358
Cramer Von Mises, Lilliefors, Chi-square and Kolmogorov – Smirnov tests, respectively. The power of all tests
increases as sample size and the level of significances increases. [In multiple regressions and when independent
variables have correlations, the regression coefficients are not multivariate-normally distributed. However, the
estimated regression coefficients (Under the assumption that errors are normally distributed.) are consistent with
the actual values in all the cases. ]
Keywords:
Normal distribution, Logistic distribution, Linear regression
Î
µÎ
µ
ĵ¦ª·
Á¦µ³®r
o
°¤¼
¨µ·
·
¤´
¤¸
o
°¤¤·
ÁºÊ
°o
ªn
µ¦³µ¦¤¸
µ¦Â·
Án
ĵ¦
°
t
, µ¦°
F
°µ´Ê
µ¦ª·
Á¦µ³®r
µ¦°¥ ¤¸
缃
°Å
¸É
ªn
µªµ¤¨µÁ¨ºÉ
°¤¸
µ¦ÂÂÂ
·
Ã¥o
µ
o
°¤¼
¨¸É
Î
µ¤µª·
Á¦µ³®r
Ťn
Á}
ŵ¤ÁºÉ
°Å
¸É
Î
µ®Åªo
È
°µn
¨n
°µ¦ª·
Á¦µ³®r
o
°¤¼
¨ Î
µÄ®o
¨
µ¦ª·
Á¦µ³®r
Ťn
¼
o
° ¨³°µÎ
µÄ®o
Á·
ªµ¤Á¸
¥®µ¥Á¤ºÉ
°Î
µ¨µµ¦ª·
Á¦µ³®r
ÅÄo
´
´Ê
µ¦¦ª°
o
°¤¼
¨
ªn
µ¤¸
¨´
¬³Á®¤µ³¤Â¨³°¨o
°´
缃
°Å
ÁºÊ
°o
¹
Á}
Á¦ºÉ
°Î
µ´
µ¦Â·
º
°Á}
µ¦Â¸É
Î
µ´
¤µ °µÁ}
缃
°Å
ĵ¦ª·
Á¦µ³®r
µ·
·
n
ª
Įn
¨o
ª Á®»
µ¦r
¸É
Á·
¹Ê
Ã¥¦¦¤µ·
n
ªÄ®n
È
¤¸
¨´
¬³Ä¨o
Á¸
¥µ¦Â·
º
°
o
°¤¼
¨³¤¸
¦¼
¦n
µ
¨´
¬³Á}
¦¼
¦³´
ªÉÎ
µ
o
°¤¼
¨n
ª¤µ³°¥¼n
¦¨µ¦° Ç n
µÁ¨¸É
¥ ¨³n
°¥ Ç ¨o
°¥¨ÅÃ¥¤¤µ¦´Ê
µo
µ¥Â¨³
ªµ ¹
Î
µÄ®o
µ¦Â·
Á}
µ¦Â¸É
·
¥¤Äo
´
°¥n
µÂ¡¦n
®¨µ¥ °¸
®¹É
µ¦ÂÂ
Ân
°ÁºÉ
°¸É
n
µÄ º
° µ¦ÂÂÂè·
·
Á}
µ¦Â¸É
¤¸
µ¦Î
µÅ¦³¥»
r
Ä®¨µ¥o
µ Án
o
µ
µ¦¨µ o
µ¸
ªª·
¥µ o
µÁÃ襸
o
µ¡¨´
µ ¸É
Î
µ´
º
°Äo
Î
µ®¦´
´
ªÂµ¦Á¦·
Á·
à (
Growth Models)
µ¦ÂÂÂè·
·
¤¸
¦¼
¦n
µ¨´
¬³Á}
¦¼
¦³´
ªÉÎ
µ ¸É
¤¸
ªµ¤¤¤µ¦
°Á
Á}
Åo
´Ê
Ân
f
¹
f
¹É
¤¸
ªµ¤Ä¨o
Á¸
¥´
µ¦Â·
¤µ Ã¥n
µ´
Á¡¸
¥n
ª®µ¸É
®µªn
µ
¨³¤¸
ªµ¤Ãn
ªn
µÁ¨È
o
°¥
Án
µ´Ê
缃
°µµ¦Â·
¨³µ¦ÂÂÂè·
·
¤¸
ªµ¤Ä¨o
Á¸
¥´
¤µ Ã¥Á¡µ³Ä¦¸
¸É
o
°¤¼
¨¼
ÁÈ
¤µÁ¡¸
¥µn
ª ®¦º
°
o
°¤¼
¨¤¸
Î
µªo
°¥ Î
µÄ®o
Ťn
µ¤µ¦Â¥Åo
ªn
µ
o
°¤¼
¨¤¸
µ¦Â·
®¦º
°¤¸
µ¦ÂÂÂè·
·
´
´Ê
¹
ĸÉ
³«¹
¬µªn
µ ´
ª·
·
ĸÉ
¤¸
¦³·
·
£µ¡Äµ¦´
¦°
o
°¤¼
¨¸É
¤¸
µ¦ÂÂÂè·
·
µµ¦Â·
o
µÎ
µ
o
°¤¼
¨¸É
¤¸
µ¦ÂÂÂè·
·
¤µÎ
µµ¦ª·
Á¦µ³®r
o
°¤¼
¨µ·
·
¸É
¤¸
缃
°Å
ÁºÊ
°o
ªn
µ¦³µ¦¤¸
µ¦Â·
³n
¨¦³°¥n
µÅ¦ ¨³³n
¨Ä
¦¸
Äo
µ
°»
¦r
¨³ª·
¸
µ¦
µª·
´
¥¦´Ê
¸Ê
Åo
Î
µ®
°Á
¨³ª·
¸
Î
µÁ·
µ¦ª·
´
¥ ´
¸Ê
1. µ¦°ªµ¤µ¤µ¦
°´
ª·
·
Î
µ®¦´
µ¦´
¦°µ¦ÂÂÂè·
·
µµ¦ÂÂ
·
Äo
´
ª·
·
° 6 ´
ª·
·
Åo
Ân
´
ª·
·
Kolmogorov - Smirnov, ´
ª·
·
Shapiro Wilk, ´
ª·
·
Anderson Darling , ´
ª·
·
Lilliefors, ´
ª·
·
Cramer Von Mises ¨³´
ª·
·
Chi-square