History of Shannon entropies of discrete probability distributions

 Display properties:   number-header: $H(X)$+Numbers:+- params:+    distribution: bernoulli+    shape: 1/2+    unit: nats+  number: '0.6931471805599453094172321214581765680755001343602552541206800094933936219696947156058633269964186875'+  comment: The omitted bits row is exactly $1$.+- params:+    distribution: bernoulli+    shape: 1/3+    unit: nats+  number: '0.6365141682948128184504238226170746592638238015825792823209076606418985452388124898030402034827862971'+- params:+    distribution: bernoulli+    shape: 1/3+    unit: bits+  number: '0.9182958340544895147870722772811498420931477410258143937890859878744315611276918958556138082514215754'+- params:+    distribution: bernoulli+    shape: 1/4+    unit: nats+  number: '0.5623351446188083502880303152244588576653823503534484194403392687586665240254327060565148378825383085'+- params:+    distribution: bernoulli+    shape: 1/4+    unit: bits+  number: '0.8112781244591328639096957920391376184301391942306392046581855090941763291542310781082896438114338184'+- params:+    distribution: bernoulli+    shape: 1/5+    unit: nats+  number: '0.5004024235381878795331879388931051306048011392921093153195598762847491925561462196607525548989097107'+- params:+    distribution: bernoulli+    shape: 1/5+    unit: bits+  number: '0.7219280948873623478703194294893901758648313930245806120547563958159347766086252158501397433593701551'+- params:+    distribution: bernoulli+    shape: 1/10+    unit: nats+  number: '0.3250829733914482395065500282238179392356184845478239629108781004200828818838563398634888464248805385'+- params:+    distribution: bernoulli+    shape: 1/10+    unit: bits+  number: '0.4689955935892812212535893303833204600971654591781147032344016176419579665787798033100348885068113193'+- params:+    distribution: bernoulli+    shape: 11/100+    unit: nats+  number: '0.3465153369186661520863132845963983869516674787760962287376525101445031561505328626958518310638733583'+- params:+    distribution: bernoulli+    shape: 11/100+    unit: bits+  number: '0.4999159581645279956404995941302756626364007555431767231334216282975329506755548763322804854150763222'+- params:+    distribution: bernoulli+    shape: 2/5+    unit: nats+  number: '0.6730116670092564359967193424894015895069069658307659492235592874943249629886144982636190944063728825'+- params:+    distribution: bernoulli+    shape: 2/5+    unit: bits+  number: '0.9709505944546686389980760631207002706089427484090919757813048030912758399320100783367714584085172098'+- params:+    distribution: bernoulli+    shape: 1/6+    unit: nats+  number: '0.4505612088663046886451779140255459064516562302925732709281677669024054254319222119543675167325011007'+- params:+    distribution: bernoulli+    shape: 1/6+    unit: bits+  number: '0.6500224216483542248951394193733246955391215801719972170767889913611525806205042159804973554519464462'+- params:+    distribution: bernoulli+    shape: 1/7+    unit: nats+  number: '0.4101163182884090186946578648311492101602355648535714405833549986825330783049518256623907141791708616'+- params:+    distribution: bernoulli+    shape: 1/7+    unit: bits+  number: '0.5916727785823273804816216509908452297040428479440141604295037344636652250384570757644777349547065776'+- params:+    distribution: bernoulli+    shape: 2/7+    unit: nats+  number: '0.5982695885852572348427440421507095390972265810014184573444473676007681223981152314501733493794807514'+- params:+    distribution: bernoulli+    shape: 2/7+    unit: bits+  number: '0.8631205685666310018203125818822663973090042023771546322096085842017960084274606894620468967706606743'+- params:+    distribution: bernoulli+    shape: 3/7+    unit: nats+  number: '0.6829081047004716551734109316670383498447314798175339901494582818147753119787286070065508013860792746'+- params:+    distribution: bernoulli+    shape: 3/7+    unit: bits+  number: '0.9852281360342514582475097698256237334582490226693631863391120149812787512360393168454550813481729671'+- params:+    distribution: bernoulli+    shape: 1/8+    unit: nats+  number: '0.3767701612564367862845127138617474407940512646966372224600736472847984860010235375033887947248684765'+- params:+    distribution: bernoulli+    shape: 1/8+    unit: bits+  number: '0.5435644431995964059882768474221480424391017022796268142823697414384692572455811368143716257260655630'+- params:+    distribution: bernoulli+    shape: 3/8+    unit: nats+  number: '0.6615632381579820598530048172622152902801905974794111417661247211947586386348196813461503991258692726'+- params:+    distribution: bernoulli+    shape: 3/8+    unit: bits+  number: '0.9544340029249649645358982525886999492995499764749567197948700071621289291967247791478074823061105623'+- params:+    distribution: bernoulli+    shape: 1/9+    unit: nats+  number: '0.3488320958430318910112048166232472277603140906848182258142419752926055945180320254649293043036810108'+- params:+    distribution: bernoulli+    shape: 1/9+    unit: bits+  number: '0.5032583347756456962408112212289663508529621487182954542448386424155297889220504583778942831695098175'+- params:+    distribution: bernoulli+    shape: 2/9+    unit: nats+  number: '0.5297061990576545211713867575096501600049151850017723670852674374361167771923430108888608269488043927'+- params:+    distribution: bernoulli+    shape: 2/9+    unit: bits+  number: '0.7642045065086202793415017522708757219099414396335192891625006348052802398070114688795579504815680958'+- params:+    distribution: bernoulli+    shape: 4/9+    unit: nats+  number: '0.6869615765973233440858622918676791046025357993983177209662020524618725959599016506363897311344366715'+- params:+    distribution: bernoulli+    shape: 4/9+    unit: bits+  number: '0.9910760598382221696461893159570829198169447081490840031033073114066771352505920051278166479698597313'+- params:+    distribution: bernoulli+    shape: 3/10+    unit: nats+  number: '0.6108643020548934630256709631973806854608950105746453085913464959200184177853213027225515296339686028'+- params:+    distribution: bernoulli+    shape: 3/10+    unit: bits+  number: '0.8812908992306926182248192242427636571881684325405377453439263926043807140667825565449529014647961329'+- params:+    distribution: bernoulli+    shape: 1/11+    unit: nats+  number: '0.3046360973492381040455877100702527474570691370021690151882696173418712514792799128605117942848181566'+- params:+    distribution: bernoulli+    shape: 1/11+    unit: bits+  number: '0.4394969869215133035899817471899837079170211683866947876266594677118444591667227019366369871420185296'+- params:+    distribution: bernoulli+    shape: 2/11+    unit: nats+  number: '0.4741393130578373564302273500086005889302677348892352989034897069067841219246593644444355952171788848'+- params:+    distribution: bernoulli+    shape: 2/11+    unit: bits+  number: '0.6840384356390416865477902293566386716417170403667990632942973019318062469656134322184868857845742744'+- params:+    distribution: bernoulli+    shape: 3/11+    unit: nats+  number: '0.5859526183035508622256429756229643227531182268361104066639855974256709141924639789694576977885216307'+- params:+    distribution: bernoulli+    shape: 3/11+    unit: bits+  number: '0.8453509366224364794392524256491157290414639599474550548248691035787583757761023811125057152183309682'+- params:+    distribution: bernoulli+    shape: 4/11+    unit: nats+  number: '0.6554817739013927612369139256226137859977437464869562341111885159023728952748692040422805165402302288'+- params:+    distribution: bernoulli+    shape: 4/11+    unit: bits+  number: '0.9456603046006400969181098448509915350225782182487693907908887304088537158986228158472161179967663528'+- params:+    distribution: bernoulli+    shape: 5/11+    unit: nats+  number: '0.6890092384766585551638835037455700421884385880791792802462508440254624939434084477998234460638345449'+- params:+    distribution: bernoulli+    shape: 5/11+    unit: bits+  number: '0.9940302114769564536471784275318066012593184882928781237665927451512157788282658568563657023500477407'+- params:+    distribution: bernoulli+    shape: 1/12+    unit: nats+  number: '0.2868359830561606448395945333708436492952595437672942160257006192545890485708647444332089264708209051'+- params:+    distribution: bernoulli+    shape: 1/12+    unit: bits+  number: '0.4138168503036336966043228177825062966151855091508603284190178126252951597176750725385801172384294608'+- params:+    distribution: bernoulli+    shape: 5/12+    unit: nats+  number: '0.6791932659915257261679373239861124820411908366752918825778068103797853723411005899466525020914862353'+- params:+    distribution: bernoulli+    shape: 5/12+    unit: bits+  number: '0.9798687566511528071666237466086692971088691287853236816211839839101049090378188137943033323357277195'+- params:+    distribution: bernoulli+    shape: 1/20+    unit: nats+  number: '0.1985152433458725564266475158490799153010913247548558525429456858721381646860597715634100674610640849'+- params:+    distribution: bernoulli+    shape: 1/20+    unit: bits+  number: '0.2863969571159561287664759777278974743059992018461232982023079014945978288134335733875670918958024613'+- params:+    distribution: bernoulli+    shape: 1/25+    unit: nats+  number: '0.1679441477341729543404547292072020865321713860696608382924307953153898226527301401167102498154905962'+- params:+    distribution: bernoulli+    shape: 1/25+    unit: bits+  number: '0.2422921890824147615450494727888765033202409546643794060719902432724152545346662116788902307973755978'+- params:+    distribution: bernoulli+    shape: 2/25+    unit: nats+  number: '0.2787693717685874089059274914703407246381728081350141408568968349045326993517255176692696852458904974'+- params:+    distribution: bernoulli+    shape: 2/25+    unit: bits+  number: '0.4021791902022728532300224743491250147907436706420105693746245581782736592995069112783853229256191531'+- params:+    distribution: bernoulli+    shape: 1/50+    unit: nats+  number: '0.09803911327973198061225941076191957703801677291684276856557109856409506639095448000232042595054971624'+- params:+    distribution: bernoulli+    shape: 1/50+    unit: bits+  number: '0.1414405425418206451543789972043919667932505991555252881020210124540406894473521781644719283451271714'+- params:+    distribution: bernoulli+    shape: 3/50+    unit: nats+  number: '0.2269675225006044055233424441093570184855659375289151396334162864250928190964406985996657696652927617'+- params:+    distribution: bernoulli+    shape: 3/50+    unit: bits+  number: '0.3274449191544761950128524133651065220106155539650904498938617310481118099811849762154853731295092786'+- params:+    distribution: bernoulli+    shape: 1/100+    unit: nats+  number: '0.05600153435484734045207319807664951317668188737045903416557898929363863110775486011793105472539861738'+- params:+    distribution: bernoulli+    shape: 1/100+    unit: bits+  number: '0.08079313589591117282486633370356863526903104839309833380744890637142774866160230872376776008689410701'+- params:+    distribution: bernoulli+    shape: 3/100+    unit: nats+  number: '0.1347421681797667398409055792082097816681308049438455532176676342286484175333051798837716748515383206'+- params:+    distribution: bernoulli+    shape: 3/100+    unit: bits+  number: '0.1943918578315761608655943296458712861413420598012773323289368456381923157762491710228600763858658681'+- params:+    distribution: bernoulli+    shape: 7/100+    unit: nats+  number: '0.2536389469216914149669073251653647230869976220647081450274849537549122188330311265755013701587141808'+- params:+    distribution: bernoulli+    shape: 7/100+    unit: bits+  number: '0.3659236509002232152780288416678172280775727639928899609816645906900039985197769117370448800692025383'+- params:+    distribution: bernoulli+    shape: 9/100+    unit: nats+  number: '0.3025378230974980861302941983649403040231137431981688933150343707334457242057590494943613968669162964'+- params:+    distribution: bernoulli+    shape: 9/100+    unit: bits+  number: '0.4364698170641029793456742550136151366876848374054825138011400363934816799136172495991028494327416565'+- params:+    distribution: binomial+    shape: 2,1/2+    unit: nats+  number: '1.039720770839917964125848182187264852113250201540382881181020014240090432954542073408794990494628031'+  comment: The omitted bits row is exactly $3/2$.+- params:+    distribution: binomial+    shape: 2,1/3+    unit: nats+  number: '0.9649629230074277216043000356971819549385364323383784516992908726200665918244273282256967060782753997'+- params:+    distribution: binomial+    shape: 2,1/3+    unit: bits+  number: '1.392147223664534585129700110117855239741851037607184343133727531304418677810939347266783172058398706'+- params:+    distribution: binomial+    shape: 2,1/4+    unit: nats+  number: '0.8647400965276372095445985849021015023024521503218011185854235339573104398122298937608309281414196092'+- params:+    distribution: binomial+    shape: 2,1/4+    unit: bits+  number: '1.247556248918265727819391584078275236860278388461278409316371018188352658308462156216579287622867637'+- params:+    distribution: binomial+    shape: 2,1/10+    unit: nats+  number: '0.5253994542821063233179982745851640962176469449108019800800337991313549118131676309179222939904057133'+- params:+    distribution: binomial+    shape: 2,1/10+    unit: bits+  number: '0.7579911871785624425071786607666409201943309183562294064688032352839159331575596066200697770136226387'+- params:+    distribution: binomial+    shape: 3,1/2+    unit: nats+  number: '1.255482325178753659705262436682635425740882484713703673561019278252060145995127421662378164878956996'+- params:+    distribution: binomial+    shape: 3,1/2+    unit: bits+  number: '1.811278124459132863909695792039137618430139194230639204658185509094176329154231078108289643811433818'+- params:+    distribution: binomial+    shape: 3,1/3+    unit: nats+  number: '1.177134312439031994421107976569540174693144366199238212472926759500699440237364824826710107239204165'+- params:+    distribution: binomial+    shape: 3,1/3+    unit: bits+  number: '1.698245835016031090058724202544905187106233617949122474396756193929229198186836645885321108142205898'+- params:+    distribution: binomial+    shape: 3,1/4+    unit: nats+  number: '1.069036021480613349454265499904455864131933612285048691720252243604909032140830574303135651564890626'+- params:+    distribution: binomial+    shape: 3,1/4+    unit: bits+  number: '1.542292966721748239661359220146766069113021978364897017468195659103161234328366542906086164292876819'+- params:+    distribution: binomial+    shape: 3,1/10+    unit: nats+  number: '0.6786236022339551018429338707023718774520330030313295367642668311781251864825445985345902854749339516'+- params:+    distribution: binomial+    shape: 3,1/10+    unit: bits+  number: '0.9790469055731314947682584762840509229263464874573742233801516361997773782318625980490889372925501326'+- params:+    distribution: binomial+    shape: 4,1/2+    unit: nats+  number: '1.407531740719315302947017354981766351955378893512138997666274649806097897713470265887785325310449522'+- params:+    distribution: binomial+    shape: 4,1/2+    unit: bits+  number: '2.030639062229566431954847896019568809215069597115319602329092754547088164577115539054144821905716909'+- params:+    distribution: binomial+    shape: 4,1/3+    unit: nats+  number: '1.330575170632721091420485089014089007531939806809174743231983914239041097966424457632203232163773415'+- params:+    distribution: binomial+    shape: 4,1/3+    unit: bits+  number: '1.919614200201813017729897323263517933678324966762275532552170325460857633806266280946717808338598427'+- params:+    distribution: binomial+    shape: 4,1/4+    unit: nats+  number: '1.221565833659991821839584204247365512438242176318701821881851540630437905895109220322547363651682035'+- params:+    distribution: binomial+    shape: 4,1/4+    unit: bits+  number: '1.762346970340662573613385109667557928904033425299924094942856710809442409191551803151115037567701035'+- params:+    distribution: binomial+    shape: 4,1/10+    unit: nats+  number: '0.8040182879587177743067798687690621806963613112249071209060917309992707804463660403917509940648632332'+- params:+    distribution: binomial+    shape: 4,1/10+    unit: bits+  number: '1.159953196822076694595705608857417958062934856498604233399456891557134492444313387101556722946226189'+- params:+    distribution: binomial+    shape: 5,1/2+    unit: nats+  number: '1.523670872042791627512178656479971573275061818199381372484867643276554295141485226434901544896975873'+- params:+    distribution: binomial+    shape: 5,1/2+    unit: bits+  number: '2.198192411043097798871575534853696710126720569039455676198665878922561146929413860140493990600590480'+- params:+    distribution: binomial+    shape: 5,1/3+    unit: nats+  number: '1.449403667489066084860237160194506660642426413181952575817963577494328849424632422492436763754927532'+- params:+    distribution: binomial+    shape: 5,1/3+    unit: bits+  number: '2.091047483332751717751134718945782391817118982762150452354899720765794418445820403852022349465059595'+- params:+    distribution: binomial+    shape: 5,1/4+    unit: nats+  number: '1.342052132566523583882733760066268972567977079209492375936745016871964149110500293925528073561723941'+- params:+    distribution: binomial+    shape: 5,1/4+    unit: bits+  number: '1.936171956268181281131634082264316669128656433497753760202343572095462577651304151905599586420148857'+- params:+    distribution: binomial+    shape: 5,1/10+    unit: nats+  number: '0.9102051201901215240709433923248535557782431572829811318473861097727732305734505727373294795585357283'+- params:+    distribution: binomial+    shape: 5,1/10+    unit: bits+  number: '1.313148413090031224815050845540697023469178840447007755535585344123164541872666990659542217628394518'+- params:+    distribution: binomial+    shape: 6,1/2+    unit: nats+  number: '1.617363315627128389966918714250924359837365210400365332805878227583171449896471574077313577437113687'+- params:+    distribution: binomial+    shape: 6,1/2+    unit: bits+  number: '2.333362034770989421647296763745659341231972269151355700908133886226205243784463743461831763835496657'+- params:+    distribution: binomial+    shape: 6,1/3+    unit: nats+  number: '1.545763808367196802452635494910837817042923694939978260573813180304124171241075868843431470972016842'+- params:+    distribution: binomial+    shape: 6,1/3+    unit: bits+  number: 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discrete-uniform+    shape: '5'+    unit: bits+  number: '2.321928094887362347870319429489390175864831393024580612054756395815934776608625215850139743359370155'+- params:+    distribution: discrete-uniform+    shape: '6'+    unit: nats+  number: '1.791759469228055000812477358380702272722990692183004705855374343130887915188303682479479081810150776'+- params:+    distribution: discrete-uniform+    shape: '6'+    unit: bits+  number: '2.584962500721156181453738943947816508759814407692481060455752654541098227794358562522280474918088242'+- params:+    distribution: discrete-uniform+    shape: '7'+    unit: nats+  number: '1.945910149055313305105352743443179729637084729581861188459390149937579862752069267787658498587871527'+- params:+    distribution: discrete-uniform+    shape: '7'+    unit: bits+  number: '2.807354922057604107441969317231830808641026625966140783677291724070320848862192986497860999170210785'+- params:+    distribution: discrete-uniform+    shape: '8'+    unit: nats+  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