in R. Generate a random sample of size 700 from a gamma distribution with shape parameter...

in R.

Generate a random sample of size 700 from a gamma distribution with shape parameter 8 and scale parameter 0.1. Create a histogram of the sample data. Draw the true parametric density (for the specified gamma distribution) on the histogram. The curve for the density should be red.
(Note: The “true parametric density” is the distribution from which the sample values were generated. It is NOT the kernel density that is estimated from the data.)

Solutions

Expert Solution

> set.seed(123)
> x=rgamma(700,shape=8,scale=0.1)
> x
[1] 0.7261421 1.2577645 0.8524465 0.8962943 0.8100865 1.0637966 0.5132419
[8] 0.5488641 0.8673218 0.5672609 1.0054602 0.4132956 1.0709271 0.6402915
[15] 0.5897996 0.6922805 0.9794569 0.8098421 1.2440842 0.7445203 0.8948960
[22] 0.9720649 0.9365638 0.8543201 0.9170074 0.4547145 0.8446669 0.4101387
[29] 0.7824609 0.5691286 1.3931220 0.8301588 0.8424295 1.2698421 1.5168628
[36] 0.3026280 0.5308125 0.6159250 0.8259505 0.7008397 0.6969304 0.6628409
[43] 0.4098256 0.6273920 1.0654469 0.8699054 0.6920524 1.0592520 1.1072152
[50] 0.8202671 0.7666252 1.3232281 0.7539873 0.6361739 0.8045667 0.8342377
[57] 0.4158623 0.5785114 0.5540159 0.9299721 0.6097351 0.7546496 0.5417740
[64] 0.3141671 0.7631323 0.6975184 1.0382416 0.8829689 0.8890381 0.9662449
[71] 0.2066224 0.9663350 0.9032985 0.5265950 0.5401370 0.4711868 1.0916141
[78] 0.9668035 1.0587481 0.4093063 0.6830550 0.4260183 0.4583232 1.1829081
[85] 0.6420203 0.8466845 0.5268728 0.7337468 1.4035091 0.7096055 0.6257919
[92] 0.8709991 1.1268500 0.9522547 1.0841129 0.9762365 0.6495027 1.3468171
[99] 1.2634551 1.5096795 0.4293510 0.8130882 0.8310663 0.6563846 0.6584094
[106] 0.7400449 0.8567449 1.4971907 0.3630157 0.7431414 0.5666476 0.8217983
[113] 0.6874539 1.1191089 0.9485858 0.7089663 0.4228837 0.8617208 0.8337967
[120] 0.5361666 0.4164194 1.5135897 0.6146478 0.7522584 0.6150444 0.9538494
[127] 0.7642277 0.6824530 0.6774121 0.8807386 0.6049754 0.4411254 1.5167205
[134] 0.9520350 1.0501817 1.0315366 0.7469310 0.8493276 1.1257999 1.2600685
[141] 0.9515774 0.4218603 0.9389579 0.9840136 0.8684611 0.7053594 0.9216017
[148] 1.2556438 0.6132407 0.4031728 0.8731397 0.5358526 1.1421523 1.1182041
[155] 0.5471550 1.6565487 1.1629724 0.8869966 0.5421059 0.6322531 0.7283824
[162] 0.5739482 0.3940164 0.6214322 1.0646989 1.0572741 0.7701700 1.5377102
[169] 0.6561928 1.0007997 0.7159538 0.3078832 0.4955044 0.9440101 0.9909227
[176] 1.0181417 0.9164731 0.8214651 1.0468034 0.7116661 0.7997619 0.8275267
[183] 0.6743751 1.5986841 0.7629803 0.5293191 0.5759588 0.9758087 1.1452942
[190] 0.6075181 0.7081564 1.0369363 0.8959389 0.2649960 0.4395863 1.0823066
[197] 1.3295924 1.2547837 0.4355949 1.0087559 0.7889486 1.1536906 0.9522508
[204] 1.6049816 0.9003246 1.1746081 0.3356781 1.1673541 0.6144812 0.2893824
[211] 0.5259653 1.1513304 0.4983153 1.1083026 0.4422136 0.7333431 1.0407703
[218] 0.6210592 0.4823015 0.5436914 1.0432505 0.4217901 0.6108809 0.5986456
[225] 0.5556287 1.0676826 0.4887474 0.8894746 0.8256050 0.7575364 0.9821963
[232] 0.8117956 0.8853387 0.8220467 0.7108487 0.8829362 0.4893551 0.3646841
[239] 0.8697659 0.3016059 0.4767202 0.5167791 1.1678543 0.5719350 0.5044869
[246] 0.7448238 0.7214336 0.6573966 0.6304259 0.7361052 0.6367861 0.4576534
[253] 0.9662553 0.3639049 0.6210399 0.8194601 0.8332324 0.9164577 0.5015196
[260] 1.2646976 0.6849648 1.0536704 0.9057415 0.7139298 0.9000165 0.9601780
[267] 0.6186325 0.9032454 0.6297311 0.7143861 0.7298441 1.2149251 0.5544656
[274] 0.9877426 0.9596658 0.7033186 0.4740083 0.9885783 0.4166752 0.7728444
[281] 0.9278097 0.9037898 0.4484660 0.5954417 1.3006869 1.0857501 0.9381048
[288] 0.6453142 0.9084756 0.4126576 1.6604249 0.9723239 0.8185071 0.8056123
[295] 1.3995674 1.5287671 0.6094658 0.6493736 0.9747385 0.5344248 0.4115891
[302] 0.7505854 0.4870877 1.5050721 0.9609021 1.0797086 0.6404775 0.7811656
[309] 0.8064657 0.5262228 0.4723171 0.7782162 1.3917517 0.3240543 0.7540119
[316] 1.3601477 0.6997370 0.7809022 1.4126327 0.7351911 1.5619231 0.4623002
[323] 0.7812231 0.5097653 0.5501270 0.5536367 0.6225557 0.5268249 0.5652445
[330] 0.6957973 0.5293514 0.8876571 0.4885601 0.7238100 0.4714464 0.9876342
[337] 0.7874591 0.7109774 1.1348942 0.5448925 0.6403852 0.8464199 0.9345873
[344] 0.5781102 0.5665776 0.5003257 0.7672171 0.7231660 0.7325368 1.1913924
[351] 0.9299521 1.1449429 0.7858560 1.0902187 0.8820487 0.6438319 0.3990705
[358] 2.8008551 0.8565581 0.8185801 0.9241775 0.7933559 0.2979338 1.0454015
[365] 1.3837782 0.5344895 0.2699220 0.9097371 0.4677365 0.5953677 0.8445639
[372] 0.3958146 0.7441789 1.0486070 1.2062913 0.6730801 0.9243744 0.7384276
[379] 0.8455144 0.7676551 0.4145160 1.0388405 1.0914029 0.3936330 0.5156904
[386] 0.8381506 0.6429574 0.5816648 0.9017047 1.0296915 0.5739039 0.5650503
[393] 0.7000276 0.7198737 0.5508280 0.8040702 1.0235463 0.7125969 0.7784940
[400] 0.4010830 1.0204027 1.0727917 0.9639846 0.7773581 0.6976318 0.5137968
[407] 0.5484589 0.6270894 0.6228611 1.1157721 0.7487842 0.8926685 0.8122203
[414] 0.7100979 0.5568421 0.5873685 1.0427777 0.5426757 0.8473808 0.6054226
[421] 1.0508852 1.0473380 0.7958132 1.6456284 1.0034519 0.7427205 0.5859804
[428] 0.8261871 0.4492368 0.8252717 1.2000037 0.7267812 0.4960402 0.4150558
[435] 0.4919350 0.6342343 0.8353427 0.8711057 0.5007829 0.4408307 1.2364132
[442] 1.0540506 0.8330619 0.4390980 0.6349920 0.7573318 0.6820404 1.3763876
[449] 0.9930492 1.2476628 0.5310578 0.6396803 1.1072467 0.7204006 0.4340079
[456] 1.5851682 0.7479853 0.9333412 0.9257214 0.7886491 0.9651195 0.2284677
[463] 1.0789191 0.9548526 0.9536164 0.4794176 0.8178927 0.7214561 0.3934200
[470] 0.5310652 0.5156203 0.6818026 1.4064872 0.2270593 1.0435729 0.5459433
[477] 0.8152939 0.8568870 1.4352083 0.7590723 0.4386921 0.6489825 0.5092228
[484] 0.7834052 0.7078122 1.1635104 1.1455131 0.5953204 0.8536294 0.4419701
[491] 1.1240836 0.8249370 0.4617554 0.5064816 0.6450445 0.7826512 1.1803461
[498] 0.6238817 1.4289982 0.6832922 1.6627792 0.7641628 0.4579708 0.4548603
[505] 1.1554284 0.6794064 0.4794295 1.0201551 0.7538110 1.2352575 0.5595768
[512] 1.0112310 0.6409666 0.8534625 1.3640496 0.9392751 0.4385663 0.5889099
[519] 0.7668460 0.3767050 0.4947013 0.9676869 0.5354566 0.8631809 1.0094775
[526] 0.8162623 0.4963203 0.7082475 0.8082470 0.5623229 0.8079673 1.5201163
[533] 0.8250206 0.9075229 0.5993452 0.5608940 0.7168208 0.9984379 0.7202980
[540] 0.6278781 0.7659756 0.6537815 0.4658206 0.5671984 0.9694592 0.7357215
[547] 0.7795027 0.8850237 0.9226795 0.6860298 1.0345415 0.4568311 0.5791311
[554] 0.3985145 0.9361587 0.6032355 0.8760527 0.8425602 0.8901350 0.3067757
[561] 0.8500907 0.6617082 0.7887177 0.5422731 0.6454695 0.6856767 0.9135452
[568] 0.6289241 0.5473429 1.0960719 0.3299953 1.1433470 0.6426050 0.7682035
[575] 0.8357382 1.5345752 0.5514216 0.4779444 0.4834729 0.7841294 1.2019942
[582] 0.9181586 0.8316864 0.6809156 1.3763491 1.0770538 0.8774050 1.1772679
[589] 0.3978535 0.8942758 0.9356764 1.5222307 0.5307556 1.5889620 1.1462226
[596] 1.1874061 0.2997786 0.5989627 0.7242488 0.9612420 0.7087779 0.9028685
[603] 0.7825736 1.1023670 0.7995865 0.7714499 0.6684863 0.6891801 0.3568199
[610] 0.8770966 0.5524704 0.9746456 1.2547557 0.6256006 1.1503729 0.9690331
[617] 0.4530697 0.9711648 0.7707195 0.8659226 0.4332424 0.7377128 0.4814675
[624] 1.0728385 0.7519224 1.5669142 0.7715590 1.5390908 0.7839747 0.7674469
[631] 0.4849953 0.8155819 0.7458920 0.7350949 0.5880478 0.9721515 1.3412546
[638] 0.8682425 0.5200699 1.1599719 1.2863277 1.0734441 0.5887210 0.2166858
[645] 0.7799513 0.6887165 1.0971683 0.5706542 0.6987321 1.0010561 0.6004868
[652] 0.6030082 0.6981712 1.3911616 0.7126917 0.9042652 1.0238161 0.6233105
[659] 0.7414379 0.8868694 0.9513463 0.7516247 0.8147179 0.5314940 0.7814335
[666] 0.8946454 0.5862416 0.6066887 0.5906787 0.8863528 0.7340588 0.9011457
[673] 1.2499191 0.6454542 0.8015713 1.0332747 0.5573483 0.4965632 1.1069560
[680] 0.2449659 0.9859800 0.7037275 0.6921864 0.8779050 0.5114995 1.3061122
[687] 0.4557770 0.6242150 1.0347030 0.6410932 0.5107775 0.6392118 0.5367732
[694] 0.7679738 1.1610478 0.4249442 0.6800061 0.4511350 0.7744056 0.7336491
> hist(x,prob=TRUE,Main=" Histogram of Gamma")
lines(sort(x),y=dgamma(sort(x),shape=8,scale=0.1),col="red",lty=2,lwd=2)
#OR
curve(dgamma(x,shape=8,scale=0.1),add=TRUE,col="red")

orchestra answered 11 months ago

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