@bunchmark/stats/src/z-table.js

The bunchmark statistical routines.

// generated with this Python script:

// from scipy import stats
// import json

// with open("./packages/stats/z-table.json","w") as zt:
//     json.dump([stats.norm.sf(z/1000) for z in range (10000)], zt)

// Get the p value by indexing zTzble with `Math.round(z*1000)` 
// (floor or ceil may be more accurate)
export {pForZ, zTable}

const pForZ = (z, silent = false) => z < 0 ? _pForZ(-z, silent) : 1 - _pForZ(z, silent)
const _pForZ = (z, silent) => zTable[Math.round(z * 1000)] || (!silent && console.warn("|z| is too large, z-table overflow"), zTable[zTable.length - 1])
// const pForZ = _pForZ
const zTable =  [
    0.5, 0.49960105778608893, 0.49920211597111985, 0.49880317495403353, 0.49840423513376836,
    0.49800529690925915, 0.4976063606794359, 0.4972074268432227, 0.49680849579953634, 0.49640956794728525,
    0.4960106436853684, 0.4956117234126739, 0.4952128075280779, 0.4948138964304433, 0.494414990518619,
    0.4940160901914378, 0.49361719584771613, 0.49321830788625237, 0.4928194267058258, 0.4924205527051952,
    0.492021686283098, 0.49162282783824884, 0.49122397776933835, 0.4908251364750321, 0.49042630435396944,
    0.49002748180476197, 0.48962866922599274, 0.48922986701621496, 0.48883107557395056, 0.4884322952976893,
    0.48803352658588733, 0.48763476983696635, 0.48723602544931194, 0.4868372938212727, 0.486438575351159,
    0.4860398704372417, 0.485641179477751, 0.48524250287087534, 0.48484384101475997, 0.48444519430750604,
    0.48404656314716926, 0.48364794793175864, 0.48324934905923544, 0.48285076692751194, 0.48245220193445026,
    0.4820536544778609, 0.48165512495550217, 0.4812566137650782, 0.48085812130423855, 0.4804596479705764,
    0.4800611941616275, 0.4796627602748694, 0.47926434670771967, 0.4788659538575351, 0.4784675821216102,
    0.47806923189717654, 0.47767090358140085, 0.4772725975713844, 0.4768743142641616, 0.47647605405669885,
    0.47607781734589316, 0.47567960452857133, 0.4752814160014885, 0.47488325216132693, 0.4744851134046951,
    0.4740870001281262, 0.4736889127280771, 0.47329085160092726, 0.47289281714297726, 0.4724948097504479,
    0.47209682981947887, 0.47169887774612773, 0.4713009539263684, 0.4709030587560903, 0.470505192631097,
    0.47010735594710523, 0.4697095490997434, 0.4693117724845505, 0.46891402649697533, 0.4685163115323747,
    0.4681186279860126, 0.46772097625305903, 0.46732335672858866, 0.4669257698075798, 0.4665282158849132,
    0.4661306953553708, 0.4657332086136346, 0.46533575605428545, 0.464938338071802, 0.4645409550605593,
    0.4641436074148279, 0.4637462955287724, 0.4633490197964505, 0.46295178061181175, 0.46255457836869623,
    0.46215741346083367, 0.46176028628184207, 0.4613631972252266, 0.46096614668437835, 0.4605691350525733,
    0.460172162722971, 0.4597752300886136, 0.4593783375424244, 0.458981485477207, 0.45858467428564387,
    0.4581879043602954, 0.45779117609359843, 0.45739448987786546, 0.4569978461052834, 0.45660124516791195,
    0.4562046874576832, 0.4558081733663999, 0.4554117032857343, 0.4550152776072276, 0.4546188967222879,
    0.4542225610221897, 0.4538262708980726, 0.4534300267409399, 0.4530338289416578, 0.4526376778909538,
    0.45224157397941617, 0.45184551759749203, 0.451449509135487, 0.45105354898356326, 0.45065763753173904,
    0.4502617751698871, 0.44986596228773373, 0.44947019927485754, 0.4490744865206883, 0.44867882441450585,
    0.44828321334543886, 0.4478876537024638, 0.44749214587440367, 0.44709669024992704, 0.4467012872175466,
    0.4463059371656183, 0.4459106404823401, 0.4455153975557508, 0.445120208773729, 0.44472507452399174,
    0.44432999519409355, 0.4439349711714254, 0.4435400028432132, 0.4431450905965171, 0.44275023481822995,
    0.4423554358950765, 0.441960694213612, 0.44156601016022123, 0.44117138412111734, 0.44077681648234057,
    0.4403823076297575, 0.4399878579490593, 0.43959346782576125, 0.43919913764520124, 0.4388048677925386,
    0.43841065865275314, 0.4380165106106441, 0.4376224240508288, 0.4372283993577415, 0.4368344369156326,
    0.4364405371085672, 0.4360467003204239, 0.4356529269348943, 0.43525921733548095, 0.434865571905497,
    0.4344719910280648, 0.43407847508611463, 0.4336850244623838, 0.43329163953941546, 0.4328983206995576,
    0.4325050683249616, 0.4321118827975815, 0.43171876449917285, 0.43132571381129114, 0.43093273111529135,
    0.43053981679232634, 0.4301469712233459, 0.4297541947890959, 0.42936148787011663, 0.4289688508467422,
    0.42857628409909926, 0.4281837880071058, 0.4277913629504702, 0.42739900930869, 0.4270067274610509,
    0.4266145177866256, 0.42622238066427276, 0.4258303164726358, 0.425438325590142, 0.42504640839500113,
    0.42465456526520456, 0.4242627965785241, 0.423871102712511, 0.42347948404449465, 0.4230879409515817,
    0.4226964738106549, 0.4223050829983719, 0.4219137688911644, 0.4215225318652368, 0.42113137229656533,
    0.42074029056089696, 0.4203492870337481, 0.41995836209040366, 0.41956751610591614, 0.4191767494551042,
    0.41878606251255185, 0.4183954556526073, 0.4180049292493819, 0.4176144836767489, 0.4172241193083428,
    0.4168338365175577, 0.4164436356775467, 0.41605351716122063, 0.415663481341247, 0.41527352859004896,
    0.41488365927980425, 0.414493873782444, 0.414104172469652, 0.4137145557128631, 0.4133250238832627,
    0.41293557735178543, 0.41254621648911394, 0.41215694166567834, 0.4117677532516545, 0.4113786516169635,
    0.41098963713127035, 0.41060071016398303, 0.41021187108425133, 0.40982312026096585, 0.4094344580627571,
    0.40904588485799415, 0.40865740101478387, 0.40826900690096973, 0.4078807028841309, 0.4074924893315809,
    0.407104366610367, 0.40671633508726873, 0.40632839512879726, 0.40594054710119404, 0.40555279137042993,
    0.40516512830220414, 0.40477755826194317, 0.40439008161479983, 0.4040026987256521, 0.40361540995910217,
    0.4032282156794756, 0.40284111625081986, 0.4024541120369038, 0.40206720340121616, 0.401680390706965,
    0.4012936743170763, 0.40090705459419307, 0.40052053190067455, 0.40013410659859483, 0.39974777904974207,
    0.39936154961561743, 0.39897541865743413, 0.3985893865361162, 0.3982034536122978, 0.39781762024632183,
    0.3974318867982395, 0.3970462536278086, 0.39666072109449313, 0.39627528955746183, 0.3958899593755875,
    0.395504730907446, 0.3951196045113149, 0.39473458054517274, 0.3943496593666983, 0.39396484133326903,
    0.3935801268019605, 0.3931955161295452, 0.3928110096724915, 0.3924266077869631, 0.39204231082881746,
    0.39165811915360516, 0.39127403311656883, 0.3908900530726422, 0.390506179376449, 0.39012241238230216,
    0.3897387524442028, 0.389355199915839, 0.3889717551505854, 0.3885884185015014, 0.38820519032133105,
    0.3878220709625014, 0.3874390607771219, 0.3870561601169835, 0.38667336933355734, 0.386290688777994,
    0.3859081188011227, 0.3855256597534499, 0.3851433119851587, 0.3847610758461079, 0.38437895168583086,
    0.38399693985353456, 0.3836150406980987, 0.3832332545680749, 0.38285158181168544, 0.3824700227768225,
    0.3820885778110474, 0.3817072472615891, 0.38132603147534394, 0.38094493079887415, 0.3805639455784072,
    0.38018307615983493, 0.3798023228887123, 0.3794216861102565, 0.3790411661693466, 0.3786607634105217,
    0.3782804781779807, 0.3779003108155812, 0.3775202616668384, 0.37714033107492423, 0.3767605193826667,
    0.3763808269325486, 0.3760012540667068, 0.37562180112693133, 0.37524246845466436, 0.37486325639099927,
    0.37448416527667994, 0.37410519545209975, 0.37372634725730053, 0.3733476210319716, 0.37296901711544944,
    0.372590535846716, 0.37221217756439823, 0.3718339426067672, 0.3714558313117371, 0.3710778440168643,
    0.37069998105934643, 0.3703222427760219, 0.36994462950336826, 0.36956714157750203, 0.3691897793341773,
    0.3688125431087852, 0.36843543323635275, 0.3680584500515422, 0.3676815938886499, 0.36730486508160576,
    0.36692826396397193, 0.3665517908689424, 0.36617544612934166, 0.3657992300776243, 0.36542314304587376,
    0.3650471853658016, 0.3646713573687467, 0.3642956593856741, 0.36392009174717477, 0.3635446547834639,
    0.3631693488243809, 0.36279417419938786, 0.36241913123756897, 0.3620442202676296, 0.3616694416178958,
    0.36129479561631284, 0.36092028259044473, 0.36054590286747346, 0.3601716567741978, 0.3597975446370328,
    0.35942356678200876, 0.3590497235347705, 0.35867601522057624, 0.3583024421642974, 0.357929004690417,
    0.35755570312302926, 0.3571825377858387, 0.3568095090021594, 0.3564366170949139, 0.3560638623866328,
    0.3556912451994533, 0.355318765855119, 0.35494642467497894, 0.35457422197998656, 0.354202158090699,
    0.3538302333272762, 0.35345844800948045, 0.353086802456675, 0.35271529698782383, 0.35234393192149044,
    0.3519727075758372, 0.3516016242686246, 0.3512306823172102, 0.3508598820385483, 0.35048922374918856,
    0.3501187077652757, 0.3497483344025484, 0.3493781039763387, 0.349008016801571, 0.34863807319276163,
    0.3482682734640176, 0.3478986179290361, 0.34752910690110383, 0.34715974069309585, 0.3467905196174752,
    0.3464214439862917, 0.3460525141111817, 0.3456837303033668, 0.3453150928736535, 0.344946602132432,
    0.3445782583896758, 0.34421006195494097, 0.34384201313736484, 0.34347411224566604, 0.343106359588143,
    0.34273875547267374, 0.34237130020671475, 0.34200399409730053, 0.34163683745104256, 0.34126983057412874,
    0.3409029737723226, 0.34053626735096265, 0.34016971161496123, 0.33980330686880456, 0.33943705341655095,
    0.3390709515618312, 0.3387050016078469, 0.33833920385737026, 0.33797355861274314, 0.33760806617587646,
    0.3372427268482495, 0.33687754093090894, 0.33651250872446836, 0.3361476305291074, 0.3357829066445712,
    0.3354183373701695, 0.335053923004776, 0.33468966384682775, 0.33432556019432413, 0.3339616123448267,
    0.3335978205954577, 0.33323418524290016, 0.3328707065833968, 0.3325073849127492, 0.3321442205263174,
    0.3317812137190191, 0.3314183647853287, 0.3310556740192772, 0.330693141714451, 0.3303307681639913,
    0.32996855366059363, 0.329606498496507, 0.32924460296353314, 0.3288828673530261, 0.3285212919558912,
    0.32815987706258487, 0.32779862296311324, 0.32743752994703235, 0.3270765983034468, 0.3267158283210093,
    0.32635522028791997, 0.32599477449192604, 0.3256344912203205, 0.3252743707599421, 0.3249144133971742,
    0.3245546194179446, 0.3241949891077243, 0.3238355227515275, 0.32347622063391035, 0.3231170830389708,
    0.32275811025034773, 0.32239930255122007, 0.3220406602243068, 0.32168218355186556, 0.32132387281569263,
    0.320965728297122, 0.3206077502770247, 0.32024993903580845, 0.3198922948534165, 0.31953481800932787,
    0.3191775087825558, 0.31882036745164766, 0.3184633942946844, 0.3181065895892794, 0.31774995361257846,
    0.31739348664125905, 0.3170371889515293, 0.31668106081912795, 0.3163251025193232, 0.3159693143269128,
    0.31561369651622256, 0.3152582493611067, 0.31490297313494653, 0.31454786811065005, 0.31419293456065167,
    0.3138381727569112, 0.3134835829709136, 0.313129165473668, 0.31277492053570766, 0.31242084842708884,
    0.31206694941739055, 0.3117132237757139, 0.3113596717706816, 0.3110062936704372, 0.3106530897426447,
    0.3103000602544878, 0.30994720547266963, 0.30959452566341183, 0.30924202109245436, 0.30888969202505456,
    0.3085375387259869, 0.30818556145954223, 0.3078337604895275, 0.3074821360792648, 0.3071306884915911,
    0.30677941798885766, 0.3064283248329295, 0.3060774092851847, 0.30572667160651423, 0.30537611205732096,
    0.3050257308975194, 0.30467552838653517, 0.3043255047833043, 0.3039756603462729, 0.30362599533339646,
    0.30327651000213957, 0.30292720460947514, 0.30257807941188397, 0.3022291346653543, 0.3018803706253812,
    0.3015317875469662, 0.30118338568461656, 0.3008351652923451, 0.3004871266236693, 0.300139269931611,
    0.2997915954686958, 0.29944410348695316, 0.29909679423791463, 0.29874966797261465, 0.2984027249415894,
    0.29805596539487644, 0.2977093895820141, 0.2973629977520412, 0.2970167901534968, 0.29667076703441875,
    0.2963249286423444, 0.29597927522430945, 0.29563380702684755, 0.29528852429599006, 0.2949434272772652,
    0.294598516215698, 0.29425379135580954, 0.2939092529416167, 0.29356490121663137, 0.2932207364238605,
    0.2928767588058051, 0.2925329686044602, 0.29218936606131435, 0.29184595141734876, 0.2915027249130374,
    0.29115968678834636, 0.2908168372827331, 0.2904741766351465, 0.2901317050840263, 0.28978942286730225,
    0.2894473302223942, 0.2891054273862115, 0.28876371459515243, 0.28842219208510395, 0.2880808600914412,
    0.28773971884902705, 0.2873987685922117, 0.2870580095548325, 0.2867174419702131, 0.2863770660711633,
    0.2860368820899787, 0.28569689025844003, 0.285357090807813, 0.28501748396884785, 0.28467806997177897,
    0.28433884904632417, 0.28399982142168484, 0.2836609873265451, 0.28332234698907166, 0.28298390063691337,
    0.28264564849720064, 0.28230759079654555, 0.2819697277610408, 0.28163205961626, 0.2812945865872566,
    0.28095730889856435, 0.28062022677419607, 0.2802833404376439, 0.2799466501118785, 0.27961015601934924,
    0.27927385838198304, 0.2789377574211849, 0.27860185335783677, 0.27826614641229763, 0.2779306368044031,
    0.27759532475346493, 0.2772602104782707, 0.27692529419708367, 0.2765905761276421, 0.2762560564871592,
    0.27592173549232246, 0.27558761335929394, 0.27525369030370916, 0.27491996654067724, 0.2745864422847803,
    0.2742531177500736, 0.2739199931500846, 0.27358706869781313, 0.2732543446057308, 0.27292182108578067,
    0.2725894983493771, 0.27225737660740534, 0.27192545607022134, 0.271593736947651, 0.27126221944899054,
    0.27093090378300566, 0.27059979015793145, 0.2702688787814721, 0.26993816986080044, 0.26960766360255795,
    0.269277360212854, 0.26894725989726614, 0.26861736286083937, 0.2682876693080859, 0.2679581794429851,
    0.26762889346898305, 0.26729981158899213, 0.26697093400539107, 0.26664226092002447, 0.2663137925342024,
    0.26598552904870054, 0.26565747066375933, 0.2653296175790844, 0.26500196999384557, 0.26467452810667724,
    0.26434729211567753, 0.26402026221840874, 0.2636934386118963, 0.26336682149262913, 0.2630404110565591,
    0.26271420749910085, 0.2623882110151316, 0.26206242179899064, 0.2617368400444796, 0.26141146594486164,
    0.26108629969286157, 0.26076134148066565, 0.2604365914999211, 0.26011204994173603, 0.2597877169966792,
    0.2594635928547797, 0.259139677705527, 0.2588159717378703, 0.2584924751402188, 0.25816918810044087,
    0.2578461108058647, 0.2575232434432772, 0.2572005861989244, 0.2568781392585108, 0.25655590280719964,
    0.25623387702961214, 0.255912062109828, 0.2555904582313845, 0.25526906557727674, 0.25494788432995735,
    0.25462691467133614, 0.2543061567827802, 0.2539856108451134, 0.2536652770386165, 0.2533451555430267,
    0.2530252465375379, 0.25270555020079977, 0.25238606671091823, 0.25206679624545525, 0.25174773898142816,
    0.25142889509531013, 0.2511102647630294, 0.2507918481599697, 0.2504736454609696, 0.2501556568403226,
    0.24983788247177702, 0.24952032252853568, 0.24920297718325574, 0.24888584660804886, 0.24856893097448052,
    0.24825223045357053, 0.2479357452157922, 0.24761947543107277, 0.24730342126879296, 0.24698758289778683,
    0.24667196048634193, 0.24635655420219882, 0.24604136421255107, 0.24572639068404534, 0.24541163378278075,
    0.24509709367430943, 0.24478277052363584, 0.24446866449521687, 0.2441547757529618, 0.243841104460232,
    0.24352765077984095, 0.24321441487405426, 0.24290139690458923, 0.24258859703261487, 0.24227601541875204,
    0.24196365222307303, 0.24165150760510168, 0.24133958172381315, 0.24102787473763382, 0.24071638680444135,
    0.24040511808156462, 0.24009406872578315, 0.23978323889332775, 0.2394726287398799, 0.23916223842057188,
    0.2388520680899867, 0.238542117902158, 0.23823238801056995, 0.23792287856815697, 0.23761358972730434,
    0.2373045216398474, 0.23699567445707165, 0.23668704832971305, 0.23637864340795772, 0.23607045984144165,
    0.23576249777925118, 0.23545475736992233, 0.2351472387614414, 0.23483994210124426, 0.23453286753621688,
    0.23422601521269487, 0.23391938527646383, 0.2336129778727588, 0.2333067931462648, 0.2330008312411163,
    0.2326950923008974, 0.232389576468642, 0.23208428388683344, 0.23177921469740453, 0.23147436904173768,
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