Te Mārama ki te Piko me te Kurtosis
He peka nui te tatauranga o te pūtaiao i roto i ngā momo mara rangahau, mai i ngā pūtaiao pāpori ki ngā pūtaiao taiao. I roto i te tātari raraunga, he mea nui te mārama ki te tohatoha raraunga hei whakatau tika me te pono. Ko ngā ariā matua e rua e whakamahia ana hei whakaahua i ngā tohatoha ko te piko me te kurtosis. Ka matapakihia e tēnei tuhinga ngā whakamāramatanga, ngā whakamaoritanga, me te hiranga o te piko me te kurtosis i roto i te tātari raraunga.
Te piko
Te Whakamāramatanga o te Hinga
Ko te piko he ine i te kore taurite o te tohatoha tūponotanga o tētahi taurangi matapōkere. I ngā kupu māmā ake, e whakaahua ana te piko i te tawhiti o te wehenga o te tohatoha raraunga mai i tētahi āhua tino taurite, e mōhiotia ana ko te tohatoha noa, ko te tohatoha Gaussian rānei.
Ngā momo piko
1. Te Piko Pai: He tohatoha raraunga e toro atu ana ki te taha matau. Ko te uara piko pai e tohu ana ko te nuinga o ngā raraunga kei te taha maui, me te hiku matau roa ake. Hei tauira, he maha ngā wā ka whakaatuhia e ngā whiwhinga takitahi o te taupori te piko pai.
2. Te Pikonga Kino: He tohatoha raraunga e piko ana ki te taha maui. I tēnei wā, ko te uara pikonga kino e tohu ana ko te nuinga o ngā raraunga kei te taha matau, me te hiku maui roa ake. Ko tētahi tauira noa ko ngā kaute whakamātautau e whiwhi ana te nuinga o ngā ākonga i ngā kaute teitei.
3. Tohatoha Ā-taurite: Mena he tata te uara piko ki te kore, ka taea te kī he tata te tohatoha raraunga ki te ā-taurite, pērā i te tohatoha noa.
Me pēhea te tatau i te piko
Ka taea te tatau i te piko mā te whakamahi i te tātai e whai ake nei:
\[ \text{Pīrori} = \frac{n}{(n-1)(n-2)} \tapeke \left(\frac{x_i – \bar{x}}{s}\right)^3 \]
Kei hea:
– \( n \) = te maha o ngā raraunga,
– \( x_i \) = uara takitahi,
– \( \bar{x} \) = te toharite o ngā raraunga,
– \( s \) = paerewa rerekētanga.
Te Whakamārama i te Hinga
Mā te whakamārama i ngā uara piko ka āwhina i te mārama ki ngā āhuatanga tohatoha o ngā raraunga. Hei aratohu whānui:
– Ko te piko e tata ana ki te 0 e tohu ana i te tohatoha ōrite.
– Ko te piko pai e tohu ana i te tohatoha e piko ana ki te taha matau.
– Ko te piko kino e tohu ana i te tohatoha e piko ana ki te taha maui.
Te Hiranga o te Hīkoi i roto i te Tātari Raraunga
He taputapu nui te piko i roto i te tātari raraunga nā te mea ka whakaratohia he mōhiohio mō te tohatoha o ngā raraunga kāore e kitea mā te titiro noa ki te toharite, ki te paerewa rerekētanga rānei. Mā te mārama tika ki te piko ka āwhina i te whakatau ko ēhea ngā panonitanga raraunga e tika ana mō ētahi atu tātaritanga, pērā i te whakamahi i ngā logarithm ki ngā raraunga he piko pai teitei.
Kurtosis (Te Kokonga)
Te Whakamāramatanga o Kurtosis
Ko te Kurtosis he ine i te teitei me te koi o ngā tihi o te tohatoha raraunga. Ko te tikanga o tēnei, e pā ana te kurtosis ki te nui o ngā raraunga kei roto i ngā hiku ina whakaritea ki ngā raraunga e tata ana ki te toharite. Mā te Kurtosis ka taea te tautuhi mēnā he momona, he māmā rānei ngā hiku o ngā raraunga ina whakaritea ki te tohatoha noa.
Ngā momo Kurtosis
1. Leptokurtic: He tohatoha he teitei ake te tihi me ngā hiku taumaha atu i te tohatoha noa. He nui ake te uara kurtosis i te 3. He maha ngā wā he nui ake ngā mea o waho o ngā raraunga he tohatoha leptokurtic.
2. Mesokurtic: He tohatoha he rite ngā āhuatanga tihi ki te tohatoha noa. Ko te uara kurtosis he 3. Ko te tohatoha noa tonu he tauira matarohia o te mesokurtic.
3. Platykurtic: He tohatoha he iti ake te tihi me ngā hiku māmā ake i te tohatoha noa. He iti iho te uara kurtosis i te 3. Ko te tohatoha platykurtic e tohu ana he ōrite ake te tohatoha o ngā raraunga puta noa i te whānuitanga o ngā uara.
Me pēhea te tatau i te Kurtosis
Ka taea te tatau i te Kurtosis mā te whakamahi i te tātai e whai ake nei:
\[ \text{Kurtosis} = \frac{n(n+1)}{(n-1)(n-2)(n-3)} \tapeke \left( \frac{x_i – \bar{x}}{s} \right)^4 – \frac{3(n-1)^2}{(n-2)(n-3)} \]
Kei hea:
– \( n \) = te maha o ngā raraunga,
– \( x_i \) = uara takitahi,
– \( \bar{x} \) = te toharite o ngā raraunga,
– \( s \) = paerewa rerekētanga.
Ko te tikanga, ka kiia te kurtosis he 'kurtosis taikaha'. Hei whakangawari, ka whakaitihia te tātai mā te 3 kia mōhio ai he 0 te kurtosis o te tohatoha noa.
Te Whakamārama o Kurtosis
Mā te uara kurtosis ka mārama ki te āhua o te tohatoha raraunga:
– Ko te kurtosis teitei e tohu ana i ngā tihi koi me ngā hiku taumaha.
– Ko te kurtosis iti e tohu ana i te tohatoha papatahi me ngā hiku māmā.
Te Hiranga o Kurtosis i roto i te Tātari Raraunga
Mā te mārama ki te kurtosis ka āwhina i te tautuhi i ngā mea o waho me te whakarite i ngā raraunga mō ētahi atu tātaritanga. Hei tauira, ko ngā raraunga he kurtosis teitei, me whai tikanga pakari ā-pūmau pea hei whakahaere i ngā mea o waho nui rawa.
Whakamahinga Mahi
1. Pūtea: I roto i ngā mākete pūtea, ka whakamahia e ngā kaipupuri moni te piko me te kurtosis hei ine i te mōrearea me te mahi a ngā rawa. Tērā pea he tohu mō te mōrearea nui o te putea he piko kino.
2. Hauora Tūmatanui: I roto i ngā rangahau mate urutā, he maha ngā wā kāore i te noa te tohatoha raraunga. Mā te piko me te kurtosis ka taea te huri i ngā raraunga kia taea ai te whakamahi i roto i ngā tauira whakatauira, i ētahi atu tātaritanga rānei.
3. Mana Kounga: He maha ngā wā ka whakamahia e ngā umanga hangahanga te piko me te kurtosis hei whakahaere i te kounga o te hua. Mēnā he piko nui ngā raraunga whakaputa, tera pea he tohu raruraru kei roto i te tukanga whakaputa.
Whakamutunga
Ko te piko me te kurtosis he tatauranga whakaahua nui e rua mō te tātari i ngā tohatoha raraunga. Mā te piko ka mārama ki te kore taurite o te tohatoha, ko te kurtosis ia e whakaatu ana i te koi me te taumaha o ngā hiku o te tohatoha. Mā te mārama ki ēnei ariā e rua ka hoatu he taputapu tāpiri ki ngā kairangahau me ngā kaitātari raraunga hei whakamārama tika ake i ngā raraunga me te whakatau pai ake i roto i ngā horopaki tono maha.
