07 March 2015 11:15:14 AM
TRUNCATED_NORMAL_PRB
C++ 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 -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 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)
-57 -1
92 1
66 1
12 1
-17 -1
-87 -1
-49 -1
-78 1
-92 1
27 -1
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 0.0661187
6 0.257578
7 0.109957
8 0.043829
9 0.633966
Number of samples was 1000
Minimum value was 0.00183837
Maximum value was 0.997908
Average value was 0.50304
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 24
1 0.333333 10.8642
2 0.666667 3.45679
3 1 0
4 1.33333 -0.987654
5 1.66667 -0.691358
6 2 0
7 2.33333 0.493827
8 2.66667 0.493827
9 3 0
10 3.33333 -0.691358
11 3.66667 -0.987654
12 4 0
13 4.33333 3.45679
14 4.66667 10.8642
15 5 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
TEST1335
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 0.539828 0.539828
0.2 0.57926 0.57926
0.3 0.617911 0.617911
0.4 0.655422 0.655422
0.5 0.691462 0.691462
0.6 0.725747 0.725747
0.7 0.758036 0.758036
0.8 0.788145 0.788145
0.9 0.81594 0.81594
1 0.841345 0.841345
1.5 0.933193 0.933193
2 0.97725 0.97725
2.5 0.99379 0.99379
3 0.99865 0.99865
3.5 0.999767 0.999767
4 0.999968 0.999968
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 0.1
0.57926 0.2 0.2
0.617911 0.3 0.3
0.655422 0.4 0.4
0.691462 0.5 0.5
0.725747 0.6 0.6
0.758036 0.7 0.7
0.788145 0.8 0.8
0.81594 0.9 0.9
0.841345 1 1
0.933193 1.5 1.5
0.97725 2 2
0.99379 2.5 2.5
0.99865 3 3
0.999767 3.5 3.5
0.999968 4 4
NORMAL_01_MEAN_TEST
NORMAL_01_MEAN computes the Normal 01 mean;
PDF mean = 0
Sample size = 1000
Sample mean = 0.00581875
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 0.053991
-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 1.67904
2 -0.56606
3 1.21293
4 1.26938
5 -1.66609
6 -2.24246
7 0.0396749
8 0.673068
9 -0.275127
10 2.164
NORMAL_01_VARIANCE_TEST
NORMAL_01_VARIANCE computes the Normal 01 variance;
PDF variance = 1
Sample size = 1000
Sample variance = 0.998375
NORMAL_MS_CDF_TEST
NORMAL_MS_CDF evaluates the Normal MS CDF;
Parameter MU = 100
Parameteter SIGMA = 15
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 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 = 100.087
Sample maximum = 149.929
Sample minimum = 54.5537
NORMAL_MOMENT_MS_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 Normal MS PDF;
Parameter MU = 100
Parameteter SIGMA = 15
X PDF
70 0.00272666
71.5 0.00275243
73 0.00277448
74.5 0.00279308
76 0.0028085
77.5 0.00282097
79 0.00283073
80.5 0.00283799
82 0.00284295
83.5 0.0028458
85 0.00284671
86.5 0.00284585
88 0.00284337
89.5 0.0028394
91 0.00283408
92.5 0.00282753
94 0.00281985
95.5 0.00281115
97 0.00280153
98.5 0.00279107
100 0.00277985
101.5 0.00276795
103 0.00275543
104.5 0.00274237
106 0.00272881
107.5 0.00271482
109 0.00270043
110.5 0.0026857
112 0.00267068
113.5 0.00265538
115 0.00263986
116.5 0.00262415
118 0.00260827
119.5 0.00259226
121 0.00257613
122.5 0.00255991
124 0.00254363
125.5 0.00252729
127 0.00251093
128.5 0.00249456
130 0.00247818
NORMAL_MS_SAMPLE_TEST
NORMAL_MS_SAMPLE returns samples from the Normal MS PDF.
Parameter MU = 100
Parameteter SIGMA = 15
1 125.186
2 91.5091
3 118.194
4 119.041
5 75.0087
6 66.363
7 100.595
8 110.096
9 95.8731
10 132.46
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 = 224.634
TRUNCATED_NORMAL_A_CDF_TEST:
TRUNCATED_NORMAL_A_CDF evaluates
the lower Truncated Normal Cumulative Density Function.
MU S A X CDF1 CDF2
100 25 50 90 0.3293202045481688 0.3293202045495739
100 25 50 92 0.3599223134505957 0.3599223134504884
100 25 50 94 0.3913175216041539 0.3913175216012952
100 25 50 96 0.4233210140873113 0.4233210140828035
100 25 50 98 0.4557365629792204 0.4557365629756831
100 25 50 100 0.4883601253415709 0.4883601253411278
100 25 50 102 0.5209836877039214 0.5209836877065723
100 25 50 104 0.5533992365958303 0.5533992365994519
100 25 50 106 0.5854027290789878 0.5854027290809604
100 25 50 108 0.6167979372325459 0.6167979372317671
100 25 50 110 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
0 82.03546056392796 0.2184182969792162 82.03546056367747
1 143.0075878300667 0.9563175765092733 143.0075878301592
2 124.1910017889437 0.829509233935064 124.1910017891749
3 104.5154909202534 0.5616954427706908 104.5154909204897
4 95.50207869815179 0.4153070814721543 95.50207869791485
5 66.07091630620891 0.06611873491948256 66.07091630673978
6 85.01611797809308 0.2575777923792841 85.01611797789074
7 71.86448157864034 0.1099567935296942 71.86448157832004
8 62.26181205048496 0.04382899777702298 62.26181205008615
9 109.114869274367 0.6339657123008282 109.1148692742633
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 = 101.3811965669759
Sample size = 1000
Sample mean = 101.503886001702
Sample maximum = 171.7819108493603
Sample minimum = 50.80550075949013
TRUNCATED_NORMAL_A_MOMENT_TEST
TRUNCATED_NORMAL_A_MOMENT evaluates the moments
of the Lower Truncated Normal Distribution.
Test = 0, Mu = 0, Sigma = 1, A = 0
Order Moment
0 1
1 0.7978845608028654
2 1
3 1.595769121605731
4 3
5 6.383076486422923
6 15
7 38.29845891853754
8 105
Test = 1, Mu = 0, Sigma = 1, A = -10
Order Moment
0 1
1 7.69459862670642e-23
2 1
3 7.848490599240547e-21
4 3
5 8.008538250676043e-19
6 15
7 8.175110921746982e-17
8 105
Test = 2, Mu = 0, Sigma = 1, A = 10
Order Moment
0 1
1 10.09809323416386
2 101.9809323416386
3 1030.005509884714
4 10404.03603118877
5 105100.9543811774
6 1061829.50357233
7 10728698.96045092
8 108413738.8666449
Test = 3, Mu = 0, Sigma = 2, A = -10
Order Moment
0 1
1 2.973439881809812e-06
2 3.999970265601182
3 0.0003211315072354596
4 47.99666974733238
5 0.03487250293386547
6 959.6360509584665
7 3.810379952222583
8 26840.07502801896
Test = 4, Mu = 0, Sigma = 2, A = 10
Order Moment
0 1
1 10.37300793467855
2 107.7300793467855
3 1120.284856945284
4 11665.76888683998
5 121654.6370579101
6 1270616.171204655
7 13292719.2240684
8 139307332.1405159
Test = 5, Mu = -5, Sigma = 1, A = -10
Order Moment
0 1
1 -4.999998513280059
2 25.99997769920089
3 -139.9997368505705
4 777.997130630514
5 -4449.969733355443
6 26139.68564793569
7 -157396.7599198702
8 969946.7319354919
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 25 50 90 0.01507373507401876 0.01507373507403181
100 25 50 92 0.01551417047139894 0.01551417047141238
100 25 50 94 0.01586560931024694 0.01586560931026069
100 25 50 96 0.01612150073158793 0.01612150073160189
100 25 50 98 0.01627701240029317 0.01627701240030727
100 25 50 100 0.01632918226724295 0.0163291822672571
100 25 50 102 0.01627701240029317 0.01627701240030727
100 25 50 104 0.01612150073158793 0.01612150073160189
100 25 50 106 0.01586560931024694 0.01586560931026069
100 25 50 108 0.01551417047139894 0.01551417047141238
100 25 50 110 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 82.03546056392796
1 143.0075878300667
2 124.1910017889437
3 104.5154909202534
4 95.50207869815179
5 66.07091630620891
6 85.01611797809308
7 71.86448157864034
8 62.26181205048496
9 109.114869274367
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 = 554.0324676945766
Sample size = 1000
Sample variance = 555.6650626460602
TRUNCATED_NORMAL_AB_CDF_TEST:
TRUNCATED_NORMAL_AB_CDF evaluates
the Truncated Normal Cumulative Density Function.
MU S A B X CDF1 CDF2
100 25 50 150 90 0.3371694242213513 0.3371694242230959
100 25 50 150 92 0.3685009225506048 0.3685009225508293
100 25 50 150 94 0.4006444233448185 0.4006444233422553
100 25 50 150 96 0.433410706690304 0.433410706686082
100 25 50 150 98 0.4665988676496338 0.4665988676464356
100 25 50 150 100 0.5 0.5000000000000001
100 25 50 150 102 0.5334011323503662 0.5334011323535645
100 25 50 150 104 0.566589293309696 0.5665892933139179
100 25 50 150 106 0.5993555766551815 0.5993555766577449
100 25 50 150 108 0.6314990774493952 0.6314990774491708
100 25 50 150 110 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
0 81.62997416083324 0.2184182969794712 81.62997416060566
1 137.9623424219791 0.9563175765111896 137.9623424224073
2 122.3665851392898 0.8295092339333726 122.3665851393498
3 103.7037803533316 0.5616954427710373 103.7037803535821
4 94.89896872307021 0.4153070814725299 94.89896872286064
5 65.83262246613882 0.06611873491934137 65.8326224666426
6 84.57429531004072 0.2575777923788141 84.57429530980696
7 71.56719070938323 0.1099567935299048 71.5671907090902
8 62.06540360199795 0.04382899777686092 62.06540360157312
9 108.1554466200941 0.6339657123017586 108.1554466200528
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 = 100.1234240569421
Sample maximum = 149.1079402806376
Sample minimum = 50.78732108028024
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 0.2911250947793833
3 0
4 0.1645003791175332
5 0
6 0.1136269903670495
7 0
8 0.08651402734872971
Test = 1, Mu = 0, Sigma = 1, A = 0, B = 1
Order Moment
0 1
1 0.4598622292821514
2 0.2911250947793833
3 0.210849553343686
4 0.1645003791175332
5 0.1345233081541275
6 0.1136269903670495
7 0.09826494370414829
8 0.08651402734872971
Test = 2, Mu = 0, Sigma = 1, A = -1, B = 0
Order Moment
0 1
1 -0.4598622292821514
2 0.2911250947793833
3 -0.210849553343686
4 0.1645003791175332
5 -0.1345233081541275
6 0.1136269903670495
7 -0.09826494370414829
8 0.08651402734872971
Test = 3, Mu = 0, Sigma = 2, A = -1, B = 1
Order Moment
0 1
1 0
2 0.3223566183950748
3 0
4 0.1906360391359723
5 0
6 0.1350774011145202
7 0
8 0.1045238496016392
Test = 4, Mu = 1, Sigma = 1, A = 0, B = 2
Order Moment
0 1
1 1
2 1.291125094779383
3 1.87337528433815
4 2.911250947793833
5 4.733752843381499
6 7.948009098820798
7 13.66652919205006
8 23.93459894967617
Test = 5, Mu = 0, Sigma = 1, A = 0.5, B = 2
Order Moment
0 1
1 1.042993334143991
2 1.238116616554702
3 1.638284875530746
4 2.356978751216315
5 3.607413548760741
6 5.777949971123758
7 9.572847783532149
8 16.27350981024338
Test = 6, Mu = 0, Sigma = 1, A = -2, B = 2
Order Moment
0 1
1 0
2 0.773741303549522
3 0
4 1.416189124846654
5 0
6 3.46080648102562
7 0
8 9.745088794348742
Test = 7, Mu = 0, Sigma = 1, A = -4, B = 4
Order Moment
0 1
1 0
2 0.9989292903724738
3 0
4 2.979656517077002
5 0
6 14.62418092073831
7 0
8 97.98363981082095
Test = 8, Mu = 5, Sigma = 0.5, A = 4, B = 7
Order Moment
0 1
1 5.027556351520714
2 25.49780173838909
3 130.4414288137665
4 673.0749973172971
5 3502.723962301956
6 18382.10051962429
7 97269.68380447358
8 518913.3079025001
TRUNCATED_NORMAL_AB_PDF_TEST:
TRUNCATED_NORMAL_AB_PDF evaluates
the Truncated Normal Probability Density Function.
MU S A B X PDF1 PDF2
100 25 50 150 90 0.01543301171801836 0.01543301171804573
100 25 50 150 92 0.01588394472270638 0.01588394472273455
100 25 50 150 94 0.01624375997031919 0.016243759970348
100 25 50 150 96 0.01650575046469259 0.01650575046472186
100 25 50 150 98 0.01666496869385951 0.01666496869388907
100 25 50 150 100 0.01671838200940538 0.01671838200943504
100 25 50 150 102 0.01666496869385951 0.01666496869388907
100 25 50 150 104 0.01650575046469259 0.01650575046472186
100 25 50 150 106 0.01624375997031919 0.016243759970348
100 25 50 150 108 0.01588394472270638 0.01588394472273455
100 25 50 150 110 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 81.62997416083324
1 137.9623424219791
2 122.3665851392898
3 103.7037803533316
4 94.89896872307021
5 65.83262246613882
6 84.57429531004072
7 71.56719070938323
8 62.06540360199795
9 108.1554466200941
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 = 483.5883147184512
Sample size = 1000
Sample variance = 486.0644394612366
TRUNCATED_NORMAL_B_CDF_TEST:
TRUNCATED_NORMAL_B_CDF evaluates
the upper Truncated Normal Cumulative Density Function.
MU S B X CDF1 CDF2
100 25 150 90 0.3525999538650271 0.3525999538673185
100 25 150 92 0.383202062767454 0.3832020627682329
100 25 150 94 0.4145972709210122 0.4145972709190397
100 25 150 96 0.4466007634041696 0.446600763400548
100 25 150 98 0.4790163122960786 0.4790163122934276
100 25 150 100 0.5116398746584291 0.5116398746588723
100 25 150 102 0.5442634370207796 0.5442634370243169
100 25 150 104 0.5766789859126887 0.5766789859171965
100 25 150 106 0.6086824783958461 0.6086824783987049
100 25 150 108 0.6400776865494043 0.6400776865495117
100 25 150 110 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
0 80.13724631066849 0.2184182969809693 80.13724631055038
1 137.7662596736219 0.956317576511031 137.7662596740247
2 122.006225594984 0.8295092339332231 122.0062255950311
3 103.0731276291453 0.5616954427708121 103.073127629387
4 94.04472935979294 0.4153070814735715 94.04472935964239
5 62.07127308919195 0.06611873491384032 62.07127308876782
6 83.2726582346192 0.257577792378394 83.27265823433953
7 68.99561491453773 0.1099567935284338 68.99561491400434
8 57.03177989276885 0.04382899777874047 57.03177989267051
9 107.607013071183 0.6339657123024837 107.6070130711876
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 = 98.61880343302406
Sample size = 1000
Sample mean = 98.71007276926947
Sample maximum = 149.0874272316052
Sample minimum = 27.20406439929408
TRUNCATED_NORMAL_B_MOMENT_TEST
For the Upper Truncated Normal PDF:
TRUNCATED_NORMAL_B_MOMENT evaluates the moments.
Test = 0, Mu = 0, Sigma = 1, B = 0
Order Moment
0 1
1 -0.7978845608028654
2 1
3 -1.595769121605731
4 3
5 -6.383076486422923
6 15
7 -38.29845891853754
8 105
Test = 1, Mu = 0, Sigma = 1, B = 10
Order Moment
0 1
1 -7.69459862670642e-23
2 1
3 -7.848490599240547e-21
4 3
5 -8.008538250676043e-19
6 15
7 -8.175110921746982e-17
8 105
Test = 2, Mu = 0, Sigma = 1, B = -10
Order Moment
0 1
1 -10.09809323416386
2 101.9809323416386
3 -1030.005509884714
4 10404.03603118877
5 -105100.9543811774
6 1061829.50357233
7 -10728698.96045092
8 108413738.8666449
Test = 3, Mu = 0, Sigma = 2, B = 10
Order Moment
0 1
1 -2.973439881809812e-06
2 3.999970265601182
3 -0.0003211315072354596
4 47.99666974733238
5 -0.03487250293386547
6 959.6360509584665
7 -3.810379952222583
8 26840.07502801896
Test = 4, Mu = 0, Sigma = 2, B = -10
Order Moment
0 1
1 -10.37300793467855
2 107.7300793467855
3 -1120.284856945284
4 11665.76888683998
5 -121654.6370579101
6 1270616.171204655
7 -13292719.2240684
8 139307332.1405159
Test = 5, Mu = 5, Sigma = 1, B = 10
Order Moment
0 1
1 4.999998513280059
2 25.99997769920089
3 139.9997368505705
4 777.997130630514
5 4449.969733355443
6 26139.68564793569
7 157396.7599198702
8 969946.7319354919
TRUNCATED_NORMAL_B_PDF_TEST:
TRUNCATED_NORMAL_B_PDF evaluates
the upper Truncated Normal Distribution.
MU S B X PDF1 PDF2
100 25 150 90 0.01507373507401876 0.01507373507403181
100 25 150 92 0.01551417047139894 0.01551417047141238
100 25 150 94 0.01586560931024694 0.01586560931026069
100 25 150 96 0.01612150073158793 0.01612150073160189
100 25 150 98 0.01627701240029317 0.01627701240030727
100 25 150 100 0.01632918226724295 0.0163291822672571
100 25 150 102 0.01627701240029317 0.01627701240030727
100 25 150 104 0.01612150073158793 0.01612150073160189
100 25 150 106 0.01586560931024694 0.01586560931026069
100 25 150 108 0.01551417047139894 0.01551417047141238
100 25 150 110 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 80.13724631066849
1 137.7662596736219
2 122.006225594984
3 103.0731276291453
4 94.04472935979294
5 62.07127308919195
6 83.2726582346192
7 68.99561491453773
8 57.03177989276885
9 107.607013071183
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 = 554.0324676945766
Sample size = 1000
Sample variance = 560.2814763974837
TRUNCATED_NORMAL_PRB
Normal end of execution.
07 March 2015 11:15:14 AM