Kugoverwa Kwakajairika: Pfungwa uye Mashandisirwo Enyika Chaiyo
Kugoverwa kwakajairika, kunowanzozivikanwa seGaussian distribution, ndeimwe yepfungwa dzakakosha muhuwandu hwezviverengero nemasvomhu. Ine mashandisirwo akawanda anoshanda muzvikamu zvakasiyana-siyana zvakaita sehupfumi, zvepfungwa, zveinjiniya, uye zvesainzi yechisikigo. Chinyorwa chino chichakurukura kugoverwa kwakajairika, hunhu hwayo, fomura yayo yemasvomhu, uye mienzaniso yakasiyana-siyana yekushandiswa kwayo muhupenyu hwezuva nezuva.
Chii chinonzi Normal Distribution?
Kugoverwa kwakajairika kugoverwa kwakaenzana, kwakaumbwa sebhero (kunozivikanwa se'chimiro chebhero'). Kugoverwa uku kunotsanangura kuti data values dzakasiyana dzinoparadzirwa sei kutenderedza avhareji (avhareji). Mukugoverwa kwakajairika, data riri pedyo neavhareji rinowanzoitika kakawanda kupfuura data riri kure neavhareji.
Kune zvinhu zvakawanda zvikuru zvinoitwa pakugoverwa kwakajairika:
1. Symmetric: Girafu yekugovera yakajairika inoenzana neavhareji iri pakati. Izvi zvinoreva kuti hafu yedata values iri pasi peavhareji, uye hafu iri pamusoro peavhareji.
2. Avhareji, Pakati, uye Modhi zvakafanana: Mukusaradzaniswa kwakajairika, avhareji, pakati, uye modhi zviri panzvimbo imwe chete.
3. Chimiro cheBheri: Girafu yekugovera yakajairika yakaita sebhero uye inodzikira zvakanyanya kuenda ku-x-axis kumativi ese epakati.
4. Kuderera Kwepfungwa: Hunhu huri kure nepakati (hunonyanya kuoneka) hushoma kana tichienzanisa nehunhu huri pedyo nepakati.
Fomura Yekugovera Yakajairika
Pamasvomhu, kugoverwa kwakajairika kunoratidzwa nebasa rinotevera rehuwandu hwehuwandu:
\[ f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x – \mu)^2}{2\sigma^2}} \]
Di mana:
– \( f(x) \) ibasa rekuwedzera mukana wehuwandu hwehuwandu.
– \( \mu \) ndiyo avhareji kana kuti avhareji yedata.
– \( \sigma \) ndiyo standard deviation, iyo inoyera kuti data rakapararira sei.
– \( e \) ndiyo hwaro hwe logarithm yechisikigo, inenge 2.718.
– \( \pi \) ndiyo pi isingachinji, inenge 3.14159.
Kugoverwa kwakajairika kunogonawo kuratidzwa muchimiro che standard kana 'standard normal' ne mean 0 uye standard deviation 1. Izvi zvinoratidzwa ne notation \( N(0, 1) \).
Hunhu hwekupararira kwakajairika
1. Mutemo weEmpirical
Mutemo we empirical inzira inowanzo shandiswa kunzwisisa kugoverwa kwakajairika. Mutemo uyu unotsanangura kuti data riri mu kugoverwa kwakajairika rinoparadzirwa sei zvichienderana neavhareji:
– Inenge 68% yedata iri mukati mechiyero chimwe chete chekutsauka kweavhareji (\( \mu \pm \sigma \)).
– Inenge 95% yedata iri mukati memaitiro maviri ekutsauka kweavhareji (\( \mu \pm 2\sigma \)).
– Inenge 99.7% yedata iri mukati mezvikamu zvitatu zvakajairwa zveavhareji (\( \mu \pm 3\sigma \)).
2. Z-chibodzwa
Chibodzwa cheZ chinoratidza kuti data reset ine ma standard deviation mangani kubva pa mean. Chinoverengwa nekupatsanura musiyano uripo pakati pe data ne mean ne standard deviation. Chibodzwa cheZ chinobatsira kuona nzvimbo ye data mukugoverwa kwakajairika.
\[ Z = \frac{(X – \mu)}{\sigma} \]
Apo \( X \) iri kukosha kwedata kwakayerwa, \( \mu \) iri mean, uye \( \sigma \) iri kutsauka kwakajairwa.
3. Mhete yeBhero
Mhete yebhero inomiririra kugoverwa kwakajairika. Nzvimbo yepamusoro, kana kuti nzvimbo yepamusoro, yemhete iri paavhareji, uye mhete inodzika zvakaenzana munzira dzese mbiri kubva paavhareji, ichiumba chimiro chebhero.
Mashandisirwo eKugoverwa Kwakajairika Munyika Yechokwadi
1. Nhamba uye Kuongorora Data
Kugoverwa kwakajairika kunoshandiswa zvakanyanya muhuwandu hwe ...
2. Psychology neSocial Sciences
Mupfungwa, kugoverwa kwakajairika kunowanzo shandiswa kutsanangura kugoverwa kwehunhu hwakasiyana-siyana hwevanhu, senge IQ scores, kureba, nezvimwewo. Miedzo yakawanda ye psychometric yakagadzirwa nepfungwa yekuti mhedzisiro yebvunzo ichatevera kugoverwa kwakajairika.
3. Zvehupfumi neBhizinesi
Nyanzvi dzezvehupfumi nevanoongorora mabhizinesi vanoshandisa nzira yakajairika yekugovera zvinhu zvakasiyana-siyana zvehupfumi zvakaita sekudzoka kwemasheya, mari inowanikwa, uye mari inoshandiswa. Kugovera uku kunobatsira pakuongorora njodzi nekuita sarudzo.
4. Uinjiniya neSainzi Yechisikigo
Muinjiniya nesainzi yechisikigo, kugoverwa kwakajairika kunoshandiswa kuongorora nekufanotaura mhedzisiro yemaitiro akasiyana-siyana echisikigo neevanhu. Semuenzaniso, mukudzora mhando, kugoverwa kwakajairika kunobatsira kuona kana chigadzirwa chichizadzisa mwero wemhando.
5. Mikana uye Kusarudza
Kugoverwa kwakajairika kunobatsira mudzidziso yekufungidzira uye mukuita sarudzo. Matekiniki akadai seMonte Carlo analysis anoshandisa kugoverwa kwakajairika kuita simulations dzinobatsira mukufanotaura nekuronga.
Mhedziso
Kugoverwa kwakajairika ndeimwe yepfungwa dzakakosha uye dzinobatsira muhuwandu hwezviverengero nedzimwe nzvimbo dzakawanda. Kunzwisisa kugoverwa uku kunotibvumira kugadzirisa nekuongorora data zvinobudirira, uye kushandisa ruzivo urwu mumabasa akasiyana-siyana anoshanda. Ingava mukuyera kwepfungwa, kuongorora bhizinesi, kana kudzora mhando yeindasitiri, kugoverwa kwakajairika kunopa hwaro hwakasimba hwekunzwisisa nekufanotaura zviitiko zvechokwadi.
