Te Tohatoha Noa: Te Ariā me ngā Taupānga o te Ao Tūturu
Ko te tohatoha noa, e mōhiotia whānuitia ana ko te tohatoha Gaussian, tētahi o ngā ariā tino taketake o te tatauranga me te pāngarau. He maha ngā tono mahi a tēnei i roto i ngā momo marautanga pēnei i te ōhanga, te hinengaro, te hangarau, me ngā pūtaiao taiao. Ka matapakihia e tēnei tuhinga te tohatoha noa, ōna āhuatanga, tōna tātai pāngarau, me ngā tauira rerekē o ōna tono i roto i te oranga o ia rā.
He aha te Tohatoha Noa?
Ko te tohatoha noa he tohatoha tūponotanga āhua pere, he ōrite te āhua (e mōhiotia ana ko te 'āhua pere'). E whakaahua ana tēnei tohatoha i te tohatoha o ngā uara raraunga rerekē huri noa i te toharite (toharite). I roto i te tohatoha noa, ka puta pinepine ake ngā raraunga e tata ana ki te toharite i ngā raraunga e tawhiti ana i te toharite.
He maha ngā āhuatanga matua o te tohatoha noa:
1. Āhua ōrite: He ōrite te kauwhata tohatoha noa, ko te toharite kei waenganui. Ko te tikanga tēnei kei raro iho i te toharite te haurua o ngā uara raraunga, ā, kei runga ake i te toharite te haurua.
2. He ōrite te toharite, te tau waenga, me te aratau: I roto i te tohatoha noa, kei te pūwāhi kotahi te toharite, te tau waenga, me te aratau.
3. Āhua Pere: He āhua pere te kauwhata tohatoha noa, ā, ka heke haere i te taupū ki te tuaka-x i ngā taha e rua o te toharite.
4. Ngā Tino Tapeke: He tino onge ngā uara e tawhiti ana i te toharite (ngā tino tapeke) ki te whakataurite ki ngā uara e tata ana ki te toharite.
Tātai Tohatoha Noa
Mā te pāngarau, ka whakaatuhia te tohatoha noa e te mahi kiato tūponotanga e whai ake nei:
\[ f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x – \mu)^2}{2\sigma^2}} \]
Kei hea:
– Ko te mahi tūponotanga kiato te \( f(x) \) .
– Ko te \( \mu \) te toharite, te toharite rānei o ngā raraunga.
– Ko te \( \sigma \) te paerewa rerekētanga, e ine ana i te horapa o ngā raraunga.
– Ko \( e \) te pūtake o te logarithm maori, tata ki te 2.718.
– Ko te pi pūmau ko \( \pi \), tata ki te 3.14159.
Ka taea hoki te whakaatu i te tohatoha noa i roto i te āhua paerewa, i te āhua 'paerewa noa' rānei, me te toharite 0 me te paerewa rerekētanga 1. Ka tohua tēnei mā te tuhi \( N(0, 1) \).
Ngā Āhuatanga o te Tohatoha Noa
1. Ture Whakamātautau
Ko te ture empirika he tikanga e whakamahia ana hei mārama ki te tohatoha noa. E whakamārama ana tēnei ture i te tohatoha o ngā raraunga i roto i te tohatoha noa huri noa i te toharite:
– Tata ki te 68% o ngā raraunga kei roto i te kotahi paerewa rerekētanga o te toharite (\( \mu \pm \sigma \)).
– Tata ki te 95% o ngā raraunga kei roto i ngā paerewa rerekētanga e rua o te toharite (\( \mu \pm 2\sigma \)).
– Tata ki te 99.7% o ngā raraunga kei roto i ngā paerewa rerekētanga e toru o te toharite (\( \mu \pm 3\sigma \)).
2. Kaute-Z
Ko te kaute-Z he ine i te maha o ngā paerewa rerekētanga o tētahi huinga raraunga mai i te toharite. Ka tatauhia mā te wehewehe i te rerekētanga i waenga i te raraunga me te toharite ki te paerewa rerekētanga. Mā te kaute-Z ka āwhina i te whakatau i te tūranga o te raraunga i roto i te tohatoha noa.
\[ Z = \frac{(X – \mu)}{\sigma} \]
Ko \( X \) te uara raraunga ine, ko \( \mu \) te toharite, ā, ko \( \sigma \) te paerewa rerekētanga.
3. Piko Pere
He whakaaturanga ā-kanohi te kōpiko pere o tētahi tohatoha noa. Kei te toharite te tihi, te pūwāhi teitei rānei, o te kōpiko, ā, ka heke ōrite te kōpiko i ngā taha e rua mai i te toharite, ka hanga he āhua pere.
Ngā Whakamahinga o te Tohatoha Noa i te Ao Tūturu
1. Ngā Tatauranga me te Tātari Raraunga
E whakamahia whānuitia ana te tohatoha noa i roto i ngā tatauranga mō te tātari raraunga. He maha ngā tikanga tatauranga e whakawhirinaki ana ki te whakaaro ka whai, ka tata rānei ngā raraunga ki tētahi tohatoha noa. Kei roto i ēnei ko te whakamātautau whakapae, ngā wā whakawhirinaki, me te tātari whakatauira.
2. Te Hinengaro me ngā Pūtaiao Pāpori
I roto i te hinengaro, ka whakamahia te tohatoha noa hei whakaahua i te tohatoha o ngā āhuatanga tangata, pērā i ngā kaute IQ, te teitei, me ērā atu mea. He maha ngā whakamātautau hinengaro ine kua hangaia me te whakaaro ka whai ngā hua o te whakamātautau i te tohatoha noa.
3. Ōhanga me te Pakihi
Ka whakamahia e ngā kaipūtea me ngā kaitātari pakihi te tohatoha noa hei whakatauira i ngā āhuatanga ōhanga maha pērā i ngā hokinga mai o ngā hea, ngā moni whiwhi, me ngā whakapaunga. Ka āwhina tēnei tohatoha i te aromatawai mōrearea me te whakatau kaupapa.
4. Te Hangarau me ngā Pūtaiao Taiao
I roto i te hangarau me ngā pūtaiao taiao, ka whakamahia te tohatoha noa hei tātari me te matapae i ngā putanga o ngā tukanga taiao me ngā tukanga hanga-tangata. Hei tauira, i roto i te whakahaere kounga, ka āwhina te tohatoha noa ki te whakatau mena ka tutuki i tētahi hua ngā paerewa kounga.
5. Te Tūponotanga me te Whakataunga
He whai hua te tohatoha noa i roto i te ariā tūponotanga me te whakatau kaupapa. Ko ngā tikanga pēnei i te tātari Monte Carlo e whakamahi ana i te tohatoha noa hei whakahaere i ngā whakatauira hei āwhina i te matapae me te whakamahere.
Whakamutunga
Ko te tohatoha noa tētahi o ngā ariā tino taketake me te whai hua i roto i ngā tatauranga me te maha atu o ngā mara. Mā te mārama ki tēnei tohatoha ka taea e tātou te tukatuka me te tātari raraunga me te whakamahi i tēnei mōhiotanga ki ngā momo tono mahi. Ahakoa i roto i te ine hinengaro, te tātari pakihi, te whakahaere kounga ahumahi rānei, ka whakaratohia e te tohatoha noa he turanga pakari mō te mārama me te matapae i ngā āhuatanga o te ao tūturu.
