Kumvetsetsa Kusakhazikika ndi Kurtosis
Ziwerengero ndi nthambi yofunika kwambiri ya sayansi m'magawo osiyanasiyana ofufuza, kuyambira sayansi ya chikhalidwe cha anthu mpaka sayansi yachilengedwe. Pakusanthula deta, kumvetsetsa kugawa deta ndikofunikira kwambiri kuti tipeze mfundo zolondola komanso zodalirika. Mfundo ziwiri zofunika zomwe zimagwiritsidwa ntchito nthawi zambiri pofotokoza kugawa ndi kusakhazikika ndi kurtosis. Nkhaniyi ifotokoza mwatsatanetsatane matanthauzidwe, matanthauzidwe, ndi kufunika kwa kusakhazikika ndi kurtosis pakusanthula deta.
Kusakhazikika
Tanthauzo la Kusakhazikika
Kutsetsereka ndi muyeso wa kusalinganika kwa kugawa kwa kuthekera kwa chosinthika chosasinthika. Mwachidule, kutsetsereka kumafotokoza momwe kugawa deta kumasiyanirana ndi mawonekedwe ofanana bwino, omwe amadziwika kuti kugawa kwabwinobwino kapena kugawa kwa Gaussian.
Mitundu ya Kufooka
1. Kusakhazikika Kwabwino: Kugawa deta komwe kumatambasulidwa kumanja. Kusakhazikika kwabwino kumasonyeza kuti zambiri mwa detazo zimayikidwa kumanzere, ndi mchira wautali wakumanja. Mwachitsanzo, ndalama zomwe munthu amapeza nthawi zambiri zimakhala ndi kusakhazikika kwabwino.
2. Kufooka Koipa: Kugawa deta komwe kwakhota kumanzere. Pankhaniyi, kusiyana kolakwika kumasonyeza kuti deta yambiri ili kumanja, ndi mchira wautali kumanzere. Chitsanzo chofala ndi zigoli za mayeso pomwe ophunzira ambiri amapeza bwino.
3. Kugawa kofanana: Ngati mtengo wolakwika uli pafupi ndi zero, kugawa deta kungaganizidwe kuti kuli pafupi ndi kofanana, monga kugawa kwabwinobwino.
Momwe Mungawerengere Kufooka
Kupindika kungawerengedwe pogwiritsa ntchito njira iyi:
\[ \text{Skewness} = \frac{n}{(n-1)(n-2)} \sum \left(\frac{x_i – \bar{x}}{s}\right)^3 \]
Kumene:
– \( n \) = chiwerengero cha deta,
– \( x_i \) = mtengo wa munthu aliyense,
– \( \bar{x} \) = avereji ya deta,
– \( s \) = kupotoka kokhazikika.
Kutanthauzira kwa Skewness
Kutanthauzira kwa mfundo zokhotakhota kungathandize kumvetsetsa makhalidwe a kugawa kwa deta. Monga chitsogozo chachikulu:
– Kupindika komwe kumayandikira 0 kumasonyeza kugawa kofanana.
- Kusakhazikika kwabwino kumasonyeza kugawa komwe kwakhota kumanja.
– Kusakhazikika koipa kumasonyeza kufalikira komwe kwakhota kumanzere.
Kufunika kwa Kusakhazikika pa Kusanthula Deta
Kusakhazikika ndi chida chofunikira kwambiri pakusanthula deta chifukwa chimapereka chidziwitso chokhudza kugawa deta komwe sikungapezeke pongoyang'ana pa kusiyana kwapakati kapena kokhazikika. Kumvetsetsa bwino kusakhazikika kungathandize kudziwa kusintha kwa deta komwe kumafunika pakusanthula kwina, monga kugwiritsa ntchito ma logarithms pa data yokhala ndi kusakhazikika kwakukulu.
Kurtosis (Kulunjika)
Tanthauzo la Kurtosis
Kurtosis ndi muyeso wa kutalika ndi kuthwa kwa nsonga za kugawa deta. Izi zikutanthauza kuti kurtosis imagwirizana ndi kuchuluka kwa deta yomwe ili m'michira poyerekeza ndi deta yomwe ili pafupi ndi avareji. Kurtosis imathandiza kudziwa ngati detayo ili ndi michira yonenepa kapena yopepuka poyerekeza ndi kugawa kwabwinobwino.
Mitundu ya Kurtosis
1. Leptokurtic: Kugawa komwe kuli ndi nsonga yayitali komanso michira yolemera kuposa kugawa kwabwinobwino. Mtengo wa kurtosis ndi woposa 3. Deta yokhala ndi kugawa kwa leptokurtic nthawi zambiri imakhala ndi zinthu zosiyana kwambiri.
2. Mesokurtic: Kugawa komwe kuli ndi mawonekedwe ofanana ndi kugawa kwabwinobwino. Mtengo wa kurtosis ndi 3. Kugawa kwabwinobwino kokha ndi chitsanzo chabwino cha mesokurtic.
3. Platykurtic: Kugawa komwe kuli ndi nsonga yotsika komanso michira yopepuka poyerekeza ndi kugawa kwabwinobwino. Mtengo wa kurtosis ndi wochepera 3. Kugawa kwa platykurtic kumasonyeza kuti deta imagawidwa mofanana pamitundu yonse.
Momwe Mungawerengere Kurtosis
Kurtosis ikhoza kuwerengedwa pogwiritsa ntchito njira iyi:
\[ \text{Kurtosis} = \frac{n(n+1)}{(n-1)(n-2)(n-3)} \sum \left( \frac{x_i – \bar{x}}{s} \right)^4 – \frac{3(n-1)^2}{(n-2)(n-3)} \]
Kumene:
– \( n \) = chiwerengero cha deta,
– \( x_i \) = mtengo wa munthu aliyense,
– \( \bar{x} \) = avereji ya deta,
– \( s \) = kupotoka kokhazikika.
Kawirikawiri, kurtosis nthawi zambiri imatchedwa 'kurtosis yowonjezera'. Kuti zikhale zosavuta, fomula nthawi zambiri imachepetsedwa ndi 3 kuti zitsimikizire kuti kugawa kwabwinobwino kumakhala ndi kurtosis ya 0.
Kutanthauzira kwa Kurtosis
Kuchuluka kwa kurtosis kumapereka chidziwitso cha mtundu wa kugawa deta:
- Kurtosis yapamwamba imasonyeza nsonga zakuthwa ndi michira yolemera.
– Kurtosis yotsika imasonyeza kufalikira kwa tsinde ndi michira yopepuka.
Kufunika kwa Kurtosis mu Kusanthula Deta
Kumvetsetsa kurtosis kumathandiza kuzindikira zinthu zosafunikira ndikukonza deta kuti iwunikidwenso. Mwachitsanzo, deta yokhala ndi kurtosis yayikulu ingafunike njira zolimba zokhazikika kuti ithetse zinthu zosafunikira kwambiri.
Mapulogalamu Othandiza
1. Zachuma: M'misika yazachuma, amalonda amagwiritsa ntchito kusakhazikika ndi kurtosis poyesa chiopsezo cha katundu ndi magwiridwe antchito. Ndalama zomwe zili ndi kusakhazikika kwakukulu zingasonyeze chiopsezo cha kutayika kwakukulu.
2. Thanzi la Anthu: Mu maphunziro a epidemiological, kufalitsa deta nthawi zambiri sikwabwinobwino. Kusakhazikika ndi kurtosis zimathandiza kusintha deta kuti igwiritsidwe ntchito mu ma regression models kapena kusanthula kwina.
3. Kuwongolera Ubwino: Makampani opanga zinthu nthawi zambiri amagwiritsa ntchito kusakhazikika ndi kurtosis kuti alamulire ubwino wa zinthu. Kusakhazikika kwakukulu kwa deta yopangira zinthu kungasonyeze mavuto pakupanga zinthu.
Mapeto
Kufooka ndi kurtosis ndi ziwerengero ziwiri zofunika kwambiri pofotokoza momwe deta imagawidwira. Kufooka kumapereka chidziwitso cha kusiyana kwa kugawa, pomwe kurtosis ikuwonetsa kuthwa ndi kulemera kwa michira ya kugawa. Kumvetsetsa mfundo ziwirizi kumapatsa ofufuza ndi akatswiri a deta zida zowonjezera kuti azitha kutanthauzira deta molondola ndikupanga zisankho zabwino m'njira zosiyanasiyana zogwiritsira ntchito.
