import math
import plotly.express as px
import numpy as np
import pandas as pd
from decimal import Decimal, InvalidOperation
precalced = dict()
def dynamic_factorial(val):
key = ('factorial', val)
try:
if key not in precalced:
precalced[key] = math.factorial(val.as_integer_ratio()[0])
return precalced[key]
except InvalidOperation:
print(val)
def poisson(lmbda, t, k):
key = ('poisson', lmbda, t, k)
if key not in precalced:
mult = Decimal(lmbda * t)
true_k = Decimal(k)
exp = (-mult).exp()
multiplication = Decimal(1) if not mult and not true_k else (mult**true_k)
nominator = multiplication*exp
denominator = dynamic_factorial(true_k)
precalced[key] = nominator / denominator
return precalced[key]
def poisson_sum(lmbda, t, start=0, end=1):
key = ('poisson_sum', lmbda, t, start, end)
if key not in precalced:
precalced[key] = sum(poisson(lmbda, t, k) for k in range(start, end))
return precalced[key]
def probability_func(n, t, lmbda, p, q, r):
key = ('probability_func', n, t, lmbda, p,q, r)
if key not in precalced:
precalced[key] = sum(
poisson_sum(lmbda*q,t,start=0, end=i)
* poisson_sum(lmbda*r,t,start=0, end=i)
* poisson(lmbda * p, t, i)
for i in range(1,n+1)
)
return precalced[key]
data_points = []
time_points = 30
n_points = list(range(1, 150, 20))
hyper_lambda = 16
hyper_p = 0.55
hyper_q = 0.30
hyper_r = 0.15
for t in range(time_points):
for n in n_points:
data_points.append({"t": t, "N": n, "Probabilidad": probability_func(n, t, hyper_lambda, hyper_p, hyper_q, hyper_r)})
df = pd.DataFrame(data_points)
fig = px.line(df, x='t', y='Probabilidad', color='N', title=r"$\text{Grafico de } P(\mathbb{N}_1(t) \geq \mathbb{N}_j(t) ~\forall j \in \{2,3\})\text{ para distintos } n \text{ tal que } n \rightarrow \infty $", line_shape="spline")
fig
data_points = []
time_points = 30
n_points = list(range(1, 150, 20))
hyper_lambda = 16
hyper_p = 0.55
hyper_q = 0.30
hyper_r = 0.15
for t in range(time_points):
for n in n_points:
data_points.append({"t": t, "N": n, "Probabilidad": probability_func(n, t, hyper_lambda, hyper_q, hyper_p, hyper_r)})
df = pd.DataFrame(data_points)
fig = px.line(df, x='t', y='Probabilidad', color='N', title=r"$\text{Grafico de } P(\mathbb{N}_2(t) \geq \mathbb{N}_j(t) ~\forall j \in \{1,3\})\text{ para distintos } n \text{ tal que } n \rightarrow \infty $", line_shape="spline")
fig
data_points = []
time_points = 30
n_points = list(range(1, 150, 20))
hyper_lambda = 16
hyper_p = 0.55
hyper_q = 0.30
hyper_r = 0.15
for t in range(time_points):
for n in n_points:
data_points.append({"t": t, "N": n, "Probabilidad": probability_func(n, t, hyper_lambda, hyper_r, hyper_p, hyper_q)})
df = pd.DataFrame(data_points)
fig = px.line(df, x='t', y='Probabilidad', color='N', title=r"$\text{Grafico de } P(\mathbb{N}_3(t) \geq \mathbb{N}_j(t) ~\forall j \in \{1,2\})\text{ para distintos } n \text{ tal que } n \rightarrow \infty $", line_shape="spline")
fig
Pregunta c
def question_b(lmbda, p, q, r, k, t):
return (
poisson(lmbda * p, t, k)
+ poisson(lmbda * q, t, k)
+ poisson(lmbda * r, t, k)
)
data_points = []
time_points = 100
n_points = list(range(1, 150, 20))
hyper_lambda = 16
hyper_p = 0.55
hyper_q = 0.30
hyper_r = 0.15
for t in range(time_points):
for n in n_points:
data_points.append({"t": t, "k": n, "Probabilidad": question_b(hyper_lambda, hyper_p, hyper_q, hyper_r, n, t)})
df = pd.DataFrame(data_points)
print(data_points)
fig = px.line(df, x='t', y='Probabilidad', color='k', title=r"$\text{Grafico de } \mathbb{N}(t) = \mathbb{N}_1(t) + \mathbb{N}_2(t) + \mathbb{N}_3(t) \text{ para distintos } k $", line_shape="spline")
fig
[{'t': 0, 'k': 1, 'Probabilidad': Decimal('0')}, {'t': 0, 'k': 21, 'Probabilidad': Decimal('0')}, {'t': 0, 'k': 41, 'Probabilidad': Decimal('0')}, {'t': 0, 'k': 61, 'Probabilidad': Decimal('0')}, {'t': 0, 'k': 81, 'Probabilidad': Decimal('0')}, {'t': 0, 'k': 101, 'Probabilidad': Decimal('0')}, {'t': 0, 'k': 121, 'Probabilidad': Decimal('0')}, {'t': 0, 'k': 141, 'Probabilidad': Decimal('0')}, {'t': 1, 'k': 1, 'Probabilidad': Decimal('0.2585523247907263566247447679')}, {'t': 1, 'k': 21, 'Probabilidad': Decimal('0.0002014053706636997695593020038')}, {'t': 1, 'k': 41, 'Probabilidad': Decimal('2.385443820240402844209470457E-15')}, {'t': 1, 'k': 61, 'Probabilidad': Decimal('1.219401924237528936644491095E-30')}, {'t': 1, 'k': 81, 'Probabilidad': Decimal('8.281180714156933882944756975E-49')}, {'t': 1, 'k': 101, 'Probabilidad': Decimal('3.950330372743093655642156078E-69')}, {'t': 1, 'k': 121, 'Probabilidad': Decimal('3.568064297541139177615766622E-91')}, {'t': 1, 'k': 141, 'Probabilidad': Decimal('1.180147337905722090814433138E-114')}, {'t': 2, 'k': 1, 'Probabilidad': Decimal('0.04015338158570306958006896568')}, {'t': 2, 'k': 21, 'Probabilidad': Decimal('0.06421851901923888708144538061')}, {'t': 2, 'k': 41, 'Probabilidad': Decimal('7.906924553663890576917107240E-7')}, {'t': 2, 'k': 61, 'Probabilidad': Decimal('4.238236338254720322216912318E-16')}, {'t': 2, 'k': 81, 'Probabilidad': Decimal('3.018078072728543173067816535E-28')}, {'t': 2, 'k': 101, 'Probabilidad': Decimal('1.509633550821745858372326312E-42')}, {'t': 2, 'k': 121, 'Probabilidad': Decimal('1.429784901057092891579414736E-58')}, {'t': 2, 'k': 141, 'Probabilidad': Decimal('4.958772441602846335743677180E-76')}, {'t': 3, 'k': 1, 'Probabilidad': Decimal('0.005383444332042309492818148873')}, {'t': 3, 'k': 21, 'Probabilidad': Decimal('0.07096402478355052009966321689')}, {'t': 3, 'k': 41, 'Probabilidad': Decimal('0.001976782525326403516286600334')}, {'t': 3, 'k': 61, 'Probabilidad': Decimal('3.523388499265426224652613935E-9')}, {'t': 3, 'k': 81, 'Probabilidad': Decimal('8.343168463061679139807059738E-18')}, {'t': 3, 'k': 101, 'Probabilidad': Decimal('1.387705351554675486378927209E-28')}, {'t': 3, 'k': 121, 'Probabilidad': Decimal('4.370404266414164594060796688E-41')}, {'t': 3, 'k': 141, 'Probabilidad': Decimal('5.040228956203507321800578548E-55')}, {'t': 4, 'k': 1, 'Probabilidad': Decimal('0.0006502839442199039395057422050')}, {'t': 4, 'k': 21, 'Probabilidad': Decimal('0.08349211529207847399728388383')}, {'t': 4, 'k': 41, 'Probabilidad': Decimal('0.03951087818729934993922790038')}, {'t': 4, 'k': 61, 'Probabilidad': Decimal('0.00002220404123101453329598791297')}, {'t': 4, 'k': 81, 'Probabilidad': Decimal('1.657972173660432486232458615E-11')}, {'t': 4, 'k': 101, 'Probabilidad': Decimal('8.695973743915114978636072376E-20')}, {'t': 4, 'k': 121, 'Probabilidad': Decimal('8.636092797635785952140778251E-30')}, {'t': 4, 'k': 141, 'Probabilidad': Decimal('3.140658284377814750786805226E-41')}, {'t': 5, 'k': 1, 'Probabilidad': Decimal('0.00007373145427223256778583419181')}, {'t': 5, 'k': 21, 'Probabilidad': Decimal('0.07687149899390139333085006382')}, {'t': 5, 'k': 41, 'Probabilidad': Decimal('0.05643582849765098126540207148')}, {'t': 5, 'k': 61, 'Probabilidad': Decimal('0.002729929275985762032768522622')}, {'t': 5, 'k': 81, 'Probabilidad': Decimal('1.768059394758443811975605793E-7')}, {'t': 5, 'k': 101, 'Probabilidad': Decimal('8.043370849839443500674560639E-14')}, {'t': 5, 'k': 121, 'Probabilidad': Decimal('6.928471479214444128515327366E-22')}, {'t': 5, 'k': 141, 'Probabilidad': Decimal('2.185451029385693942768145373E-31')}, {'t': 6, 'k': 1, 'Probabilidad': Decimal('0.000008026430265180116549232785597')}, {'t': 6, 'k': 21, 'Probabilidad': Decimal('0.05008144668192467268000761178')}, {'t': 6, 'k': 41, 'Probabilidad': Decimal('0.02124025904361321428772468861')}, {'t': 6, 'k': 61, 'Probabilidad': Decimal('0.02782383267190920833714759903')}, {'t': 6, 'k': 81, 'Probabilidad': Decimal('0.00006908541000629320410002009136')}, {'t': 6, 'k': 101, 'Probabilidad': Decimal('1.204904157548801695014578994E-9')}, {'t': 6, 'k': 121, 'Probabilidad': Decimal('3.979025886515712525607049141E-16')}, {'t': 6, 'k': 141, 'Probabilidad': Decimal('4.811775221784298179558063126E-24')}, {'t': 7, 'k': 1, 'Probabilidad': Decimal('8.494973524305586516924646141E-7')}, {'t': 7, 'k': 21, 'Probabilidad': Decimal('0.05898964574945790477266466740')}, {'t': 7, 'k': 41, 'Probabilidad': Decimal('0.03029990972075488043580421902')}, {'t': 7, 'k': 61, 'Probabilidad': Decimal('0.05086671145037800862711682518')}, {'t': 7, 'k': 81, 'Probabilidad': Decimal('0.002756035827819880060059406472')}, {'t': 7, 'k': 101, 'Probabilidad': Decimal('0.000001049027358940005282622428016')}, {'t': 7, 'k': 121, 'Probabilidad': Decimal('7.560436482687352571925122898E-12')}, {'t': 7, 'k': 141, 'Probabilidad': Decimal('1.995313902718789771006660660E-18')}, {'t': 8, 'k': 1, 'Probabilidad': Decimal('8.807389034365433936117790815E-8')}, {'t': 8, 'k': 21, 'Probabilidad': Decimal('0.08066512130245256868272372393')}, {'t': 8, 'k': 41, 'Probabilidad': Decimal('0.05709886158872276101101211540')}, {'t': 8, 'k': 61, 'Probabilidad': Decimal('0.02661265149403671508189397706')}, {'t': 8, 'k': 81, 'Probabilidad': Decimal('0.02069384250455043604750556214')}, {'t': 8, 'k': 101, 'Probabilidad': Decimal('0.0001138104181193149505396551596')}, {'t': 8, 'k': 121, 'Probabilidad': Decimal('1.185170990456148236938566493E-8')}, {'t': 8, 'k': 141, 'Probabilidad': Decimal('4.519436738790381251320911511E-14')}, {'t': 9, 'k': 1, 'Probabilidad': Decimal('8.988618379005235044454073355E-9')}, {'t': 9, 'k': 21, 'Probabilidad': Decimal('0.08606030889448118599447188534')}, {'t': 9, 'k': 41, 'Probabilidad': Decimal('0.05879814834908584337950978443')}, {'t': 9, 'k': 61, 'Probabilidad': Decimal('0.007239160651414770864184349438')}, {'t': 9, 'k': 81, 'Probabilidad': Decimal('0.04339152278270634769811430489')}, {'t': 9, 'k': 101, 'Probabilidad': Decimal('0.002516490790162002832170406492')}, {'t': 9, 'k': 121, 'Probabilidad': Decimal('0.000002763406584402260043772234973')}, {'t': 9, 'k': 141, 'Probabilidad': Decimal('1.111216127943860079029366547E-10')}, {'t': 10, 'k': 1, 'Probabilidad': Decimal('9.060322906953913363663575771E-10')}, {'t': 10, 'k': 21, 'Probabilidad': Decimal('0.07129498476096624163939486839')}, {'t': 10, 'k': 41, 'Probabilidad': Decimal('0.03677282383042606290736090263')}, {'t': 10, 'k': 61, 'Probabilidad': Decimal('0.01058409326607602984027036573')}, {'t': 10, 'k': 81, 'Probabilidad': Decimal('0.03326732907010143905507083352')}, {'t': 10, 'k': 101, 'Probabilidad': Decimal('0.01586757104350163580464364345')}, {'t': 10, 'k': 121, 'Probabilidad': Decimal('0.0001433209588879014107013949010')}, {'t': 10, 'k': 141, 'Probabilidad': Decimal('4.740381170098611526475956897E-8')}, {'t': 11, 'k': 1, 'Probabilidad': Decimal('9.041273452239731049141014685E-11')}, {'t': 11, 'k': 21, 'Probabilidad': Decimal('0.04785941100808936221049066075')}, {'t': 11, 'k': 41, 'Probabilidad': Decimal('0.01686398535457669975157281958')}, {'t': 11, 'k': 61, 'Probabilidad': Decimal('0.02784849951076358980737165951')}, {'t': 11, 'k': 81, 'Probabilidad': Decimal('0.01136666351212678091496250372')}, {'t': 11, 'k': 101, 'Probabilidad': Decimal('0.03625602818907510969517083609')}, {'t': 11, 'k': 121, 'Probabilidad': Decimal('0.002203094714455073827700500750')}, {'t': 11, 'k': 141, 'Probabilidad': Decimal('0.000004902193286838380776021159600')}, {'t': 12, 'k': 1, 'Probabilidad': Decimal('8.947699884130713486650639642E-12')}, {'t': 12, 'k': 21, 'Probabilidad': Decimal('0.02699091052318714253893588678')}, {'t': 12, 'k': 41, 'Probabilidad': Decimal('0.01069345574502287217575627864')}, {'t': 12, 'k': 61, 'Probabilidad': Decimal('0.04622876828091339406198991902')}, {'t': 12, 'k': 81, 'Probabilidad': Decimal('0.002613251620973021744479052857')}, {'t': 12, 'k': 101, 'Probabilidad': Decimal('0.03582896052296300482120835678')}, {'t': 12, 'k': 121, 'Probabilidad': Decimal('0.01240673755239111697430838258')}, {'t': 12, 'k': 141, 'Probabilidad': Decimal('0.0001573207744099749302168809002')}, {'t': 13, 'k': 1, 'Probabilidad': Decimal('8.793601051471074009651312913E-13')}, {'t': 13, 'k': 21, 'Probabilidad': Decimal('0.01314966694250449459480097377')}, {'t': 13, 'k': 41, 'Probabilidad': Decimal('0.01629436246797543674528016651')}, {'t': 13, 'k': 61, 'Probabilidad': Decimal('0.05020956137482882213913164688')}, {'t': 13, 'k': 81, 'Probabilidad': Decimal('0.003714988885797023125555929144')}, {'t': 13, 'k': 101, 'Probabilidad': Decimal('0.01751691949239000977756191801')}, {'t': 13, 'k': 121, 'Probabilidad': Decimal('0.03006637101280148121021601820')}, {'t': 13, 'k': 141, 'Probabilidad': Decimal('0.001889955668643827443333779051')}, {'t': 14, 'k': 1, 'Probabilidad': Decimal('8.591019116971189551918339054E-14')}, {'t': 14, 'k': 21, 'Probabilidad': Decimal('0.005655699468649857876808173430')}, {'t': 14, 'k': 41, 'Probabilidad': Decimal('0.02921607496315708029214166058')}, {'t': 14, 'k': 61, 'Probabilidad': Decimal('0.03797567019788690284383547354')}, {'t': 14, 'k': 81, 'Probabilidad': Decimal('0.01173668199932715983107974977')}, {'t': 14, 'k': 101, 'Probabilidad': Decimal('0.004727363541990355961141306738')}, {'t': 14, 'k': 121, 'Probabilidad': Decimal('0.03553335968019374871998104053')}, {'t': 14, 'k': 141, 'Probabilidad': Decimal('0.009833328141823739873099679424')}, {'t': 15, 'k': 1, 'Probabilidad': Decimal('8.350282188876853671658184211E-15')}, {'t': 15, 'k': 21, 'Probabilidad': Decimal('0.002184777709457107315103604298')}, {'t': 15, 'k': 41, 'Probabilidad': Decimal('0.04462659191571377693499497936')}, {'t': 15, 'k': 61, 'Probabilidad': Decimal('0.02105649795936765182136330792')}, {'t': 15, 'k': 81, 'Probabilidad': Decimal('0.02579436051834225843156140002')}, {'t': 15, 'k': 101, 'Probabilidad': Decimal('0.0009753162580687809948555951496')}, {'t': 15, 'k': 121, 'Probabilidad': Decimal('0.02261494543129384053419609932')}, {'t': 15, 'k': 141, 'Probabilidad': Decimal('0.02487273755626115592387051772')}, {'t': 16, 'k': 1, 'Probabilidad': Decimal('8.080218768682072909604859718E-16')}, {'t': 16, 'k': 21, 'Probabilidad': Decimal('0.0007686058666447779118192073052')}, {'t': 16, 'k': 41, 'Probabilidad': Decimal('0.05705100042900763309983839341')}, {'t': 16, 'k': 61, 'Probabilidad': Decimal('0.009048432568267367791838977612')}, {'t': 16, 'k': 81, 'Probabilidad': Decimal('0.03955760831513378588946101751')}, {'t': 16, 'k': 101, 'Probabilidad': Decimal('0.001316664263982633714898399463')}, {'t': 16, 'k': 121, 'Probabilidad': Decimal('0.008396862002431389758416599783')}, {'t': 16, 'k': 141, 'Probabilidad': Decimal('0.03357238342936326038350569834')}, {'t': 17, 'k': 1, 'Probabilidad': Decimal('7.788347156271314618636798320E-17')}, {'t': 17, 'k': 21, 'Probabilidad': Decimal('0.0002490603830074535079780393287')}, {'t': 17, 'k': 41, 'Probabilidad': Decimal('0.06214765171308503206330641392')}, {'t': 17, 'k': 61, 'Probabilidad': Decimal('0.003614733863227153845060706995')}, {'t': 17, 'k': 81, 'Probabilidad': Decimal('0.04418353821019043400088688064')}, {'t': 17, 'k': 101, 'Probabilidad': Decimal('0.004660626929296893850551285634')}, {'t': 17, 'k': 121, 'Probabilidad': Decimal('0.001950571671916555887665122684')}, {'t': 17, 'k': 141, 'Probabilidad': Decimal('0.02609582941163509541424810132')}, {'t': 18, 'k': 1, 'Probabilidad': Decimal('7.481042613787243802511154014E-18')}, {'t': 18, 'k': 21, 'Probabilidad': Decimal('0.00007504005665830698851470574579')}, {'t': 18, 'k': 41, 'Probabilidad': Decimal('0.05873314296416167913634985373')}, {'t': 18, 'k': 61, 'Probabilidad': Decimal('0.002775847482815612504941519005')}, {'t': 18, 'k': 81, 'Probabilidad': Decimal('0.03726989766278988386153148873')}, {'t': 18, 'k': 101, 'Probabilidad': Decimal('0.01231767556790791997574582033')}, {'t': 18, 'k': 121, 'Probabilidad': Decimal('0.0003721675943234682997247128832')}, {'t': 18, 'k': 141, 'Probabilidad': Decimal('0.01244244055193148042273095487')}, {'t': 19, 'k': 1, 'Probabilidad': Decimal('7.163684785266324936995628122E-19')}, {'t': 19, 'k': 21, 'Probabilidad': Decimal('0.00002118797293726854196157263975')}, {'t': 19, 'k': 41, 'Probabilidad': Decimal('0.04889914488925765501263922006')}, {'t': 19, 'k': 61, 'Probabilidad': Decimal('0.005046335995211763491373002362')}, {'t': 19, 'k': 81, 'Probabilidad': Decimal('0.02447506461892157385676642803')}, {'t': 19, 'k': 101, 'Probabilidad': Decimal('0.02385047641915768242171479681')}, {'t': 19, 'k': 121, 'Probabilidad': Decimal('0.0004709462756392216744017552176')}, {'t': 19, 'k': 141, 'Probabilidad': Decimal('0.003836910697590478641260122240')}, {'t': 20, 'k': 1, 'Probabilidad': Decimal('6.840787597156488510189039424E-20')}, {'t': 20, 'k': 21, 'Probabilidad': Decimal('0.000005643999179150871812230647586')}, {'t': 20, 'k': 41, 'Probabilidad': Decimal('0.03633512658443256333944681848')}, {'t': 20, 'k': 61, 'Probabilidad': Decimal('0.01012745926009554638142630579')}, {'t': 20, 'k': 81, 'Probabilidad': Decimal('0.01284141520703755084305954755')}, {'t': 20, 'k': 101, 'Probabilidad': Decimal('0.03489789639179929991026095041')}, {'t': 20, 'k': 121, 'Probabilidad': Decimal('0.001798569023807739379372267252')}, {'t': 20, 'k': 141, 'Probabilidad': Decimal('0.0008034561468067580778535340397')}, {'t': 21, 'k': 1, 'Probabilidad': Decimal('6.516113621867173655772463527E-21')}, {'t': 21, 'k': 21, 'Probabilidad': Decimal('0.000001426446427999245986866531444')}, {'t': 21, 'k': 41, 'Probabilidad': Decimal('0.02436582841627417512412984541')}, {'t': 21, 'k': 61, 'Probabilidad': Decimal('0.01796576035990502351405201139')}, {'t': 21, 'k': 81, 'Probabilidad': Decimal('0.005515611492554620774224966441')}, {'t': 21, 'k': 101, 'Probabilidad': Decimal('0.03965563787899641462292664076')}, {'t': 21, 'k': 121, 'Probabilidad': Decimal('0.005415912101666341302690767407')}, {'t': 21, 'k': 141, 'Probabilidad': Decimal('0.0001443116698883962971997917656')}, {'t': 22, 'k': 1, 'Probabilidad': Decimal('6.192774669473874034881474985E-22')}, {'t': 22, 'k': 21, 'Probabilidad': Decimal('3.437318829429955036233051281E-7')}, {'t': 22, 'k': 41, 'Probabilidad': Decimal('0.01488720794086724792537241361')}, {'t': 22, 'k': 61, 'Probabilidad': Decimal('0.02782452062634813710385559835')}, {'t': 22, 'k': 81, 'Probabilidad': Decimal('0.002028233854346002539222839966')}, {'t': 22, 'k': 101, 'Probabilidad': Decimal('0.03582889671743110751754472067')}, {'t': 22, 'k': 121, 'Probabilidad': Decimal('0.01240674289738097293665094822')}, {'t': 22, 'k': 141, 'Probabilidad': 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Decimal('3.678309088036867553233887326E-10')}, {'t': 95, 'k': 1, 'Probabilidad': Decimal('2.181689658681489556897602984E-97')}, {'t': 95, 'k': 21, 'Probabilidad': Decimal('6.153837181158548473490860910E-70')}, {'t': 95, 'k': 41, 'Probabilidad': Decimal('1.354434252564358902564220538E-52')}, {'t': 95, 'k': 61, 'Probabilidad': Decimal('1.286409115078318743995723353E-39')}, {'t': 95, 'k': 81, 'Probabilidad': Decimal('1.623184891716579298934007300E-29')}, {'t': 95, 'k': 101, 'Probabilidad': Decimal('1.438641700464742603671399625E-21')}, {'t': 95, 'k': 121, 'Probabilidad': Decimal('2.414323132743474493201753963E-15')}, {'t': 95, 'k': 141, 'Probabilidad': Decimal('1.483687547757204874523009256E-10')}, {'t': 96, 'k': 1, 'Probabilidad': Decimal('2.000017723435110648367425834E-98')}, {'t': 96, 'k': 21, 'Probabilidad': Decimal('6.955677338571132072738917412E-71')}, {'t': 96, 'k': 41, 'Probabilidad': Decimal('1.887573664471239533308680348E-53')}, {'t': 96, 'k': 61, 'Probabilidad': Decimal('2.210434472375841690666499799E-40')}, {'t': 96, 'k': 81, 'Probabilidad': Decimal('3.438896324536373667004114188E-30')}, {'t': 96, 'k': 101, 'Probabilidad': Decimal('3.757995804076395112250512819E-22')}, {'t': 96, 'k': 121, 'Probabilidad': Decimal('7.775916651849168050268889218E-16')}, {'t': 96, 'k': 141, 'Probabilidad': Decimal('5.891843574931823012859789917E-11')}, {'t': 97, 'k': 1, 'Probabilidad': Decimal('1.833274885210468765334071671E-99')}, {'t': 97, 'k': 21, 'Probabilidad': Decimal('7.844101358965680680071741236E-72')}, {'t': 97, 'k': 41, 'Probabilidad': Decimal('2.618892688253998670428629579E-54')}, {'t': 97, 'k': 61, 'Probabilidad': Decimal('3.773127345513619195208787166E-41')}, {'t': 97, 'k': 81, 'Probabilidad': Decimal('7.221924198530788629176314214E-31')}, {'t': 97, 'k': 101, 'Probabilidad': Decimal('9.709573601904120246590099043E-23')}, {'t': 97, 'k': 121, 'Probabilidad': Decimal('2.471755383393138407650107824E-16')}, {'t': 97, 'k': 141, 'Probabilidad': Decimal('2.304173218246697760066033138E-11')}, {'t': 98, 'k': 1, 'Probabilidad': Decimal('1.680254912320741490472036413E-100')}, {'t': 98, 'k': 21, 'Probabilidad': Decimal('8.826278162436774977000607654E-73')}, {'t': 98, 'k': 41, 'Probabilidad': Decimal('3.617753272539262528510758586E-55')}, {'t': 98, 'k': 61, 'Probabilidad': Decimal('6.398962036384476052793013924E-42')}, {'t': 98, 'k': 81, 'Probabilidad': Decimal('1.503653691091815359573998954E-31')}, {'t': 98, 'k': 101, 'Probabilidad': Decimal('2.481886322405560030904529594E-23')}, {'t': 98, 'k': 121, 'Probabilidad': Decimal('7.756647308679275513765327114E-17')}, {'t': 98, 'k': 141, 'Probabilidad': Decimal('8.877087669861246062189393936E-12')}, {'t': 99, 'k': 1, 'Probabilidad': Decimal('1.539846875344039638264399052E-101')}, {'t': 99, 'k': 21, 'Probabilidad': Decimal('9.909742065865554023588158559E-74')}, {'t': 99, 'k': 41, 'Probabilidad': Decimal('4.976294377900511558600584411E-56')}, {'t': 99, 'k': 61, 'Probabilidad': Decimal('1.078348231062145127562243212E-42')}, {'t': 99, 'k': 81, 'Probabilidad': Decimal('3.104414472787374134350624722E-32')}, {'t': 99, 'k': 101, 'Probabilidad': Decimal('6.277636121155053533010554244E-24')}, {'t': 99, 'k': 121, 'Probabilidad': Decimal('2.403646934722577555984835179E-17')}, {'t': 99, 'k': 141, 'Probabilidad': Decimal('3.370152226905245186883258078E-12')}]
import random
import statistics
random.seed(16624823)
staying = 0.45
moving = 0.35
falling = 0.2
def simulate(prob_staying, prob_moving, prob_falling, boxes, iterations, max_seconds=math.inf):
outcomes = []
for _ in range(iterations):
on_tempered = True
steps_taken = 0
seconds_passed = 0
while on_tempered and steps_taken < boxes and seconds_passed < max_seconds:
choice, *_ = random.choices(["stay", "move", "fall"],[prob_staying, prob_moving, prob_falling], k=1)
if choice == "move":
steps_taken += 1
elif choice == "fall":
on_tempered = False
steps_taken += 1
seconds_passed += 1
outcomes.append(steps_taken)
return outcomes
simulation = simulate(staying, moving, falling, 25, 10000)
print("Promedio de casilla", statistics.mean(simulation))
print("Proporción personas que llegan a una casilla k>=13", (len(list(filter(lambda steps: steps >= 13, simulation))) / len(simulation))*100)
simulation2 = simulate(staying, moving, falling, 25, 10000, max_seconds=60)
print("Casilla mas probable despues de 60 segundos transcurridos:", sorted(simulation2, key=lambda steps: simulation2.count(steps), reverse=True)[0])
sorted(simulation2, key=lambda steps: simulation2.count(steps), reverse=True)
Promedio de casilla 2.754
Proporción personas que llegan a una casilla k>=13 0.5700000000000001
Casilla mas probable despues de 60 segundos transcurridos: 1
def simulate_dynamic(prob_staying, prob_moving, prob_falling, boxes, iterations, lmbda, max_seconds=math.inf, hard_break_step=None):
outcomes = []
for _ in range(iterations):
on_tempered = True
steps_taken = 0
seconds_passed = 0
if not hard_break_step:
hard_break_step = boxes
while on_tempered and steps_taken < hard_break_step and seconds_passed < max_seconds:
lambda_k = lmbda * steps_taken
dyn_staying = prob_staying + lambda_k
dyn_moving = prob_moving - lambda_k/2
dyn_falling = prob_falling - lambda_k/2
choice, *_ = random.choices(["stay", "move", "fall"],[dyn_staying, dyn_moving, dyn_falling], k=1)
if choice == "move":
steps_taken += 1
elif choice == "fall":
on_tempered = False
steps_taken += 1
seconds_passed += 1
outcomes.append(steps_taken)
return outcomes
from functools import partial
def to_prob_of_reaching(simulation, k):
hits = sum(filter(lambda outcome: outcome >= k, simulation))
total = len(simulation)
return hits/total
values = []
partial_sim = partial(simulate_dynamic, staying, moving, falling, 25, 10000, hard_break_step=13)
for pre_lmbda in range(0, int(0.1/0.01)):
calculated_lmbda = pre_lmbda*0.01
for max_seconds in range(0, 300):
values.append([calculated_lmbda, max_seconds, to_prob_of_reaching(partial_sim(calculated_lmbda, max_seconds=max_seconds), k=13)])
df = pd.DataFrame(np.array(values), columns=['Lambda','t', 'Probabilidad'])
fig = px.line(df, x='t', y='Probabilidad',color='Lambda', title=r"$\text{Grafico de probabilidad de que lleguen a la casilla } k=13$", line_shape="linear")
fig