How to simulate normal distribution for a fixed limit in R?

To simulate the normal distribution, we can use rnorm function in R but we cannot put a limit on the range of values for the simulation. If we want simulate this distribution for a fixed limit then truncnorm function of truncnorm package can be used. In this function, we can pass the limits with and without mean and standard deviation.

Loading and installing truncnorm package −

>install.packages("truncnorm") 
>library(truncnorm)

Example

rtruncnorm(n=10,a=0,b=10)

[1] 0.76595522 0.33315633 1.29565988 0.67154230 0.04957334 0.38338705
[7] 0.75753005 0.65265304 0.63616552 0.45710877

rtruncnorm(n=50,a=0,b=100)

[1] 0.904997947 0.035692016 0.402963452 1.001102057 1.445190636 0.109245234
[7] 0.205630845 0.312428027 0.465876772 0.424647787 0.309222394 0.442172805
[13] 0.365503292 1.277570451 0.235747661 1.128447123 0.598871145 0.308236501
[19] 0.286879685 0.895142846 0.466224583 0.943387991 1.064863073 1.249080962
[25] 0.085842256 0.976095792 1.593634799 0.571843828 0.351724413 0.005417383
[31] 0.219855141 0.882968293 0.284468927 0.172589884 0.770687691 0.100598918
[37] 0.059773068 0.891556100 0.665798487 1.380145993 0.765260739 0.594810520
[43] 0.248493619 0.069473449 1.310351419 0.917684778 0.667651666 0.259194497
[49] 0.167753536 0.330810042

rtruncnorm(n=50,a=0,b=100,mean=50,sd=1)

[1] 48.43188 50.93369 50.88936 48.59129 48.52075 49.21784 49.26158 49.33846
[9] 49.96582 50.40672 49.71015 49.42354 49.67626 51.59695 48.93448 50.34689
[17] 51.99731 51.37153 49.12334 50.93896 49.27460 51.26491 51.32564 49.77611
[25] 48.93062 50.29788 50.68128 50.83197 50.89842 49.78674 50.49390 50.69491
[33] 51.10983 48.19102 50.75529 50.53974 49.45053 50.03020 51.42043 50.18587
[41] 47.93208 51.91030 50.50000 49.99998 49.65636 48.22464 49.06306 49.71244
[49] 50.30020 49.90839

rtruncnorm(n=50,a=100,b=1000,mean=50,sd=1)

[1] 100.0269 100.0092 100.0073 100.0349 100.0253 100.0212 100.0281 100.0131
[9] 100.0427 100.0017 100.0236 100.0160 100.0003 100.0083 100.0333 100.0551
[17] 100.0891 100.0014 100.0078 100.0125 100.0075 100.0224 100.0208 100.0357
[25] 100.0280 100.0054 100.0066 100.0291 100.0282 100.0031 100.0226 100.0220
[33] 100.0086 100.0018 100.0157 100.0019 100.0002 100.0149 100.0083 100.0199
[41] 100.0369 100.0041 100.0128 100.0206 100.0437 100.0164 100.0144 100.0192
[49] 100.0011 100.0236

rtruncnorm(n=50,a=100,b=1000,mean=500,sd=50)

[1] 595.5563 429.8853 540.3906 478.8280 431.6173 448.3574 521.7457 526.5902
[9] 494.9212 515.5765 421.4012 526.5601 582.1344 470.9365 451.7576 486.2514
[17] 444.7247 433.0940 529.2073 543.7203 431.2336 546.4882 405.7282 437.9558
[25] 504.2556 547.4954 514.5959 496.1003 584.9742 516.8204 500.2668 528.0662
[33] 516.5181 475.7749 527.6779 550.5650 533.0702 426.9620 519.6474 481.8744
[41] 502.4718 489.8762 558.6940 501.7477 425.1007 497.6584 546.2818 529.8647
[49] 375.1648 476.3856

rtruncnorm(n=50,a=100,b=200,mean=110,sd=5)

[1] 113.1825 105.8578 104.3472 106.5285 112.1612 111.7534 103.0770 109.6500
[9] 107.8533 106.5465 107.8265 109.5017 106.1975 110.3207 107.9621 111.5617
[17] 104.9291 109.8316 112.7709 108.7816 112.3979 102.2871 121.4476 112.6206
[25] 112.0858 108.1987 105.6250 108.7097 109.6807 107.6362 102.9960 105.7521
[33] 109.5967 110.5990 114.3580 104.9275 111.2434 111.5357 116.5991 113.9652
[41] 102.3476 110.6442 106.7582 108.8348 109.9405 115.4166 110.0341 110.5289
[49] 107.1778 110.0811

rtruncnorm(n=50,a=100,b=200,mean=150,sd=5)

[1] 142.9484 152.6989 146.2057 145.6735 148.5461 147.9396 147.3329 156.8228
[9] 151.5704 146.8341 145.9517 147.5259 148.7496 161.7972 150.6340 142.4240
[17] 144.7043 153.4120 148.7925 143.5692 143.9185 141.9358 156.4370 135.4372
[25] 152.0932 151.2913 151.2202 149.4101 149.7199 152.1015 146.9029 145.0410
[33] 150.3115 156.3192 150.4947 156.8857 155.3724 147.3547 154.7947 150.1900
[41] 152.4731 144.9843 148.2241 150.2902 145.1237 147.7011 153.4473 151.6803
[49] 149.5316 151.8152

rtruncnorm(n=50,a=1,b=10,mean=4.5,sd=0.96)

[1] 2.764336 4.321889 5.497576 5.268754 2.999608 5.234163 4.547379 3.709919
[9] 4.230514 4.918631 4.684352 5.333103 4.222377 3.933808 3.785856 5.055154
[17] 3.517594 6.469732 5.119742 3.884569 4.707952 6.648635 3.269040 5.608978
[25] 3.787292 4.409029 5.088346 5.855674 3.771203 4.145066 3.969038 5.237388
[33] 3.357416 5.847389 5.399381 4.363114 3.449466 4.213360 5.310839 3.639487
[41] 4.912864 4.811979 3.923816 3.702720 4.293520 5.311537 4.590208 5.074307
[49] 4.035909 3.574105

round(rtruncnorm(n=50,a=1,b=10,mean=4.5,sd=0.96),0)

[1] 5 4 4 5 4 4 6 5 3 4 6 2 5 5 3 6 4 5 5 5 6 4 4 2 4 4 5 5 3 6 4 3 4 4 3 5 4 5 [39] 6 4 5 5 4 4 5 3 5 4 4 5

round(rtruncnorm(n=100,a=1,b=50,mean=25,sd=2.5),0)

[1] 27 26 24 26 24 28 26 26 25 22 25 24 24 27 28 22 24 23 27 26 27 25 28 25 24
[26] 20 26 27 24 25 26 26 28 25 25 30 29 26 21 24 25 23 25 25 22 27 26 24 25 25
[51] 25 28 24 22 22 19 30 28 28 26 26 25 21 24 25 27 26 24 24 22 31 25 27 29 23
[76] 20 22 26 25 25 25 26 25 25 24 25 29 24 27 22 24 20 27 26 28 28 26 30 25 25

round(rtruncnorm(n=100,a=1,b=5,mean=4,sd=2.5),2)

[1] 2.75 3.03 1.22 4.63 4.34 2.33 4.25 3.92 4.36 1.86 4.68 4.73 1.67 3.25 1.35
[16] 2.75 2.36 4.66 3.74 3.16 1.72 2.75 3.96 1.97 1.27 3.93 3.41 2.05 4.93 2.65
[31] 1.95 4.70 2.36 3.71 3.61 3.54 2.28 4.77 1.93 4.50 3.18 3.11 2.67 4.66 3.78
[46] 2.59 1.30 2.34 4.54 3.77 3.80 3.85 4.66 2.51 4.82 4.10 1.80 4.11 2.87 3.27
[61] 4.21 3.27 3.37 3.34 2.56 3.55 1.74 2.53 4.01 4.94 4.55 2.88 4.16 4.40 4.32
[76] 4.18 2.63 2.07 1.53 4.79 3.49 4.22 4.17 4.99 1.78 1.07 4.90 4.39 3.17 3.90
[91] 4.15 3.34 4.04 3.72 4.61 3.27 2.20 4.66 1.88 2.74

round(rtruncnorm(n=100,a=10,b=99,mean=54,sd=5),1)

[1] 55.6 47.7 57.3 58.8 49.6 56.4 56.7 50.5 59.2 53.2 61.3 46.1 49.2 58.7 55.6
[16] 53.5 57.5 58.0 57.1 54.7 51.3 61.1 50.6 52.5 55.5 56.2 54.0 52.0 67.2 51.6
[31] 50.3 58.5 50.1 49.5 55.4 51.9 57.0 45.2 45.1 58.8 47.4 55.3 59.7 54.1 53.1
[46] 60.1 50.8 57.8 54.3 55.0 45.9 43.5 59.0 55.7 49.5 48.2 53.1 54.8 54.6 52.6
[61] 56.0 53.0 55.5 52.2 60.6 52.4 55.9 60.2 54.7 58.3 56.5 54.3 53.3 56.0 50.1
[76] 49.9 55.5 56.8 45.2 49.7 55.3 51.3 44.2 57.9 52.3 55.1 54.0 53.0 47.1 56.6
[91] 56.6 49.0 56.5 58.7 52.7 63.0 59.3 55.9 55.1 52.3

Nizamuddin Siddiqui

Updated on: 09-Oct-2020

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