Isingeniso ku-Skewness kanye ne-Kurtosis
Emkhakheni wezibalo, ukuhlaziywa kwedatha kubalulekile ekuchazeni nasekuqondeni amaphethini ayisisekelo ngaphakathi kwamasethi edatha. Imibono ebalulekile esiza ekuchazeni nasekufingqeni lawa masethi edatha ukuchezuka kanye ne-kurtosis. Lezi zilinganiso ezimbili zinikeza ukuqonda okubalulekile ngesimo kanye nokusatshalaliswa kwedatha, okudlulela ngale kokuphambuka okuphakathi kanye nokujwayelekile.
Ukungalingani: Ukuqonda Ukungalingani Kwedatha
I-Skewness ichaza ukungalingani noma ukuntuleka kokulingana ekusatshalalisweni kwamaphuzu edatha. Ekusabalalisweni okulinganayo ngokuphelele, njengokusabalalisa okuvamile, izinhlangothi zesobunxele nesokudla ze-histogram ziyizithombe zesibuko. Kodwa-ke, idatha yangempela ayivami ukuhambisana nokulingana okuphelele, okuholela ekungalingani.
1. Izinhlobo Zokuxeketha:
– Ukugoba Okuhle (Okugoba Ngesokudla): Kulesi simo, umsila ohlangothini lwesokudla lokusabalalisa mude noma ukhuluphele kunohlangothi lwesobunxele. Lokhu kubonisa ukuthi iningi lamaphuzu edatha ligxile kwesobunxele, kanti ambalwa angaphandle adlulela emananini aphezulu. Isibonelo kungaba imali engenayo yasekhaya, lapho abantu abaningi bethola khona ngaphansi komkhawulo othile, kodwa abantu abambalwa bathola imali ephezulu kakhulu.
– Ukugoba Okubi (Okugoba Kwesobunxele): Lapha, umsila ohlangothini lwesobunxele lokusabalalisa mude noma ukhuluphele. Amaphuzu amaningi edatha agxile ngakwesokudla, kanye nenani eliphansi elingaphandle. Isibonelo singase sihlanganise iminyaka yokuthatha umhlalaphansi, lapho iningi lithatha umhlalaphansi phakathi kweminyaka ethile, kodwa abambalwa bathatha umhlalaphansi ngaphambi kwesikhathi.
– Ukungasheleli Okungaphelele: Lokhu kwenzeka ngokusatshalaliswa okulinganayo ngokuphelele, lapho imisila yesobunxele nesokudla ifana khona. Isibonelo esivamile ukusatshalaliswa okuvamile.
2. Ukubala Ukungaqondi:
Ukugoba kungalinganiswa kusetshenziswa ifomula elandelayo:
\[
\text{Skewness} = \frac{n}{(n-1)(n-2)} \sum_{i=1}^n \left( \frac{x_i – \bar{x}}{s} \right)^3
\]
– n inani lokubonwa
– x_i imelela ukubonwa ngakunye
– \(\bar{x}\) iyisilinganiso sokubonwayo
– s ukuphambuka okujwayelekile
Amanani amahle abonisa ukuthambekela kwesokudla, kuyilapho amanani angemahle abonisa ukuthambekela kwesobunxele.
I-Kurtosis: Ukuqonda Ubunzima Bomsila Wedatha
I-Kurtosis ilinganisa "ubude bemisila" yokusatshalaliswa kwedatha. Ngenkathi ukugoba kubhekana nokulingana, i-kurtosis ibhekana nokuphakama nokubukhali kwesihloko esiphakathi kanye nobunzima bemisila. I-Kurtosis ngokuvamile ihlukaniswe ngezinhlobo ezintathu:
1. Izinhlobo ze-Kurtosis:
– I-Leptokurtic: Ukusatshalaliswa okunamanani amahle e-kurtosis kubonisa ukuthi amanani edatha amaningi agxile ku-average, okuholela eziqongweni ezibukhali kanye nemisila ekhuluphele. Lokhu kusho amathuba aphezulu okuba yizinto ezingaphandle. Imbuyiselo yemakethe yamasheya ivame ukukhombisa ukuziphatha kwe-leptokurtic, okubonisa izinguquko ezinkulu.
– I-Platykurtic: Ukusatshalaliswa okune-negative kurtosis kukhombisa iziqongo ezisicaba kanye nemisila emincane, okusho ukuthi amaphuzu edatha asatshalaliswa ngokulinganayo eduze kwesilinganiso. Amasethi ezinombolo ezingahleliwe avame ukubonisa izici ze-platykurtic.
– I-Mesokurtic: Ukusabalalisa okunenani le-kurtosis eliseduze no-zero, njengokusabalalisa okuvamile, kubonisa ukuphakama okuphakathi kanye nobukhulu bomsila.
2. Ukubala i-Kurtosis:
I-Kurtosis ibalwa kusetshenziswa ifomula:
\[
\text{Kurtosis} = \frac{n(n+1)}{(n-1)(n-2)(n-3)} \sum_{i=1}^n \left( \frac{x_i – \bar{x}}{s} \right)^4 – 3 \frac{(n-1)^2}{(n-2)(n-3)}
\]
Ngokufana nokungaguquguquki, u-n uyinani lokubonwa, u-x_i uwukubonwa ngakunye, u-\(\bar{x}\) uyi-mean, kanti u-s uwukuphambuka okujwayelekile. Ukususa ngo-three kusetshenziselwa ukwenza i-kurtosis yokusatshalaliswa okuvamile ilingane no-zero. Amanani amahle asho ukusatshalaliswa kwe-leptokurtic, kuyilapho amanani amabi abonisa ukusatshalaliswa kwe-platykurtic.
Imithelela Engokoqobo Nezicelo
Ukungaqondi kahle kanye ne-kurtosis akuzona nje izakhi zefilosofi kodwa kunemiphumela ewusizo emikhakheni esukela kwezezimali kuya ekulawulweni kwekhwalithi kanye ne-biology.
1. Ezezimali:
– Ekuphathweni kwezingozi, ukuchezuka kanye ne-kurtosis kusetshenziselwa ukwenza amamodeli nokubikezela imbuyiselo yezezimali. Ukuchezuka kwazisa ingozi yezinguquko ezinhle kakhulu noma ezimbi, kuyilapho i-kurtosis isiza ekuqondeni amathuba ezenzakalo ezimbi kakhulu noma izenzakalo ze-black swan.
– Abaphathi bephothifoliyo bacabangela ukungachemi kanye nokungakhuli kahle lapho bekhetha izimpahla, belwela ibhalansi efanele phakathi kwengozi kanye nenzuzo.
2. Ukulawulwa Kwekhwalithi:
– Ekukhiqizeni, ukuhlaziya ukuchezuka kwedatha evela ezinqubweni zokukhiqiza kungagqamisa ukungasebenzi kahle noma ukuphambuka kwekhwalithi. I-Kurtosis ingakhomba izinto ezingaba khona ezingaphandle ezingase zibonise amaphutha noma amaphutha angavamile.
3. Ibhayoloji kanye Nezokwelapha:
– Ku-epidemiology, ukuthambekela kungabonisa ukusabalala kwezifo, kuyilapho i-kurtosis ingabonisa ukuba khona kwezifo ezisakazeka kakhulu. Ku-genetics, lezi zinyathelo zisiza ekuhlaziyeni ukusatshalaliswa kwezici ngaphakathi kwemiphakathi.
4. Isayensi Yezemvelo:
– Abacwaningi basebenzisa ukuphambuka ukuze bafunde idatha yokungcola, beveza izitayela zokusabalala kokungcola. I-Kurtosis iyasiza ekuqondeni izehlakalo ezingavamile kodwa ezibalulekile zemvelo, njengokuchitheka kukawoyela noma ukubonwa kwezinhlobo ezingavamile.
Isiphetho
Ukuqonda ukuchezuka kanye ne-kurtosis kunikeza umbono ocebile nonomqondo obanzi wedatha, okusiza ekwenzeni izinqumo ezingcono emikhakheni eyahlukahlukene. Ngenkathi ukuchezuka kwembula ukungalingani, i-kurtosis igqamisa ukuziphatha komsila kokusatshalaliswa. Ndawonye, lezi zilinganiso zinikeza ukuqonda okubalulekile ngale kwezibalo zesifinyezo ezivamile, okuthuthukisa ikhono lethu lokuhumusha nokubikezela izehlakalo eziyinkimbinkimbi.
Njenganoma yiliphi ithuluzi lezibalo, kubalulekile ukukhumbula ukuthi ukuchezuka kanye ne-kurtosis kufundisa kakhulu uma kusetshenziswa kanye nezinye izibalo ezichazayo. Le ndlela ephelele iqinisekisa ukuqonda okuphelele kokusatshalaliswa kwedatha, iqhuba izinqumo ezinolwazi futhi ikhuthaza ukutholwa okusha.
