241971 1.10000 0.217852 1.20000 0.194186 1.30000 0.171369 1.40000 0.149727 1.50000 0.129518 1.60000 0.110921 1.70000 0.940491E-01 1.80000 0.789502E-01 1.90000 0.656158E-01 2.00000 0.539910E-01 NORMAL_01_SAMPLE_TEST NORMAL_01_SAMPLE returns samples from the normal distribution with mean 0 and standard deviation 1. 1 -1.85730 2 0.494497 3 -1.82035 4 0.483313 5 -0.241820 6 1.41663 7 -0.347924 8 -2.16847 9 -0.369473 10 0.856631 NORMAL_01_VARIANCE_TEST NORMAL_01_VARIANCE returns the Normal 01 variance. PDF variance = 1.00000 Sample size = 1000 Sample variance = 0.991662 NORMAL_MS_CDF_TEST NORMAL_MS_CDF evaluates the Normal MS CDF; PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 X CDF 70.0000 0.227501E-01 71.5000 0.287166E-01 73.0000 0.359303E-01 74.5000 0.445655E-01 76.0000 0.547993E-01 77.5000 0.668072E-01 79.0000 0.807567E-01 80.5000 0.968005E-01 82.0000 0.115070 83.5000 0.135666 85.0000 0.158655 86.5000 0.184060 88.0000 0.211855 89.5000 0.241964 91.0000 0.274253 92.5000 0.308538 94.0000 0.344578 95.5000 0.382089 97.0000 0.420740 98.5000 0.460172 100.000 0.500000 101.500 0.539828 103.000 0.579260 104.500 0.617911 106.000 0.655422 107.500 0.691462 109.000 0.725747 110.500 0.758036 112.000 0.788145 113.500 0.815940 115.000 0.841345 116.500 0.864334 118.000 0.884930 119.500 0.903200 121.000 0.919243 122.500 0.933193 124.000 0.945201 125.500 0.955435 127.000 0.964070 128.500 0.971283 130.000 0.977250 NORMAL_MS_CDF_INV_TEST NORMAL_MS_CDF_INV inverts the Normal MS CDF; PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 X CDF CDF_INV 70.0000 0.227501E-01 70.0000 71.5000 0.287166E-01 71.5000 73.0000 0.359303E-01 73.0000 74.5000 0.445655E-01 74.5000 76.0000 0.547993E-01 76.0000 77.5000 0.668072E-01 77.5000 79.0000 0.807567E-01 79.0000 80.5000 0.968005E-01 80.5000 82.0000 0.115070 82.0000 83.5000 0.135666 83.5000 85.0000 0.158655 85.0000 86.5000 0.184060 86.5000 88.0000 0.211855 88.0000 89.5000 0.241964 89.5000 91.0000 0.274253 91.0000 92.5000 0.308538 92.5000 94.0000 0.344578 94.0000 95.5000 0.382089 95.5000 97.0000 0.420740 97.0000 98.5000 0.460172 98.5000 100.000 0.500000 100.000 101.500 0.539828 101.500 103.000 0.579260 103.000 104.500 0.617911 104.500 106.000 0.655422 106.000 107.500 0.691462 107.500 109.000 0.725747 109.000 110.500 0.758036 110.500 112.000 0.788145 112.000 113.500 0.815940 113.500 115.000 0.841345 115.000 116.500 0.864334 116.500 118.000 0.884930 118.000 119.500 0.903200 119.500 121.000 0.919243 121.000 122.500 0.933193 122.500 124.000 0.945201 124.000 125.500 0.955435 125.500 127.000 0.964070 127.000 128.500 0.971283 128.500 130.000 0.977250 130.000 NORMAL_MS_MEAN_TEST NORMAL_MS_MEAN computes the mean for tne Normal MS PDF PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 PDF mean = 100.000 Sample size = 1000 Sample mean = 100.108 Sample maximum = 155.501 Sample minimum = 52.5937 NORMAL_MS_MOMENT_TEST NORMAL_MS_MOMENT returns the moments for tne Normal MS PDF PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 Order Moment 0 1.00000 1 100.000 2 10225.0 3 0.106750E+07 4 0.113652E+09 5 0.123259E+11 6 0.136045E+13 7 0.152685E+15 8 0.174112E+17 9 0.201596E+19 10 0.236853E+21 NORMAL_MS_MOMENT_CENTRAL_TEST NORMAL_MS_MOMENT_CENTRAL returns central moments for tne Normal MS PDF PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 Order Moment 0 1.00000 1 0.00000 2 225.000 3 0.00000 4 151875. 5 0.00000 6 0.170859E+09 7 0.00000 8 0.269104E+12 9 0.00000 10 0.544935E+15 NORMAL_MS_MOMENT_CENTRAL_VALUES_TEST NORMAL_MS_MOMENT_CENTRAL_VALUES returns values of selected central moments for tne Normal MS PDF PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 Order Moment 0 1.00000 1 0.00000 2 225.000 3 0.00000 4 151875. 5 0.00000 6 0.170859E+09 7 0.00000 8 0.269104E+12 9 0.00000 10 0.544935E+15 NORMAL_MS_PDF_TEST NORMAL_MS_PDF evaluates the Normal MS PDF; PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 X PDF 70.0000 0.359940E-02 71.5000 0.437439E-02 73.0000 0.526334E-02 74.5000 0.626994E-02 76.0000 0.739472E-02 77.5000 0.863451E-02 79.0000 0.998183E-02 80.5000 0.114246E-01 82.0000 0.129457E-01 83.5000 0.145235E-01 85.0000 0.161314E-01 86.5000 0.177390E-01 88.0000 0.193128E-01 89.5000 0.208169E-01 91.0000 0.222150E-01 92.5000 0.234710E-01 94.0000 0.245513E-01 95.5000 0.254259E-01 97.0000 0.260695E-01 98.5000 0.264635E-01 100.000 0.265962E-01 101.500 0.264635E-01 103.000 0.260695E-01 104.500 0.254259E-01 106.000 0.245513E-01 107.500 0.234710E-01 109.000 0.222150E-01 110.500 0.208169E-01 112.000 0.193128E-01 113.500 0.177390E-01 115.000 0.161314E-01 116.500 0.145235E-01 118.000 0.129457E-01 119.500 0.114246E-01 121.000 0.998183E-02 122.500 0.863451E-02 124.000 0.739472E-02 125.500 0.626994E-02 127.000 0.526334E-02 128.500 0.437439E-02 130.000 0.359940E-02 NORMAL_MS_SAMPLE_TEST NORMAL_MS_SAMPLE returns samples the Normal MS PDF. PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 SEED = 123456789 1 82.6752 2 83.2957 3 112.866 4 99.9620 5 110.721 6 78.8164 7 106.978 8 109.891 9 105.831 10 107.093 NORMAL_MS_VARIANCE_TEST NORMAL_MS_VARIANCE returns the Normal MS variance. PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 PDF variance = 225.000 Sample size = 1000 Sample variance = 219.606 TRUNCATED_NORMAL_A_CDF_TEST: TRUNCATED_NORMAL_A_CDF evaluates the CDF of the lower Truncated Normal Distribution. 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 lower Truncated Normal CDF; Lower limit A = 50.0000 PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 SEED = 123456789 X CDF CDF_INV 91.1651 0.277933 91.1651 112.959 0.806187 112.959 108.551 0.715693 108.551 98.1444 0.450774 98.1444 122.907 0.936640 122.907 69.9805 0.226800E-01 69.9805 73.1071 0.364978E-01 73.1071 115.809 0.854038 115.809 64.2697 0.860899E-02 64.2697 103.249 0.585746 103.249 TRUNCATED_NORMAL_A_MEAN_TEST TRUNCATED_NORMAL_A_MEAN computes the mean for tne Lower Truncated Normal PDF Lower limit A = 50.0000 PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 PDF mean = 100.023 Sample size = 1000 Sample mean = 100.537 Sample maximum = 163.414 Sample minimum = 51.0360 TRUNCATED_NORMAL_A_MOMENT_TEST TRUNCATED_NORMAL_A_MOMENT evaluates the moments. of the Lower Truncated Normal PDF: Test = 1 Mu = 0.00000 Sigma = 1.00000 A = 0.00000 Order Moment 0 1.00000 1 0.797885 2 1.00000 3 1.59577 4 3.00000 5 6.38308 6 15.0000 7 38.2985 8 105.000 Test = 2 Mu = 0.00000 Sigma = 1.00000 A = -10.0000 Order Moment 0 1.00000 1 0.769460E-22 2 1.00000 3 0.784849E-20 4 3.00000 5 0.800854E-18 6 15.0000 7 0.817511E-16 8 105.000 Test = 3 Mu = 0.00000 Sigma = 1.00000 A = 10.0000 Order Moment 0 1.00000 1 10.0981 2 101.981 3 1030.01 4 10404.0 5 105101. 6 0.106183E+07 7 0.107287E+08 8 0.108414E+09 Test = 4 Mu = 0.00000 Sigma = 2.00000 A = -10.0000 Order Moment 0 1.00000 1 0.297344E-05 2 3.99997 3 0.321132E-03 4 47.9967 5 0.348725E-01 6 959.636 7 3.81038 8 26840.1 Test = 5 Mu = 0.00000 Sigma = 2.00000 A = 10.0000 Order Moment 0 1.00000 1 10.3730 2 107.730 3 1120.28 4 11665.8 5 121655. 6 0.127062E+07 7 0.132927E+08 8 0.139307E+09 Test = 6 Mu = -5.00000 Sigma = 1.00000 A = -10.0000 Order Moment 0 1.00000 1 -5.00000 2 26.0000 3 -140.000 4 777.997 5 -4449.97 6 26139.7 7 -157397. 8 969947. TRUNCATED_NORMAL_A_PDF_TEST: TRUNCATED_NORMAL_A_PDF evaluates the PDF of the lower Truncated Normal Distribution. MU S A X PDF1 PDF2 100.0 25.0 50.0 90.0 0.1507373507401876E-01 0.1507373507403181E-01 100.0 25.0 50.0 92.0 0.1551417047139894E-01 0.1551417047141238E-01 100.0 25.0 50.0 94.0 0.1586560931024694E-01 0.1586560931026069E-01 100.0 25.0 50.0 96.0 0.1612150073158793E-01 0.1612150073160189E-01 100.0 25.0 50.0 98.0 0.1627701240029317E-01 0.1627701240030727E-01 100.0 25.0 50.0 100.0 0.1632918226724295E-01 0.1632918226725710E-01 100.0 25.0 50.0 102.0 0.1627701240029317E-01 0.1627701240030727E-01 100.0 25.0 50.0 104.0 0.1612150073158793E-01 0.1612150073160189E-01 100.0 25.0 50.0 106.0 0.1586560931024694E-01 0.1586560931026069E-01 100.0 25.0 50.0 108.0 0.1551417047139894E-01 0.1551417047141238E-01 100.0 25.0 50.0 110.0 0.1507373507401876E-01 0.1507373507403181E-01 TRUNCATED_NORMAL_A_SAMPLE_TEST TRUNCATED_NORMAL_A_SAMPLE samples the lower Truncated Normal PDF. Lower limit A = 50.0000 PDF parameter MU = 100.000 PDF parameter SIGMA = 25.0000 SEED = 123456789 1 85.7717 2 103.510 3 116.192 4 112.666 5 104.711 6 79.2645 7 76.9862 8 75.0572 9 91.6212 10 128.123 TRUNCATED_NORMAL_A_VARIANCE_TEST TRUNCATED_NORMAL_A_VARIANCE returns the variance of the lower Truncated Normal distribution. Lower limit A = 50.0000 PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 PDF variance = 223.842 Sample size = 1000 Sample variance = 247.081 TRUNCATED_NORMAL_AB_CDF_TEST: TRUNCATED_NORMAL_AB_CDF evaluates the CDF of the Truncated Normal Distribution. MU S A B X CDF1 CDF2 100.0 25.0 50.0 150.0 90.0000 0.3371694242213513 0.3371694242230959 100.0 25.0 50.0 150.0 92.0000 0.3685009225506048 0.3685009225508293 100.0 25.0 50.0 150.0 94.0000 0.4006444233448185 0.4006444233422553 100.0 25.0 50.0 150.0 96.0000 0.4334107066903040 0.4334107066860820 100.0 25.0 50.0 150.0 98.0000 0.4665988676496338 0.4665988676464356 100.0 25.0 50.0 150.0 100.000 0.5000000000000000 0.5000000000000001 100.0 25.0 50.0 150.0 102.000 0.5334011323503662 0.5334011323535645 100.0 25.0 50.0 150.0 104.000 0.5665892933096960 0.5665892933139179 100.0 25.0 50.0 150.0 106.000 0.5993555766551815 0.5993555766577449 100.0 25.0 50.0 150.0 108.000 0.6314990774493952 0.6314990774491708 100.0 25.0 50.0 150.0 110.000 0.6628305757786487 0.6628305757769042 TRUNCATED_NORMAL_AB_CDF_INV_TEST TRUNCATED_NORMAL_AB_CDF_INV inverts the Truncated Normal CDF; Lower limit A = 50.0000 Upper limite B = 150.000 PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 SEED = 123456789 X CDF CDF_INV 101.703 0.545187 101.703 109.982 0.747121 109.982 131.240 0.981360 131.240 108.450 0.713392 108.450 99.4597 0.485632 99.4597 73.3547 0.378374E-01 73.3547 100.933 0.524805 100.933 87.6432 0.205031 87.6432 76.4289 0.580443E-01 76.4289 65.3380 0.104220E-01 65.3380 TRUNCATED_NORMAL_AB_MEAN_TEST TRUNCATED_NORMAL_AB_MEAN computes the mean for the Truncated Normal PDF Lower limit A = 50.0000 Upper limit B = 150.000 PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 PDF mean = 100.000 Sample size = 1000 Sample mean = 100.613 Sample maximum = 146.922 Sample minimum = 53.3278 TRUNCATED_NORMAL_AB_MOMENT_TEST: TRUNCATED_NORMAL_AB_MOMENT evaluates the moments of the Truncated Normal PDF: Test = 1 Mu = 0.00000 Sigma = 1.00000 A = -1.00000 B = 1.00000 Order Moment 0 1.00000 1 0.00000 2 0.291125 3 0.00000 4 0.164500 5 0.00000 6 0.113627 7 0.00000 8 0.865140E-01 Test = 2 Mu = 0.00000 Sigma = 1.00000 A = 0.00000 B = 1.00000 Order Moment 0 1.00000 1 0.459862 2 0.291125 3 0.210850 4 0.164500 5 0.134523 6 0.113627 7 0.982649E-01 8 0.865140E-01 Test = 3 Mu = 0.00000 Sigma = 1.00000 A = -1.00000 B = 0.00000 Order Moment 0 1.00000 1 -0.459862 2 0.291125 3 -0.210850 4 0.164500 5 -0.134523 6 0.113627 7 -0.982649E-01 8 0.865140E-01 Test = 4 Mu = 0.00000 Sigma = 2.00000 A = -1.00000 B = 1.00000 Order Moment 0 1.00000 1 0.00000 2 0.322357 3 0.00000 4 0.190636 5 0.00000 6 0.135077 7 0.00000 8 0.104524 Test = 5 Mu = 1.00000 Sigma = 1.00000 A = 0.00000 B = 2.00000 Order Moment 0 1.00000 1 1.00000 2 1.29113 3 1.87338 4 2.91125 5 4.73375 6 7.94801 7 13.6665 8 23.9346 Test = 6 Mu = 0.00000 Sigma = 1.00000 A = 0.500000 B = 2.00000 Order Moment 0 1.00000 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 = 0.00000 Sigma = 1.00000 A = -2.00000 B = 2.00000 Order Moment 0 1.00000 1 0.00000 2 0.773741 3 0.00000 4 1.41619 5 0.00000 6 3.46081 7 0.00000 8 9.74509 Test = 8 Mu = 0.00000 Sigma = 1.00000 A = -4.00000 B = 4.00000 Order Moment 0 1.00000 1 0.00000 2 0.998929 3 0.00000 4 2.97966 5 0.00000 6 14.6242 7 0.00000 8 97.9836 Test = 9 Mu = 5.00000 Sigma = 0.500000 A = 4.00000 B = 7.00000 Order Moment 0 1.00000 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 90.0000 0.1543301171801836E-01 0.1543301171804573E-01 100.0 25.0 50.0 150.0 92.0000 0.1588394472270638E-01 0.1588394472273455E-01 100.0 25.0 50.0 150.0 94.0000 0.1624375997031919E-01 0.1624375997034800E-01 100.0 25.0 50.0 150.0 96.0000 0.1650575046469259E-01 0.1650575046472186E-01 100.0 25.0 50.0 150.0 98.0000 0.1666496869385951E-01 0.1666496869388907E-01 100.0 25.0 50.0 150.0 100.000 0.1671838200940538E-01 0.1671838200943504E-01 100.0 25.0 50.0 150.0 102.000 0.1666496869385951E-01 0.1666496869388907E-01 100.0 25.0 50.0 150.0 104.000 0.1650575046469259E-01 0.1650575046472186E-01 100.0 25.0 50.0 150.0 106.000 0.1624375997031919E-01 0.1624375997034800E-01 100.0 25.0 50.0 150.0 108.000 0.1588394472270638E-01 0.1588394472273455E-01 100.0 25.0 50.0 150.0 110.000 0.1543301171801836E-01 0.1543301171804573E-01 TRUNCATED_NORMAL_AB_SAMPLE_TEST TRUNCATED_NORMAL_AB_SAMPLE samples the Truncated Normal PDF. Lower limit A = 50.0000 Upper limit B = 150.000 PDF parameter MU = 100.000 PDF parameter SIGMA = 25.0000 SEED = 123456789 1 84.5384 2 53.2759 3 92.5602 4 128.263 5 99.2531 6 135.773 7 146.447 8 79.1477 9 99.5172 10 114.569 TRUNCATED_NORMAL_AB_VARIANCE_TEST TRUNCATED_NORMAL_AB_VARIANCE returns the variance of the Truncated Normal distribution. Lower limit A = 50.0000 Upper limit B = 150.000 PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 PDF variance = 222.685 Sample size = 1000 Sample variance = 218.092 TRUNCATED_NORMA_B_CDF_TEST: TRUNCATED_NORMAL_B_CDF 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 0.3832020627674540 0.3832020627682329 100.0 25.0 150.0 94.0 0.4145972709210122 0.4145972709190397 100.0 25.0 150.0 96.0 0.4466007634041696 0.4466007634005480 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 Truncated Normal CDF; Upper limite B = 150.000 PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 SEED = 123456789 X CDF CDF_INV 111.825 0.784757 111.825 86.0285 0.175814 86.0285 104.323 0.613401 104.323 114.874 0.839310 114.874 123.445 0.940972 123.445 118.065 0.885766 118.065 100.705 0.518735 100.705 110.261 0.753030 110.261 99.8716 0.496585 99.8716 95.0561 0.370854 95.0561 TRUNCATED_NORMAL_B_MEAN_TEST TRUNCATED_NORMAL_B_MEAN computes the mean for the Upper Truncated Normal PDF Upper limit B = 150.000 PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 PDF mean = 99.9769 Sample size = 1000 Sample mean = 99.7712 Sample maximum = 149.888 Sample minimum = 58.3656 TRUNCATED_NORMAL_B_MOMENT_TEST TRUNCATED_NORMAL_B_MOMENT evaluates the moments for the Upper Truncated Normal PDF: Test = 1 Mu = 0.00000 Sigma = 1.00000 B = 0.00000 Order Moment 0 1.00000 1 -0.797885 2 1.00000 3 -1.59577 4 3.00000 5 -6.38308 6 15.0000 7 -38.2985 8 105.000 Test = 2 Mu = 0.00000 Sigma = 1.00000 B = 10.0000 Order Moment 0 1.00000 1 -0.769460E-22 2 1.00000 3 -0.784849E-20 4 3.00000 5 -0.800854E-18 6 15.0000 7 -0.817511E-16 8 105.000 Test = 3 Mu = 0.00000 Sigma = 1.00000 B = -10.0000 Order Moment 0 1.00000 1 -10.0981 2 101.981 3 -1030.01 4 10404.0 5 -105101. 6 0.106183E+07 7 -0.107287E+08 8 0.108414E+09 Test = 4 Mu = 0.00000 Sigma = 2.00000 B = 10.0000 Order Moment 0 1.00000 1 -0.297344E-05 2 3.99997 3 -0.321132E-03 4 47.9967 5 -0.348725E-01 6 959.636 7 -3.81038 8 26840.1 Test = 5 Mu = 0.00000 Sigma = 2.00000 B = -10.0000 Order Moment 0 1.00000 1 -10.3730 2 107.730 3 -1120.28 4 11665.8 5 -121655. 6 0.127062E+07 7 -0.132927E+08 8 0.139307E+09 Test = 6 Mu = 5.00000 Sigma = 1.00000 B = 10.0000 Order Moment 0 1.00000 1 5.00000 2 26.0000 3 140.000 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 0.1507373507401876E-01 0.1507373507403181E-01 100.0 25.0 150.0 92.0 0.1551417047139894E-01 0.1551417047141238E-01 100.0 25.0 150.0 94.0 0.1586560931024694E-01 0.1586560931026069E-01 100.0 25.0 150.0 96.0 0.1612150073158793E-01 0.1612150073160189E-01 100.0 25.0 150.0 98.0 0.1627701240029317E-01 0.1627701240030727E-01 100.0 25.0 150.0 100.0 0.1632918226724295E-01 0.1632918226725710E-01 100.0 25.0 150.0 102.0 0.1627701240029317E-01 0.1627701240030727E-01 100.0 25.0 150.0 104.0 0.1612150073158793E-01 0.1612150073160189E-01 100.0 25.0 150.0 106.0 0.1586560931024694E-01 0.1586560931026069E-01 100.0 25.0 150.0 108.0 0.1551417047139894E-01 0.1551417047141238E-01 100.0 25.0 150.0 110.0 0.1507373507401876E-01 0.1507373507403181E-01 TRUNCATED_NORMAL_B_SAMPLE_TEST TRUNCATED_NORMAL_B_SAMPLE samples the lower Truncated Normal PDF. Upper limit B = 150.000 PDF parameter MU = 100.000 PDF parameter SIGMA = 25.0000 SEED = 123456789 1 106.385 2 95.4384 3 105.773 4 141.603 5 127.923 6 137.835 7 51.5349 8 71.6259 9 142.606 10 101.014 TRUNCATED_NORMAL_B_VARIANCE_TEST TRUNCATED_NORMAL_B_VARIANCE returns the variance of the upper Truncated Normal distribution. Upper limit B = 150.000 PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 PDF variance = 223.842 Sample size = 1000 Sample variance = 216.769 TRUNCATED_NORMAL_TEST Normal end of execution. 17 September 2021 11:54:35.909 PM