OpenTURNS
Monte Carlo simulationΒΆ
Using the probability distribution the probability distribution of a random
vector 
, we seek to evaluate the following probability:
Here, is a random vector, 
the function known as limit state function
which enables the definition of the event 
.
If we have the set 
of 
independent samples of the random vector ,
we can estimate 
as follows:
where 
describes the indicator function equal to 1 if 
and equal to 0 otherwise; the idea here is in fact to estimate the required
probability by the proportion of cases, among the samples of ,
for which the event 
occurs.
By the law of large numbers, we know that this estimation converges to the
required value 
as the sample size tends to infinity.
The Central Limit Theorem allows one to build an asymptotic confidence interval using the normal limit distribution as follows:
![\lim_{\sampleSize\rightarrow\infty}\Prob{P_f\in[\widehat{P}_{f,\inf},\widehat{P}_{f,\sup}]} = \alpha](data:image/svg+xml;base64,<?xml version='1.0' encoding='UTF-8'?>
<!-- This file was generated by dvisvgm 3.4.2 -->
<svg version='1.1' xmlns='http://www.w3.org/2000/svg' xmlns:xlink='http://www.w3.org/1999/xlink' width='163.030934pt' height='21.519522pt' viewBox='112.756013 -22.117157 163.030934 21.519522'>
<defs>
<path id='g6-102' d='M1.522291-3.172105H2.478705V-3.435118H1.498381V-4.335741C1.498381-5.029141 1.888917-5.387796 2.239601-5.387796C2.367123-5.387796 2.438854-5.355915 2.470735-5.347945C2.327273-5.276214 2.287422-5.140722 2.287422-5.037111C2.287422-4.829888 2.438854-4.678456 2.646077-4.678456C2.86127-4.678456 3.004732-4.829888 3.004732-5.037111C3.004732-5.379826 2.669988-5.610959 2.247572-5.610959C1.649813-5.610959 .940473-5.180573 .940473-4.327771V-3.435118H.286924V-3.172105H.940473V-.621669C.940473-.263014 .844832-.263014 .334745-.263014V0C.645579-.02391 1.083935-.02391 1.275218-.02391C1.745455-.02391 1.761395-.02391 2.279452 0V-.263014H2.12005C1.538232-.263014 1.522291-.350685 1.522291-.637609V-3.172105Z'/>
<path id='g6-105' d='M1.554172-4.909589C1.554172-5.140722 1.370859-5.355915 1.107846-5.355915C.876712-5.355915 .669489-5.172603 .669489-4.917559C.669489-4.638605 .900623-4.471233 1.107846-4.471233C1.3868-4.471233 1.554172-4.702366 1.554172-4.909589ZM.358655-3.427148V-3.164134C.868742-3.164134 .940473-3.116314 .940473-2.725778V-.621669C.940473-.263014 .844832-.263014 .334745-.263014V0C.645579-.02391 1.091905-.02391 1.211457-.02391C1.315068-.02391 1.793275-.02391 2.072229 0V-.263014C1.554172-.263014 1.522291-.302864 1.522291-.613699V-3.514819L.358655-3.427148Z'/>
<path id='g6-110' d='M3.873474-2.414944C3.873474-3.084433 3.57061-3.514819 2.733748-3.514819C1.944707-3.514819 1.586052-2.940971 1.490411-2.749689H1.482441V-3.514819L.326775-3.427148V-3.164134C.868742-3.164134 .932503-3.108344 .932503-2.717808V-.621669C.932503-.263014 .836862-.263014 .326775-.263014V0C.669489-.02391 1.020174-.02391 1.235367-.02391C1.466501-.02391 1.801245-.02391 2.14396 0V-.263014C1.633873-.263014 1.538232-.263014 1.538232-.621669V-2.064259C1.538232-2.901121 2.175841-3.291656 2.662017-3.291656S3.267746-2.948941 3.267746-2.446824V-.621669C3.267746-.263014 3.172105-.263014 2.662017-.263014V0C3.004732-.02391 3.355417-.02391 3.57061-.02391C3.801743-.02391 4.136488-.02391 4.479203 0V-.263014C3.969116-.263014 3.873474-.263014 3.873474-.621669V-2.414944Z'/>
<path id='g6-112' d='M2.096139 1.283188C1.586052 1.283188 1.490411 1.283188 1.490411 .924533V-.390535C1.865006 .01594 2.271482 .079701 2.526526 .079701C3.53873 .079701 4.415442-.70137 4.415442-1.721544C4.415442-2.717808 3.610461-3.514819 2.646077-3.514819C2.335243-3.514819 1.872976-3.435118 1.466501-3.020672V-3.514819L.278954-3.427148V-3.164134C.844832-3.164134 .884682-3.116314 .884682-2.781569V.924533C.884682 1.283188 .789041 1.283188 .278954 1.283188V1.546202C.621669 1.522291 .972354 1.522291 1.187547 1.522291C1.41868 1.522291 1.753425 1.522291 2.096139 1.546202V1.283188ZM1.490411-2.654047C1.673724-2.972852 2.072229-3.267746 2.574346-3.267746C3.188045-3.267746 3.706102-2.590286 3.706102-1.721544C3.706102-.804981 3.132254-.143462 2.486675-.143462C2.207721-.143462 1.841096-.263014 1.586052-.661519C1.490411-.797011 1.490411-.804981 1.490411-.956413V-2.654047Z'/>
<path id='g6-115' d='M2.83736-3.347447C2.83736-3.474969 2.83736-3.55467 2.733748-3.55467C2.693898-3.55467 2.669988-3.55467 2.542466-3.427148C2.526526-3.419178 2.454795-3.347447 2.430884-3.347447C2.422914-3.347447 2.406974-3.347447 2.359153-3.379328C2.231631-3.466999 2.000498-3.55467 1.641843-3.55467C.526027-3.55467 .278954-2.948941 .278954-2.566376C.278954-2.16787 .573848-1.936737 .597758-1.912827C.916563-1.673724 1.099875-1.641843 1.633873-1.546202C2.008468-1.474471 2.622167-1.362889 2.622167-.820922C2.622167-.510087 2.414944-.143462 1.681694-.143462C.876712-.143462 .645579-.765131 .541968-1.187547C.510087-1.291158 .502117-1.331009 .406476-1.331009C.278954-1.331009 .278954-1.267248 .278954-1.115816V-.127522C.278954 0 .278954 .079701 .382565 .079701C.430386 .079701 .438356 .071731 .581818-.079701C.621669-.119552 .70934-.223163 .749191-.263014C1.107846 .063761 1.482441 .079701 1.689664 .079701C2.701868 .079701 3.052553-.502117 3.052553-1.028144C3.052553-1.41071 2.82142-1.968618 1.872976-2.14396C1.809215-2.1599 1.362889-2.239601 1.331009-2.239601C1.083935-2.295392 .70934-2.462765 .70934-2.781569C.70934-3.020672 .884682-3.355417 1.641843-3.355417C2.534496-3.355417 2.574346-2.701868 2.590286-2.478705C2.598257-2.414944 2.654047-2.391034 2.709838-2.391034C2.83736-2.391034 2.83736-2.446824 2.83736-2.598257V-3.347447Z'/>
<path id='g6-117' d='M2.662017-3.427148V-3.164134C3.203985-3.164134 3.267746-3.108344 3.267746-2.717808V-1.331009C3.267746-.645579 2.8533-.143462 2.255542-.143462C1.570112-.143462 1.538232-.486177 1.538232-.884682V-3.514819L.326775-3.427148V-3.164134C.932503-3.164134 .932503-3.140224 .932503-2.430884V-1.235367C.932503-.661519 .932503 .079701 2.207721 .079701C2.956912 .079701 3.243836-.494147 3.283686-.565878H3.291656V.079701L4.479203 0V-.263014C3.937235-.263014 3.873474-.318804 3.873474-.70934V-3.514819L2.662017-3.427148Z'/>
<path id='g5-11' d='M5.535243-3.024658C5.535243-4.184309 4.877709-5.272229 3.610461-5.272229C2.044334-5.272229 .478207-3.56264 .478207-1.865006C.478207-.824907 1.123786 .119552 2.343213 .119552C3.084433 .119552 3.969116-.167372 4.817933-.884682C4.985305-.215193 5.355915 .119552 5.869988 .119552C6.515567 .119552 6.838356-.549938 6.838356-.705355C6.838356-.812951 6.75467-.812951 6.718804-.812951C6.623163-.812951 6.611208-.777086 6.575342-.681445C6.467746-.382565 6.192777-.119552 5.905853-.119552C5.535243-.119552 5.535243-.884682 5.535243-1.613948C6.75467-3.072478 7.041594-4.578829 7.041594-4.590785C7.041594-4.698381 6.945953-4.698381 6.910087-4.698381C6.802491-4.698381 6.790535-4.662516 6.742715-4.447323C6.587298-3.921295 6.276463-2.988792 5.535243-2.008468V-3.024658ZM4.782067-1.171606C3.730012-.227148 2.785554-.119552 2.367123-.119552C1.518306-.119552 1.279203-.872727 1.279203-1.43462C1.279203-1.948692 1.542217-3.16812 1.912827-3.825654C2.402989-4.662516 3.072478-5.033126 3.610461-5.033126C4.770112-5.033126 4.770112-3.514819 4.770112-2.510585C4.770112-2.211706 4.758157-1.900872 4.758157-1.601993C4.758157-1.362889 4.770112-1.303113 4.782067-1.171606Z'/>
<path id='g5-59' d='M2.331258 .047821C2.331258-.645579 2.10411-1.159651 1.613948-1.159651C1.231382-1.159651 1.0401-.848817 1.0401-.585803S1.219427 0 1.625903 0C1.78132 0 1.912827-.047821 2.020423-.155417C2.044334-.179328 2.056289-.179328 2.068244-.179328C2.092154-.179328 2.092154-.011955 2.092154 .047821C2.092154 .442341 2.020423 1.219427 1.327024 1.996513C1.195517 2.139975 1.195517 2.163885 1.195517 2.187796C1.195517 2.247572 1.255293 2.307347 1.315068 2.307347C1.41071 2.307347 2.331258 1.422665 2.331258 .047821Z'/>
<path id='g5-80' d='M3.53873-3.801743H5.547198C7.197011-3.801743 8.846824-5.021171 8.846824-6.38406C8.846824-7.316563 8.057783-8.16538 6.551432-8.16538H2.857285C2.630137-8.16538 2.52254-8.16538 2.52254-7.938232C2.52254-7.81868 2.630137-7.81868 2.809465-7.81868C3.53873-7.81868 3.53873-7.723039 3.53873-7.591532C3.53873-7.567621 3.53873-7.49589 3.490909-7.316563L1.876961-.884682C1.769365-.466252 1.745455-.3467 .908593-.3467C.681445-.3467 .561893-.3467 .561893-.131507C.561893 0 .669489 0 .74122 0C.968369 0 1.207472-.02391 1.43462-.02391H2.833375C3.060523-.02391 3.311582 0 3.53873 0C3.634371 0 3.765878 0 3.765878-.227148C3.765878-.3467 3.658281-.3467 3.478954-.3467C2.761644-.3467 2.749689-.430386 2.749689-.549938C2.749689-.609714 2.761644-.6934 2.773599-.753176L3.53873-3.801743ZM4.399502-7.352428C4.507098-7.79477 4.554919-7.81868 5.021171-7.81868H6.204732C7.10137-7.81868 7.84259-7.531756 7.84259-6.635118C7.84259-6.324284 7.687173-5.308095 7.137235-4.758157C6.933998-4.542964 6.360149-4.088667 5.272229-4.088667H3.58655L4.399502-7.352428Z'/>
<path id='g1-16' d='M6.156912 20.897634C6.180822 20.909589 6.288418 21.029141 6.300374 21.029141H6.563387C6.599253 21.029141 6.694894 21.017186 6.694894 20.909589C6.694894 20.861768 6.670984 20.837858 6.647073 20.801993C6.216687 20.371606 5.571108 19.714072 4.829888 18.399004C3.53873 16.103611 3.060523 13.150685 3.060523 10.281445C3.060523 4.97335 4.566874 1.853051 6.659029-.263014C6.694894-.298879 6.694894-.334745 6.694894-.358655C6.694894-.478207 6.611208-.478207 6.467746-.478207C6.312329-.478207 6.288418-.478207 6.180822-.382565C5.045081 .597758 3.765878 2.259527 2.940971 4.782067C2.426899 6.360149 2.15193 8.284932 2.15193 10.269489C2.15193 13.102864 2.666002 16.306849 4.542964 19.080448C4.865753 19.5467 5.308095 20.036862 5.308095 20.048817C5.427646 20.192279 5.595019 20.383562 5.69066 20.467248L6.156912 20.897634Z'/>
<path id='g1-17' d='M4.97335 10.269489C4.97335 6.838356 4.172354 3.19203 1.817186 .502117C1.649813 .310834 1.207472-.155417 .920548-.406476C.836862-.478207 .812951-.478207 .657534-.478207C.537983-.478207 .430386-.478207 .430386-.358655C.430386-.310834 .478207-.263014 .502117-.239103C.908593 .179328 1.554172 .836862 2.295392 2.15193C3.58655 4.447323 4.064757 7.400249 4.064757 10.269489C4.064757 15.458032 2.630137 18.626152 .478207 20.813948C.454296 20.837858 .430386 20.873724 .430386 20.909589C.430386 21.029141 .537983 21.029141 .657534 21.029141C.812951 21.029141 .836862 21.029141 .944458 20.933499C2.080199 19.953176 3.359402 18.291407 4.184309 15.768867C4.710336 14.131009 4.97335 12.194271 4.97335 10.269489Z'/>
<path id='g1-98' d='M3.311582-8.18929L6.563387-6.718804L6.706849-6.981818L3.323537-8.894645L-.059776-6.981818L.071731-6.718804L3.311582-8.18929Z'/>
<path id='g0-80' d='M3.132254-3.682192C3.180075-3.682192 3.431133-3.682192 3.455044-3.670237H3.861519C6.288418-3.670237 7.161146-4.805978 7.161146-5.941719C7.161146-7.639352 5.630884-8.18929 4.088667-8.18929H.597758C.382565-8.18929 .191283-8.18929 .191283-7.974097C.191283-7.770859 .418431-7.770859 .514072-7.770859C1.135741-7.770859 1.183562-7.675218 1.183562-7.089415V-1.099875C1.183562-.514072 1.135741-.418431 .526027-.418431C.406476-.418431 .191283-.418431 .191283-.215193C.191283 0 .382565 0 .597758 0H3.801743C4.016936 0 4.196264 0 4.196264-.215193C4.196264-.418431 3.993026-.418431 3.861519-.418431C3.180075-.418431 3.132254-.514072 3.132254-1.099875V-3.682192ZM5.104857-4.220174C5.487422-4.722291 5.523288-5.475467 5.523288-5.953674C5.523288-6.587298 5.463512-7.220922 5.152677-7.663263C5.810212-7.507846 6.742715-7.149191 6.742715-5.941719C6.742715-5.104857 6.204732-4.495143 5.104857-4.220174ZM3.132254-7.12528C3.132254-7.364384 3.132254-7.770859 3.849564-7.770859C4.710336-7.770859 5.104857-7.44807 5.104857-5.953674C5.104857-4.244085 4.471233-4.100623 3.730012-4.100623H3.132254V-7.12528ZM1.506351-.418431C1.601993-.633624 1.601993-.920548 1.601993-1.075965V-7.113325C1.601993-7.268742 1.601993-7.555666 1.506351-7.770859H2.86924C2.713823-7.579577 2.713823-7.340473 2.713823-7.161146V-1.075965C2.713823-.956413 2.713823-.633624 2.809465-.418431H1.506351Z'/>
<path id='g2-33' d='M6.957908-1.809215C6.686924-1.609963 6.439851-1.354919 6.248568-1.067995C5.905853-.549938 5.818182-.039851 5.818182-.00797C5.818182 .111582 5.929763 .111582 6.001494 .111582C6.089166 .111582 6.160897 .111582 6.184807 .00797C6.39203-.876712 6.902117-1.546202 7.866501-1.872976C7.930262-1.888917 7.994022-1.912827 7.994022-1.992528S7.922291-2.096139 7.890411-2.10411C6.830386-2.462765 6.36812-3.211955 6.200747-3.913325C6.160897-4.072727 6.160897-4.096638 6.001494-4.096638C5.929763-4.096638 5.818182-4.096638 5.818182-3.977086C5.818182-3.961146 5.897883-3.435118 6.248568-2.909091C6.479701-2.574346 6.758655-2.327273 6.957908-2.175841H.773101C.645579-2.175841 .470237-2.175841 .470237-1.992528S.645579-1.809215 .773101-1.809215H6.957908Z'/>
<path id='g2-49' d='M4.303861-2.183811C3.833624-2.749689 3.769863-2.81345 3.490909-3.020672C3.124284-3.299626 2.638107-3.514819 2.11208-3.514819C1.139726-3.514819 .470237-2.662017 .470237-1.713574C.470237-.781071 1.131756 .079701 2.080199 .079701C2.733748 .079701 3.498879-.263014 4.160399-1.251308C4.630635-.68543 4.694396-.621669 4.97335-.414446C5.339975-.135492 5.826152 .079701 6.352179 .079701C7.324533 .079701 7.994022-.773101 7.994022-1.721544C7.994022-2.654047 7.332503-3.514819 6.38406-3.514819C5.730511-3.514819 4.96538-3.172105 4.303861-2.183811ZM4.542964-1.888917C4.845828-2.391034 5.499377-3.211955 6.439851-3.211955C7.292653-3.211955 7.770859-2.438854 7.770859-1.721544C7.770859-.948443 7.181071-.350685 6.479701-.350685S5.308095-.932503 4.542964-1.888917ZM3.921295-1.546202C3.618431-1.044085 2.964882-.223163 2.024408-.223163C1.171606-.223163 .6934-.996264 .6934-1.713574C.6934-2.486675 1.283188-3.084433 1.984558-3.084433S3.156164-2.502615 3.921295-1.546202Z'/>
<path id='g4-59' d='M1.490411-.119552C1.490411 .398506 1.378829 .852802 .884682 1.346949C.852802 1.370859 .836862 1.3868 .836862 1.42665C.836862 1.490411 .900623 1.538232 .956413 1.538232C1.052055 1.538232 1.713574 .908593 1.713574-.02391C1.713574-.533998 1.522291-.884682 1.171606-.884682C.892653-.884682 .73325-.661519 .73325-.446326C.73325-.223163 .884682 0 1.179577 0C1.370859 0 1.490411-.111582 1.490411-.119552Z'/>
<path id='g4-102' d='M3.052553-3.172105H3.793773C3.953176-3.172105 4.048817-3.172105 4.048817-3.323537C4.048817-3.435118 3.945205-3.435118 3.809714-3.435118H3.100374C3.227895-4.152428 3.307597-4.606725 3.387298-4.96538C3.419178-5.100872 3.443088-5.188543 3.56264-5.284184C3.666252-5.371856 3.730012-5.387796 3.817684-5.387796C3.937235-5.387796 4.064757-5.363885 4.168369-5.300125C4.128518-5.284184 4.080697-5.260274 4.040847-5.236364C3.905355-5.164633 3.809714-5.021171 3.809714-4.861768C3.809714-4.678456 3.953176-4.566874 4.128518-4.566874C4.359651-4.566874 4.574844-4.766127 4.574844-5.045081C4.574844-5.419676 4.192279-5.610959 3.809714-5.610959C3.53873-5.610959 3.036613-5.483437 2.781569-4.750187C2.709838-4.566874 2.709838-4.550934 2.494645-3.435118H1.896887C1.737484-3.435118 1.641843-3.435118 1.641843-3.283686C1.641843-3.172105 1.745455-3.172105 1.880946-3.172105H2.446824L1.872976-.079701C1.721544 .72528 1.601993 1.40274 1.179577 1.40274C1.155666 1.40274 .988294 1.40274 .836862 1.307098C1.203487 1.219427 1.203487 .884682 1.203487 .876712C1.203487 .6934 1.060025 .581818 .884682 .581818C.669489 .581818 .438356 .765131 .438356 1.067995C.438356 1.40274 .781071 1.625903 1.179577 1.625903C1.665753 1.625903 2.000498 1.115816 2.10411 .916563C2.391034 .390535 2.574346-.605729 2.590286-.68543L3.052553-3.172105Z'/>
<path id='g4-110' d='M1.594022-1.307098C1.617933-1.42665 1.697634-1.729514 1.721544-1.849066C1.833126-2.279452 1.833126-2.287422 2.016438-2.550436C2.279452-2.940971 2.654047-3.291656 3.188045-3.291656C3.474969-3.291656 3.642341-3.124284 3.642341-2.749689C3.642341-2.311333 3.307597-1.40274 3.156164-1.012204C3.052553-.749191 3.052553-.70137 3.052553-.597758C3.052553-.143462 3.427148 .079701 3.769863 .079701C4.550934 .079701 4.877709-1.036115 4.877709-1.139726C4.877709-1.219427 4.813948-1.243337 4.758157-1.243337C4.662516-1.243337 4.646575-1.187547 4.622665-1.107846C4.431382-.454296 4.096638-.143462 3.793773-.143462C3.666252-.143462 3.602491-.223163 3.602491-.406476S3.666252-.765131 3.745953-.964384C3.865504-1.267248 4.216189-2.183811 4.216189-2.630137C4.216189-3.227895 3.801743-3.514819 3.227895-3.514819C2.582316-3.514819 2.16787-3.124284 1.936737-2.82142C1.880946-3.259776 1.530262-3.514819 1.123786-3.514819C.836862-3.514819 .637609-3.331507 .510087-3.084433C.318804-2.709838 .239103-2.311333 .239103-2.295392C.239103-2.223661 .294894-2.191781 .358655-2.191781C.462267-2.191781 .470237-2.223661 .526027-2.430884C.621669-2.82142 .765131-3.291656 1.099875-3.291656C1.307098-3.291656 1.354919-3.092403 1.354919-2.917061C1.354919-2.773599 1.315068-2.622167 1.251308-2.359153C1.235367-2.295392 1.115816-1.825156 1.083935-1.713574L.789041-.518057C.757161-.398506 .70934-.199253 .70934-.167372C.70934 .01594 .860772 .079701 .964384 .079701C1.107846 .079701 1.227397-.01594 1.283188-.111582C1.307098-.159402 1.370859-.430386 1.41071-.597758L1.594022-1.307098Z'/>
<path id='g3-50' d='M6.551432-2.749689C6.75467-2.749689 6.969863-2.749689 6.969863-2.988792S6.75467-3.227895 6.551432-3.227895H1.482441C1.625903-4.829888 3.000747-5.977584 4.686426-5.977584H6.551432C6.75467-5.977584 6.969863-5.977584 6.969863-6.216687S6.75467-6.455791 6.551432-6.455791H4.662516C2.618182-6.455791 .992279-4.901619 .992279-2.988792S2.618182 .478207 4.662516 .478207H6.551432C6.75467 .478207 6.969863 .478207 6.969863 .239103S6.75467 0 6.551432 0H4.686426C3.000747 0 1.625903-1.147696 1.482441-2.749689H6.551432Z'/>
<path id='g7-61' d='M8.069738-3.873474C8.237111-3.873474 8.452304-3.873474 8.452304-4.088667C8.452304-4.315816 8.249066-4.315816 8.069738-4.315816H1.028144C.860772-4.315816 .645579-4.315816 .645579-4.100623C.645579-3.873474 .848817-3.873474 1.028144-3.873474H8.069738ZM8.069738-1.649813C8.237111-1.649813 8.452304-1.649813 8.452304-1.865006C8.452304-2.092154 8.249066-2.092154 8.069738-2.092154H1.028144C.860772-2.092154 .645579-2.092154 .645579-1.876961C.645579-1.649813 .848817-1.649813 1.028144-1.649813H8.069738Z'/>
<path id='g7-91' d='M2.988792 2.988792V2.546451H1.829141V-8.524035H2.988792V-8.966376H1.3868V2.988792H2.988792Z'/>
<path id='g7-93' d='M1.853051-8.966376H.251059V-8.524035H1.41071V2.546451H.251059V2.988792H1.853051V-8.966376Z'/>
<path id='g7-105' d='M2.080199-7.364384C2.080199-7.675218 1.829141-7.950187 1.494396-7.950187C1.183562-7.950187 .920548-7.699128 .920548-7.376339C.920548-7.017684 1.207472-6.790535 1.494396-6.790535C1.865006-6.790535 2.080199-7.10137 2.080199-7.364384ZM.430386-5.140722V-4.794022C1.195517-4.794022 1.303113-4.722291 1.303113-4.136488V-.884682C1.303113-.3467 1.171606-.3467 .394521-.3467V0C.729265-.02391 1.303113-.02391 1.649813-.02391C1.78132-.02391 2.47472-.02391 2.881196 0V-.3467C2.10411-.3467 2.056289-.406476 2.056289-.872727V-5.272229L.430386-5.140722Z'/>
<path id='g7-108' d='M2.056289-8.296887L.394521-8.16538V-7.81868C1.207472-7.81868 1.303113-7.734994 1.303113-7.149191V-.884682C1.303113-.3467 1.171606-.3467 .394521-.3467V0C.729265-.02391 1.315068-.02391 1.673724-.02391S2.630137-.02391 2.964882 0V-.3467C2.199751-.3467 2.056289-.3467 2.056289-.884682V-8.296887Z'/>
<path id='g7-109' d='M8.571856-2.905106C8.571856-4.016936 8.571856-4.351681 8.296887-4.734247C7.950187-5.200498 7.388294-5.272229 6.981818-5.272229C5.989539-5.272229 5.487422-4.554919 5.296139-4.088667C5.128767-5.009215 4.483188-5.272229 3.730012-5.272229C2.570361-5.272229 2.116065-4.27995 2.020423-4.040847H2.008468V-5.272229L.382565-5.140722V-4.794022C1.195517-4.794022 1.291158-4.710336 1.291158-4.124533V-.884682C1.291158-.3467 1.159651-.3467 .382565-.3467V0C.6934-.02391 1.338979-.02391 1.673724-.02391C2.020423-.02391 2.666002-.02391 2.976837 0V-.3467C2.211706-.3467 2.068244-.3467 2.068244-.884682V-3.108344C2.068244-4.363636 2.893151-5.033126 3.634371-5.033126S4.542964-4.423412 4.542964-3.694147V-.884682C4.542964-.3467 4.411457-.3467 3.634371-.3467V0C3.945205-.02391 4.590785-.02391 4.925529-.02391C5.272229-.02391 5.917808-.02391 6.228643 0V-.3467C5.463512-.3467 5.32005-.3467 5.32005-.884682V-3.108344C5.32005-4.363636 6.144956-5.033126 6.886177-5.033126S7.79477-4.423412 7.79477-3.694147V-.884682C7.79477-.3467 7.663263-.3467 6.886177-.3467V0C7.197011-.02391 7.84259-.02391 8.177335-.02391C8.524035-.02391 9.169614-.02391 9.480448 0V-.3467C8.88269-.3467 8.583811-.3467 8.571856-.705355V-2.905106Z'/>
</defs>
<g id='page1'>
<use x='115.664327' y='-8.368612' xlink:href='#g7-108'/>
<use x='118.915988' y='-8.368612' xlink:href='#g7-105'/>
<use x='122.16765' y='-8.368612' xlink:href='#g7-109'/>
<use x='112.756013' y='-1.195514' xlink:href='#g4-110'/>
<use x='117.894216' y='-1.195514' xlink:href='#g2-33'/>
<use x='126.362581' y='-1.195514' xlink:href='#g2-49'/>
<use x='136.823445' y='-8.368612' xlink:href='#g0-80'/>
<use x='146.121896' y='-21.638962' xlink:href='#g1-16'/>
<use x='153.261808' y='-8.368612' xlink:href='#g5-80'/>
<use x='160.807076' y='-6.575349' xlink:href='#g4-102'/>
<use x='169.572804' y='-8.368612' xlink:href='#g3-50'/>
<use x='180.863772' y='-8.368612' xlink:href='#g7-91'/>
<use x='186.355598' y='-11.39062' xlink:href='#g1-98'/>
<use x='184.115433' y='-8.368612' xlink:href='#g5-80'/>
<use x='191.660701' y='-6.575349' xlink:href='#g4-102'/>
<use x='196.137003' y='-6.575349' xlink:href='#g4-59'/>
<use x='198.489327' y='-6.575349' xlink:href='#g6-105'/>
<use x='200.84165' y='-6.575349' xlink:href='#g6-110'/>
<use x='205.546298' y='-6.575349' xlink:href='#g6-102'/>
<use x='209.261568' y='-8.368612' xlink:href='#g5-59'/>
<use x='216.745892' y='-11.39062' xlink:href='#g1-98'/>
<use x='214.505727' y='-8.368612' xlink:href='#g5-80'/>
<use x='222.050995' y='-6.575349' xlink:href='#g4-102'/>
<use x='226.527296' y='-6.575349' xlink:href='#g4-59'/>
<use x='228.87962' y='-6.575349' xlink:href='#g6-115'/>
<use x='232.219923' y='-6.575349' xlink:href='#g6-117'/>
<use x='236.924571' y='-6.575349' xlink:href='#g6-112'/>
<use x='242.12735' y='-8.368612' xlink:href='#g7-93'/>
<use x='245.379012' y='-21.638962' xlink:href='#g1-17'/>
<use x='255.839742' y='-8.368612' xlink:href='#g7-61'/>
<use x='268.265223' y='-8.368612' xlink:href='#g5-11'/>
</g>
</svg>
<!-- DEPTH=0 -->)
with
and 
is the 
-quantile of the standard normal distribution.
One can also use a convergence indicator that is independent of the confidence
level 
: the coefficient of variation, which is the ratio between the
asymptotic standard deviation of the estimate and its mean value.
It is a relative measure of dispersion given by:
It must be emphasized that these results are asymptotic and as such needs that 
.
The convergence to the standard normal distribution is dominated by the skewness
of
divided by the sample size , it means 
.
In the usual case 
, the distribution is highly skewed and this
term is approximately equal to 
.
A rule of thumb is that if 
with 
, the asymptotic nature of the Central Limit Theorem is not problematic.
(Source code, png)
The method is also referred to as Direct sampling, Crude Monte Carlo method, Classical Monte Carlo integration.