Luis A. Afonso
Posts:
4,725
From:
LIsbon (Portugal)
Registered:
2/16/05


Chisquared to normal approximation
Posted:
May 18, 2013 6:47 PM


Our remote colleagues Wilson, E. B. & Hilferty M. M., did provide a paper: The distribution of chisquare able to attain the transformation Chisquared to Standard normal reported at Proceedings of the National Academy of Sciences USA, 17, 684688, Dec. 1931. As cited at Matthew Shultz www.rasch.org/rmt/rmt162g.htm the transform is, Y Chisquared r df, p=1/3, approximately W~N(0,1),
___W(Y) = [(Y/r)^p  (1 2*p*p / r)] / sqrt( 2*p*p / r
For r= 100 (50) 600 we obtained correctly 1.245(.900), 1.645(.950), 1.960(.975), 2.326(.990) as the normal fractiles. Note: the inputted Chisquares fractiles are those Kalkulator provide. See routine below. Well done, Wilson, Hilferty . . .
Luis A. Afonso
REM "VINCE" CLS DEFDBL AZ DIM CHI(9, 12) REM "0.010 ,0.025 ,0.050 ,0.100 ,0.900 ,0.950 ,0.975 ,0.990 " REM DATA 70.06,74.22,77.93,82.36,118.50,124.34,129.56,135.81 FOR j = 1 TO 8: READ CHI(j, 1): NEXT j DATA 112.67,117.98,122.69,128.28,172.58,179.58,185.80,193.21 FOR j = 1 TO 8: READ CHI(j, 2): NEXT j DATA 156.43,162.73,168.28,174.84,226.02,233.99,241.06,249.45 FOR j = 1 TO 8: READ CHI(j, 3): NEXT j DATA 200.94,208.10,214.39,221.81,279.05,287.88,295.69,304.94 FOR j = 1 TO 8: READ CHI(j, 4): NEXT j DATA 245.97,253.91,260.88,269.07,331.79,341.40,349.87,359.91 FOR j = 1 TO 8: READ CHI(j, 5): NEXT j DATA 291.41,300.06,307.65,316.55,384.31,394.63,403.72,414.47 FOR j = 1 TO 8: READ CHI(j, 6): NEXT j DATA 337.16,346.48,354.64,364.21,436.65,447.63,457.31,468.72 FOR j = 1 TO 8: READ CHI(j, 7): NEXT j DATA 383.16,393.12,401.82,412.01,488.85,500.46,510.67,522.72 FOR j = 1 TO 8: READ CHI(j, 8): NEXT j DATA 429.39,439.94,449.15,459.93,540.93,553.13,563.85,576.49 FOR j = 1 TO 8: READ CHI(j, 9): NEXT j DATA 475.80,486.91,496.61,507.95,592.91,605.67,616.88,630.08 FOR j = 1 TO 8: READ CHI(j, 10): NEXT j DATA 522.37,534.02,544.18,556.06,644.80,658.09,669.77,683.52 FOR j = 1 TO 8: READ CHI(j, 11): NEXT j REM p = 1 / 3 FOR k = 1 TO 11: r = 100 + (k  1) * 50 FOR j = 1 TO 8 y = CHI(j, k) y1 = (y / r) ^ p: u = 2 * p * p / r y2 = y1  (1  u) y3 = y2 / SQR(u) PRINT USING "###.### "; y3; NEXT j PRINT NEXT k END

