one can sample an exponential distribution by sampling -log(r), where r is a uniform random number between 0 and 1, avoiding 0. previously similar: Zipf.
below are 100 samples. these samples could be interpreted as the time interval between clicks of a Geiger counter with a radioactive source whose radioactivity is not changing appreciably over the course of sampling, i.e., it's not running out of radioactive nuclei.
perhaps this is useful for rhythms for randomly generated music. do exponentially distributed intervals of time sound natural to the human ear?
- 0.329822540170288
- 2.01570117173415
- 0.830904930508312
- 0.259590046333096
- 0.210671751828385
- 0.981880069850274
- 0.806434405652764
- 1.15050564549307
- 0.373349932361676
- 4.23392451058767
- 0.172415567301495
- 0.653248201207598
- 0.96666339503192
- 0.13534487233904
- 0.289088688952651
- 0.531836620254011
- 2.32181489702822
- 0.384826959312606
- 1.63305210397679
- 0.886589969323164
- 0.105894896633003
- 0.748437035755276
- 1.37988086336003
- 0.306905320284676
- 0.592224886912056
- 0.168501440777515
- 3.32794912019537
- 0.0465486432724408
- 0.586012697230455
- 0.777131966567865
- 0.665789558925646
- 1.98969777447592
- 0.942378843476661
- 3.1394392472996
- 0.610809962724662
- 2.35923395358543
- 1.05532024392878
- 1.05108093027308
- 0.136479496280007
- 3.3094550400202
- 1.36981816389664
- 0.00673437989245406
- 1.29292125772523
- 1.23548146817635
- 2.21806669289339
- 1.51344618543233
- 0.263745821722615
- 1.11239526317473
- 1.25975294252588
- 0.578795550843225
- 2.16620179735083
- 1.36928119780205
- 1.59908602306717
- 1.1078295748761
- 0.37561225295492
- 0.572176602060967
- 0.0243590936172701
- 1.20920788375038
- 1.55734595506995
- 1.20052457907533
- 2.26781380265669
- 0.267104356255194
- 1.74182608161748
- 1.43040706052358
- 0.159788594534832
- 1.33818083679037
- 1.10031066700435
- 0.0290666906855637
- 1.56324690397278
- 2.32822866561526
- 1.38569406218654
- 1.345596044791
- 0.798852463928619
- 0.200689616173405
- 0.922370348252729
- 0.201207579893621
- 1.58083072548718
- 2.59288826325467
- 0.630164645071796
- 0.991009771558706
- 5.11062256536374
- 0.774943061148945
- 0.144718079806899
- 3.39733531614352
- 1.40354727764776
- 1.70284248658825
- 0.504035869192759
- 1.44673965697313
- 0.813505112238803
- 1.43741073402435
- 1.08158037197166
- 0.103234581551111
- 8.73063234335683
- 0.708871337206872
- 0.882810598009307
- 0.195284601504594
- 0.10173084752825
- 1.45148285731879
- 0.0238642031706031
- 0.124148652311142
below are same 100 samples sorted, also giving the difference between consecutive sorted samples. this models starting with exactly 100 radioactive nuclei which all eventually decay. the time interval between clicks generally gets larger over time, but not monotonically.
- 0.00673437989245406 +0.017129823278149
- 0.0238642031706031 +0.000494890446667073
- 0.0243590936172701 +0.0047075970682936
- 0.0290666906855637 +0.017481952586877
- 0.0465486432724408 +0.055182204255809
- 0.10173084752825 +0.00150373402286151
- 0.103234581551111 +0.00266031508189132
- 0.105894896633003 +0.0182537556781393
- 0.124148652311142 +0.0111962200278977
- 0.13534487233904 +0.00113462394096783
- 0.136479496280007 +0.0082385835268915
- 0.144718079806899 +0.0150705147279326
- 0.159788594534832 +0.00871284624268331
- 0.168501440777515 +0.00391412652398004
- 0.172415567301495 +0.0228690342030988
- 0.195284601504594 +0.00540501466881174
- 0.200689616173405 +0.000517963720216008
- 0.201207579893621 +0.00946417193476323
- 0.210671751828385 +0.0489182945047117
- 0.259590046333096 +0.00415577538951839
- 0.263745821722615 +0.00335853453257873
- 0.267104356255194 +0.0219843326974573
- 0.289088688952651 +0.0178166313320254
- 0.306905320284676 +0.0229172198856117
- 0.329822540170288 +0.0435273921913881
- 0.373349932361676 +0.00226232059324394
- 0.37561225295492 +0.00921470635768601
- 0.384826959312606 +0.119208909880153
- 0.504035869192759 +0.0278007510612511
- 0.531836620254011 +0.0403399818069564
- 0.572176602060967 +0.00661894878225777
- 0.578795550843225 +0.00721714638723048
- 0.586012697230455 +0.00621218968160075
- 0.592224886912056 +0.0185850758126059
- 0.610809962724662 +0.0193546823471338
- 0.630164645071796 +0.0230835561358026
- 0.653248201207598 +0.0125413577180475
- 0.665789558925646 +0.0430817782812257
- 0.708871337206872 +0.0395656985484044
- 0.748437035755276 +0.0265060253936694
- 0.774943061148945 +0.00218890541891947
- 0.777131966567865 +0.0217204973607538
- 0.798852463928619 +0.0075819417241455
- 0.806434405652764 +0.00707070658603859
- 0.813505112238803 +0.0173998182695091
- 0.830904930508312 +0.0519056675009956
- 0.882810598009307 +0.00377937131385653
- 0.886589969323164 +0.0357803789295648
- 0.922370348252729 +0.0200084952239324
- 0.942378843476661 +0.0242845515552587
- 0.96666339503192 +0.0152166748183544
- 0.981880069850274 +0.00912970170843175
- 0.991009771558706 +0.0600711587143735
- 1.05108093027308 +0.00423931365569774
- 1.05532024392878 +0.0262601280428876
- 1.08158037197166 +0.0187302950326871
- 1.10031066700435 +0.00751890787174547
- 1.1078295748761 +0.00456568829863735
- 1.11239526317473 +0.038110382318332
- 1.15050564549307 +0.0500189335822674
- 1.20052457907533 +0.00868330467504475
- 1.20920788375038 +0.0262735844259698
- 1.23548146817635 +0.024271474349532
- 1.25975294252588 +0.0331683151993496
- 1.29292125772523 +0.0452595790651393
- 1.33818083679037 +0.00741520800063311
- 1.345596044791 +0.0236851530110431
- 1.36928119780205 +0.000536966094591973
- 1.36981816389664 +0.0100626994633939
- 1.37988086336003 +0.00581319882650755
- 1.38569406218654 +0.0178532154612179
- 1.40354727764776 +0.0268597828758255
- 1.43040706052358 +0.00700367350077191
- 1.43741073402435 +0.00932892294877297
- 1.44673965697313 +0.00474320034566444
- 1.45148285731879 +0.0619633281135412
- 1.51344618543233 +0.0438997696376127
- 1.55734595506995 +0.00590094890283654
- 1.56324690397278 +0.0175838215144004
- 1.58083072548718 +0.018255297579985
- 1.59908602306717 +0.0339660809096198
- 1.63305210397679 +0.069790382611461
- 1.70284248658825 +0.0389835950292317
- 1.74182608161748 +0.247871692858435
- 1.98969777447592 +0.0260033972582321
- 2.01570117173415 +0.150500625616687
- 2.16620179735083 +0.0518648955425562
- 2.21806669289339 +0.0497471097633002
- 2.26781380265669 +0.054001094371531
- 2.32181489702822 +0.00641376858703468
- 2.32822866561526 +0.0310052879701721
- 2.35923395358543 +0.233654309669237
- 2.59288826325467 +0.546550984044933
- 3.1394392472996 +0.170015792720605
- 3.3094550400202 +0.0184940801751643
- 3.32794912019537 +0.0693861959481543
- 3.39733531614352 +0.836589194444144
- 4.23392451058767 +0.876698054776075
- 5.11062256536374 +3.62000977799309
- 8.73063234335683
popcorn.
wikipedia article, which cites the book by Devroye (mentioned previously) for efficiently generating a sorted list of samples.
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