I ka honua o nā helu, ʻike mau ʻoe i nā hiʻohiʻona kahaha i hiki ke kahaha a me ka hoʻomālamalama. ʻO kekahi o ia ʻano hoihoi ʻo Benford's Law, ʻike ʻia hoʻi ʻo Law of the First Digit. Hōʻike kēia hanana makemakika i ka puʻunaue alapine o nā huahelu mua i nā pūʻulu ʻikepili maoli a hāʻawi i nā ʻike hoihoi i ke ʻano o nā helu i ka wā e puka mai ai i ko mākou kaiapuni.
ʻO ke kānāwai o Benford, i kapa ʻia ma muli o ke kauka lapaʻau ʻo Frank Benford nāna i ʻike hou iā ia i ka makahiki 1938, he mea hoihoi loa ia: i loko o nā pūʻulu ʻikepili kūlohelohe, hoʻokele waiwai a ʻepekema, ʻaʻole i puunaue like ka helu mua o nā helu. Akā, 'ike pinepine 'ia ka huahelu \(1\) ma ke 'ano he huahelu mua. ʻO ke kikoʻī hou aku, hāʻawi ʻia ka probalika e hoʻomaka kahi helu me kahi huahelu \(d\) e ka formula
$$P(d) = \log_{10}(1 + \frac{1}{d})$$
kahi \(d\) kekahi o nā huahelu \(1\) a i \(9\) . Ke ʻōlelo nei kēia kumuhana, no ka laʻana, ʻike ʻia ka huahelu \(1\) ma ke ʻano he huahelu mua ma kahi o \(30,1 \%\) o ka manawa, ʻoiai ʻo ka huahelu \(9\) ʻike wale ʻia ma kahi o \(4,6 \%\) hiki mai ka manawa.
Hiki ke wehewehe ʻia ke kānāwai e ka hoʻohālikelike ʻana o ka logarithms. Inā ʻoe e nānā i nā helu mai nā ʻāpana like ʻole o ka nui a kau ʻia ma ka pālākiō logarithmic, e puʻunaue ʻia nā huahelu mua e like me ka wānana ʻia e ke kānāwai o Benford. ʻO kēia no ka mea \(100\) ʻoi aku ka nui o ka manawa logarithmic ma waena \(1000\) ʻelua mau mana o \(10\) \(100\) e laʻa. ʻO ia hoʻi, ʻoi aku ka nui o nā huahelu mua liʻiliʻi a no laila e hiki mai ana.
He mau noi ko Benford's Law ma nā wahi like ʻole, mai forensics a hiki i ka ʻepekema data:
- ʻIke hoʻopunipuni: Hoʻohana ka poʻe loiloi i ke kānāwai e ʻike i nā hewa i ka ʻikepili kālā. Inā haʻalele ka puʻunaue o nā huahelu mua o ka waihona koena o ka hui mai ke kānāwai o Benford, hōʻike paha kēia i ka hoʻopunipuni a hoʻopunipuni paha.
- Ka ʻikepili ʻepekema: Hoʻohana nā mea noiʻi i ke kānāwai e hoʻāʻo i ka hilinaʻi o nā pūʻulu ʻikepili. Hiki ke hōʻike i nā hewa o ka hōʻiliʻili ʻikepili i ka ʻae ʻana mai ka puʻunaue i manaʻo ʻia.
ʻOiai ka hoʻohana ākea ʻana, ʻaʻole kūpono ke kānāwai o Benford. Hoʻohana nui ia i nā pūʻulu ʻikepili i loaʻa nā helu o nā nui like ʻole a puʻunaue maoli ʻia. ʻAʻole hahai nā moʻo helu i loko o kahi ʻāpana liʻiliʻi a i ʻole i kaupalena ʻia (e like me nā code zip a i ʻole nā helu palekana kaiapili) ʻaʻole hahai i kēia kānāwai.
ʻO ke kānāwai ʻo Benford kekahi o nā hiʻohiʻona hoihoi loa o ka hiki ke ʻike ʻia nā loina makemakika i ka honua maoli ma nā ala i manaʻo ʻole ʻia a me ka ʻike. Hōʻike kona hoʻohana ʻana ma ka hoʻomaʻamaʻa ʻana ʻaʻole he ʻepekema abstract wale nō ka makemakika, akā he mea hana pono no ka nānā ʻana i ka ʻoiaʻiʻo. No ka ʻike ʻana i ka hoʻopunipuni a i ʻole ka hōʻoia ʻana i ka ʻikepili ʻepekema, hāʻawi ʻo Benford's Law i kahi hiʻohiʻona kūʻokoʻa e pili ana i nā helu e hoʻohālike i ko mākou honua.