{
  "kind": "analytical_large_N_limit",
  "formula": "P(x)=-x*ln(x)",
  "domain": [
    0,
    1
  ],
  "endpoint_values_by_continuity": [
    0,
    0
  ],
  "maximizer": 0.36787944117144233,
  "maximum_probability": 0.36787944117144233,
  "observations": "No empirical observations or simulation runs are represented.",
  "x": [
    0.0,
    0.0025,
    0.005,
    0.0075,
    0.01,
    0.0125,
    0.015,
    0.0175,
    0.02,
    0.0225,
    0.025,
    0.0275,
    0.03,
    0.0325,
    0.035,
    0.0375,
    0.04,
    0.0425,
    0.045,
    0.0475,
    0.05,
    0.0525,
    0.055,
    0.0575,
    0.06,
    0.0625,
    0.065,
    0.0675,
    0.07,
    0.0725,
    0.075,
    0.0775,
    0.08,
    0.0825,
    0.085,
    0.08750000000000001,
    0.09,
    0.0925,
    0.095,
    0.0975,
    0.1,
    0.10250000000000001,
    0.105,
    0.1075,
    0.11,
    0.1125,
    0.115,
    0.11750000000000001,
    0.12,
    0.1225,
    0.125,
    0.1275,
    0.13,
    0.1325,
    0.135,
    0.1375,
    0.14,
    0.14250000000000002,
    0.145,
    0.1475,
    0.15,
    0.1525,
    0.155,
    0.1575,
    0.16,
    0.1625,
    0.165,
    0.1675,
    0.17,
    0.17250000000000001,
    0.17500000000000002,
    0.1775,
    0.18,
    0.1825,
    0.185,
    0.1875,
    0.19,
    0.1925,
    0.195,
    0.1975,
    0.2,
    0.2025,
    0.20500000000000002,
    0.20750000000000002,
    0.21,
    0.2125,
    0.215,
    0.2175,
    0.22,
    0.2225,
    0.225,
    0.2275,
    0.23,
    0.2325,
    0.23500000000000001,
    0.23750000000000002,
    0.24,
    0.2425,
    0.245,
    0.2475,
    0.25,
    0.2525,
    0.255,
    0.2575,
    0.26,
    0.2625,
    0.265,
    0.2675,
    0.27,
    0.2725,
    0.275,
    0.2775,
    0.28,
    0.28250000000000003,
    0.28500000000000003,
    0.28750000000000003,
    0.29,
    0.2925,
    0.295,
    0.2975,
    0.3,
    0.3025,
    0.305,
    0.3075,
    0.31,
    0.3125,
    0.315,
    0.3175,
    0.32,
    0.3225,
    0.325,
    0.3275,
    0.33,
    0.3325,
    0.335,
    0.3375,
    0.34,
    0.3425,
    0.34500000000000003,
    0.34750000000000003,
    0.35000000000000003,
    0.3525,
    0.355,
    0.3575,
    0.36,
    0.3625,
    0.365,
    0.3675,
    0.37,
    0.3725,
    0.375,
    0.3775,
    0.38,
    0.3825,
    0.385,
    0.3875,
    0.39,
    0.3925,
    0.395,
    0.3975,
    0.4,
    0.4025,
    0.405,
    0.40750000000000003,
    0.41000000000000003,
    0.41250000000000003,
    0.41500000000000004,
    0.4175,
    0.42,
    0.4225,
    0.425,
    0.4275,
    0.43,
    0.4325,
    0.435,
    0.4375,
    0.44,
    0.4425,
    0.445,
    0.4475,
    0.45,
    0.4525,
    0.455,
    0.4575,
    0.46,
    0.4625,
    0.465,
    0.4675,
    0.47000000000000003,
    0.47250000000000003,
    0.47500000000000003,
    0.47750000000000004,
    0.48,
    0.4825,
    0.485,
    0.4875,
    0.49,
    0.4925,
    0.495,
    0.4975,
    0.5,
    0.5025000000000001,
    0.505,
    0.5075000000000001,
    0.51,
    0.5125,
    0.515,
    0.5175,
    0.52,
    0.5225,
    0.525,
    0.5275,
    0.53,
    0.5325,
    0.535,
    0.5375,
    0.54,
    0.5425,
    0.545,
    0.5475,
    0.55,
    0.5525,
    0.555,
    0.5575,
    0.56,
    0.5625,
    0.5650000000000001,
    0.5675,
    0.5700000000000001,
    0.5725,
    0.5750000000000001,
    0.5775,
    0.58,
    0.5825,
    0.585,
    0.5875,
    0.59,
    0.5925,
    0.595,
    0.5975,
    0.6,
    0.6025,
    0.605,
    0.6075,
    0.61,
    0.6125,
    0.615,
    0.6175,
    0.62,
    0.6225,
    0.625,
    0.6275000000000001,
    0.63,
    0.6325000000000001,
    0.635,
    0.6375000000000001,
    0.64,
    0.6425,
    0.645,
    0.6475,
    0.65,
    0.6525,
    0.655,
    0.6575,
    0.66,
    0.6625,
    0.665,
    0.6675,
    0.67,
    0.6725,
    0.675,
    0.6775,
    0.68,
    0.6825,
    0.685,
    0.6875,
    0.6900000000000001,
    0.6925,
    0.6950000000000001,
    0.6975,
    0.7000000000000001,
    0.7025,
    0.705,
    0.7075,
    0.71,
    0.7125,
    0.715,
    0.7175,
    0.72,
    0.7225,
    0.725,
    0.7275,
    0.73,
    0.7325,
    0.735,
    0.7375,
    0.74,
    0.7425,
    0.745,
    0.7475,
    0.75,
    0.7525000000000001,
    0.755,
    0.7575000000000001,
    0.76,
    0.7625000000000001,
    0.765,
    0.7675000000000001,
    0.77,
    0.7725,
    0.775,
    0.7775,
    0.78,
    0.7825,
    0.785,
    0.7875,
    0.79,
    0.7925,
    0.795,
    0.7975,
    0.8,
    0.8025,
    0.805,
    0.8075,
    0.81,
    0.8125,
    0.8150000000000001,
    0.8175,
    0.8200000000000001,
    0.8225,
    0.8250000000000001,
    0.8275,
    0.8300000000000001,
    0.8325,
    0.835,
    0.8375,
    0.84,
    0.8425,
    0.845,
    0.8475,
    0.85,
    0.8525,
    0.855,
    0.8575,
    0.86,
    0.8625,
    0.865,
    0.8675,
    0.87,
    0.8725,
    0.875,
    0.8775000000000001,
    0.88,
    0.8825000000000001,
    0.885,
    0.8875000000000001,
    0.89,
    0.8925000000000001,
    0.895,
    0.8975,
    0.9,
    0.9025,
    0.905,
    0.9075,
    0.91,
    0.9125,
    0.915,
    0.9175,
    0.92,
    0.9225,
    0.925,
    0.9275,
    0.93,
    0.9325,
    0.935,
    0.9375,
    0.9400000000000001,
    0.9425,
    0.9450000000000001,
    0.9475,
    0.9500000000000001,
    0.9525,
    0.9550000000000001,
    0.9575,
    0.96,
    0.9625,
    0.965,
    0.9675,
    0.97,
    0.9725,
    0.975,
    0.9775,
    0.98,
    0.9825,
    0.985,
    0.9875,
    0.99,
    0.9925,
    0.995,
    0.9975,
    1.0
  ],
  "probability": [
    0.0,
    0.014978661367769954,
    0.026491586832740183,
    0.036696391938299044,
    0.04605170185988091,
    0.054775332933423515,
    0.06299557616819891,
    0.07079720196592171,
    0.07824046010856292,
    0.08537039931986465,
    0.09222198635284841,
    0.09882315504351431,
    0.10519673691959945,
    0.11136174366350948,
    0.11733425261224532,
    0.12312803797521644,
    0.128755032994728,
    0.13422567612970007,
    0.13954917551453178,
    0.14473371447722322,
    0.14978661367769955,
    0.15471446074268935,
    0.15952321515623163,
    0.16421829404278285,
    0.1688046430056022,
    0.17328679513998632,
    0.1776689205906225,
    0.1819548684744966,
    0.18614820258529446,
    0.1902522319913093,
    0.19427003740843699,
    0.1982044940532698,
    0.20205829154466046,
    0.20583395131542392,
    0.20953384191180477,
    0.21316019249162474,
    0.21671510477866848,
    0.22020056368789756,
    0.22361844680125162,
    0.2269705328453877,
    0.23025850929940456,
    0.23348397924137662,
    0.23664846752658444,
    0.23975342637705013,
    0.2428002404508693,
    0.24579023145048698,
    0.24872466232117202,
    0.251604741084256,
    0.2544316243440109,
    0.257206420502176,
    0.25993019270997947,
    0.26260396158391613,
    0.2652287077084521,
    0.2678053739461515,
    0.27033486757340053,
    0.2728180622578828,
    0.2752557998921966,
    0.27764889229646406,
    0.27999812280142655,
    0.28230424772233376,
    0.28456799773288216,
    0.2867900791475373,
    0.288971175119748,
    0.2911119467628408,
    0.29321303419972966,
    0.29527505754700606,
    0.2972986178384568,
    0.29928429789260014,
    0.3012326631284188,
    0.30314426233309966,
    0.30501962838525903,
    0.30685927893683335,
    0.30866371705654677,
    0.31043343183762534,
    0.31216889897220523,
    0.3138705812946884,
    0.31553892929611366,
    0.3171743816114524,
    0.3187773654815861,
    0.3203482971915897,
    0.3218875824868201,
    0.3233956169681975,
    0.3248727864679644,
    0.3263194674071122,
    0.32773602713558037,
    0.3291228242562539,
    0.330480208933712,
    0.3318085231886141,
    0.3331081011785506,
    0.33437926946612484,
    0.3356223472749863,
    0.3368376467344825,
    0.33802547311355663,
    0.3391861250444738,
    0.34031989473692487,
    0.3414270681830173,
    0.342507925353635,
    0.3435627403866153,
    0.3445917817671655,
    0.3455953125009146,
    0.34657359027997264,
    0.3475268676423474,
    0.3484553921250463,
    0.3493594064111742,
    0.35023914847131843,
    0.3510948516994954,
    0.3519267450439174,
    0.35273505313282527,
    0.3535199963956158,
    0.35428179117948344,
    0.35502064986178056,
    0.3557367809582923,
    0.3564303892276085,
    0.3571016757717687,
    0.3577508381333437,
    0.3583780703891104,
    0.35898356324046904,
    0.35956750410074106,
    0.3601300771794836,
    0.3606714635639447,
    0.3611918412977808,
    0.3616913854571504,
    0.3621702682242912,
    0.36262865895868607,
    0.36306672426591297,
    0.3634846280642753,
    0.36388253164929873,
    0.3642605937561816,
    0.36461897062027676,
    0.3649578160356849,
    0.36527728141202986,
    0.36557751582948694,
    0.3658586660921317,
    0.3661208767796709,
    0.3663642902976187,
    0.366589046925974,
    0.3667952848664562,
    0.36698314028835105,
    0.3671527473730182,
    0.3673042383571084,
    0.3674377435745372,
    0.3675533914972593,
    0.36765130877488605,
    0.36773162027318673,
    0.3677944491115133,
    0.3678399166991852,
    0.36786814277087065,
    0.36787924542099776,
    0.36787334113723075,
    0.36785054483303975,
    0.3678109698793973,
    0.36775472813562926,
    0.36768192997944815,
    0.3675926843361966,
    0.3674870987073259,
    0.36736527919813494,
    0.36722733054479356,
    0.36707335614067205,
    0.366903458062001,
    0.3667177370928808,
    0.366516292749662,
    0.36629922330471637,
    0.36606662580961713,
    0.36581859611774703,
    0.3655552289063513,
    0.3652766176980531,
    0.3649828548818471,
    0.36467403173358726,
    0.3643502384359837,
    0.36401156409812385,
    0.3636580967745311,
    0.36328992348377526,
    0.36290713022664745,
    0.3625098020039128,
    0.362098022833652,
    0.3616718757682047,
    0.3612314429107253,
    0.36077680543136265,
    0.36030804358307406,
    0.3598252367170841,
    0.3593284632979972,
    0.3588178009185757,
    0.3582933263141899,
    0.3577551153769517,
    0.35720324316953833,
    0.3566377839387164,
    0.35605881112857307,
    0.3554663973934623,
    0.3548606146106754,
    0.35424153389284047,
    0.35360922560006053,
    0.35296375935179564,
    0.3523052040384962,
    0.351633627832994,
    0.35094909820165715,
    0.3502516819153147,
    0.3495414450599577,
    0.34881845304722175,
    0.34808277062465615,
    0.34733446188578604,
    0.34657359027997264,
    0.34580021862207533,
    0.3450144091019225,
    0.3442162232935938,
    0.3434057221645205,
    0.3425829660844066,
    0.3417480148339765,
    0.34090092761355223,
    0.3400417630514653,
    0.3391705792123068,
    0.33828743360501945,
    0.3373923831908354,
    0.33648548439106385,
    0.33556679309473153,
    0.3346363646660798,
    0.3336942539519216,
    0.33274051528886117,
    0.3317752025103809,
    0.3307983689537966,
    0.32981006746708597,
    0.32881035041559126,
    0.32779926968860157,
    0.32677687670581484,
    0.32574322242368375,
    0.3246983573416476,
    0.3236423315082535,
    0.3225751945271683,
    0.32149699556308375,
    0.32040778334751846,
    0.3193076061845175,
    0.31819651195625226,
    0.31707454812852387,
    0.31594176175616984,
    0.31479819948837895,
    0.3136439075739142,
    0.31247893186624603,
    0.31130331782859944,
    0.3101171105389141,
    0.30892035469472184,
    0.3077130946179416,
    0.30649537425959444,
    0.3052672372044395,
    0.3040287266755339,
    0.3027798855387159,
    0.30152075630701586,
    0.30025138114499367,
    0.2989718018730058,
    0.29768205997140296,
    0.29638219658465986,
    0.2950722525254383,
    0.29375226827858475,
    0.29242228400506426,
    0.29108233954583196,
    0.28973247442564204,
    0.28837272785679785,
    0.28700313874284183,
    0.28562374568218846,
    0.28423458697169973,
    0.28283570061020513,
    0.28142712430196765,
    0.2800088954600953,
    0.2785810512099008,
    0.27714362839220974,
    0.275696663566618,
    0.27424019301469943,
    0.27277425274316586,
    0.27129887848697815,
    0.26981410571241143,
    0.26831996962007393,
    0.26681650514788113,
    0.26530374697398484,
    0.26378172951966045,
    0.2622504869521496,
    0.26071005318746265,
    0.2591604618931395,
    0.25760174649096984,
    0.256033940159674,
    0.2544570758375456,
    0.25287118622505467,
    0.25127630378741495,
    0.2496724607571126,
    0.24805968913640092,
    0.24643802069975723,
    0.2448074869963066,
    0.24316811935221094,
    0.24151994887302367,
    0.23986300644601255,
    0.23819732274244892,
    0.23652292821986598,
    0.2348398531242847,
    0.23314812749241018,
    0.23144778115379608,
    0.22973884373298117,
    0.22802134465159496,
    0.2262953131304358,
    0.22456077819151957,
    0.222817768660102,
    0.22106631316667213,
    0.21930644014892028,
    0.21753817785367838,
    0.21576155433883568,
    0.21397659747522743,
    0.21218333494849984,
    0.21038179426094916,
    0.20857200273333784,
    0.20675398750668486,
    0.2049277755440349,
    0.20309339363220233,
    0.2012508683834938,
    0.19940022623740775,
    0.19754149346231228,
    0.19567469615710148,
    0.1937998602528297,
    0.19191701151432602,
    0.19002617554178694,
    0.1881273777723498,
    0.1862206434816452,
    0.18430599778533086,
    0.18238346564060506,
    0.1804530718477021,
    0.17851484105136778,
    0.17656879774231782,
    0.17461496625867678,
    0.17265337078740028,
    0.17068403536567855,
    0.16870698388232364,
    0.16672224007913852,
    0.1647298275522706,
    0.1627297697535473,
    0.1607220899917968,
    0.15870681143415122,
    0.15668395710733554,
    0.1546535498989395,
    0.1526156125586755,
    0.15057016769962014,
    0.14851723779944176,
    0.14645684520161334,
    0.14438901211661004,
    0.14231376062309395,
    0.1402311126690831,
    0.1381410900731087,
    0.13604371452535655,
    0.1339390075887972,
    0.13182699070030104,
    0.12970768517174194,
    0.12758111219108664,
    0.12544729282347294,
    0.12330624801227397,
    0.12115799858015167,
    0.11900256523009653,
    0.1168399685464573,
    0.1146702289959569,
    0.1124933669286987,
    0.11030940257915965,
    0.10811835606717367,
    0.10592024739890245,
    0.10371509646779685,
    0.101502923055546,
    0.09928374683301709,
    0.09705758736118357,
    0.09482446409204366,
    0.09258439636952874,
    0.09033740343040086,
    0.0880835044051416,
    0.08582271831882958,
    0.08355506409201008,
    0.08128056054155337,
    0.07899922638150526,
    0.07671108022392693,
    0.07441614057972706,
    0.07211442585948342,
    0.06980595437425721,
    0.0674907443363969,
    0.06516881386033521,
    0.06284018096337575,
    0.06050486356647298,
    0.05816287949500217,
    0.05581424647952287,
    0.05345898215653255,
    0.05109710406921396,
    0.04872862966817294,
    0.04635357631217016,
    0.04397196126884343,
    0.0415838017154242,
    0.03918911473944496,
    0.036787917339440326,
    0.03438022642564087,
    0.03196605882065865,
    0.029545431260167315,
    0.027118360393573432,
    0.02468486278468265,
    0.022244954912357316,
    0.019798653171169075,
    0.017345973872043098,
    0.01488693324289746,
    0.012421547429274322,
    0.009949832494966436,
    0.007471804422635588,
    0.004987479114426565,
    0.002496872392573181,
    -0.0
  ]
}