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Hi --
How will you be using the distribution?
How much accuracy do you need?
Here is afl code that will initialize an array with the Cumulative Distribution Function of the Normal Distribution.
//---------------------------
// InitializeNormalCDF.afl
//
function InitializeNormalCDF()
// Initialize the array that holds the coefficients
// for the Normal Cumulative Distribution function.
{
NormCDF[0] = -3.090;
NormCDF[1] = -2.326;
NormCDF[2] = -2.053;
NormCDF[3] = -1.881;
NormCDF[4] = -1.751;
NormCDF[5] = -1.645;
NormCDF[6] = -1.555;
NormCDF[7] = -
1.476;
NormCDF[8] = -1.405;
NormCDF[9] = -1.341;
NormCDF[10] = -1.282;
NormCDF[11] = -1.227;
NormCDF[12] = -1.175;
NormCDF[13] = -1.126;
NormCDF[14] = -1.080;
NormCDF[15] = -
1.036;
NormCDF[16] = -0.994;
NormCDF[17] = -0.954;
NormCDF[18] = -0.915;
NormCDF[19] = -0.878;
NormCDF[20] = -0.842;
NormCDF[21] = -0.806;
NormCDF[22] = -0.772;
NormCDF[23] = -
0.739;
NormCDF[24] = -0.706;
NormCDF[25] = -0.674;
NormCDF[26] = -0.643;
NormCDF[27] = -0.613;
NormCDF[28] = -0.583;
NormCDF[29] = -0.553;
NormCDF[30] = -0.524;
NormCDF[31] = -
0.496;
NormCDF[32] = -0.468;
NormCDF[33] = -0.440;
NormCDF[34] = -0.412;
NormCDF[35] = -0.385;
NormCDF[36] = -0.358;
NormCDF[37] = -0.332;
NormCDF[38] = -0.305;
NormCDF[39] = -
0.279;
NormCDF[40] = -0.253;
NormCDF[41] = -0.228;
NormCDF[42] = -0.202;
NormCDF[43] = -0.176;
NormCDF[44] = -0.151;
NormCDF[45] = -0.126;
NormCDF[46] = -0.100;
NormCDF[47] = -
0.075;
NormCDF[48] = -0.050;
NormCDF[49] = -0.025;
NormCDF[50] = 0.000;
NormCDF[51] = 0.025;
NormCDF[52] = 0.050;
NormCDF[53] = 0.075;
NormCDF[54] = 0.100;
NormCDF[55] =
0.126;
NormCDF[56] = 0.151;
NormCDF[57] = 0.176;
NormCDF[58] = 0.202;
NormCDF[59] = 0.228;
NormCDF[60] = 0.253;
NormCDF[61] = 0.279;
NormCDF[62] = 0.305;
NormCDF[63] =
0.332;
NormCDF[64] = 0.358;
NormCDF[65] = 0.385;
NormCDF[66] = 0.412;
NormCDF[67] = 0.440;
NormCDF[68] = 0.468;
NormCDF[69] = 0.496;
NormCDF[70] = 0.524;
NormCDF[71] =
0.553;
NormCDF[72] = 0.583;
NormCDF[73] = 0.613;
NormCDF[74] = 0.643;
NormCDF[75] = 0.674;
NormCDF[76] = 0.706;
NormCDF[77] = 0.739;
NormCDF[78] = 0.772;
NormCDF[79] =
0.806;
NormCDF[80] = 0.842;
NormCDF[81] = 0.878;
NormCDF[82] = 0.915;
NormCDF[83] = 0.954;
NormCDF[84] = 0.994;
NormCDF[85] = 1.036;
NormCDF[86] = 1.080;
NormCDF[87] =
1.126;
NormCDF[88] = 1.175;
NormCDF[89] = 1.227;
NormCDF[90] = 1.281;
NormCDF[91] = 1.341;
NormCDF[92] = 1.405;
NormCDF[93] = 1.476;
NormCDF[94] = 1.555;
NormCDF[95] =
1.645;
NormCDF[96] = 1.751;
NormCDF[97] = 1.881;
NormCDF[98] = 2.054;
NormCDF[99] = 2.326;
NormCDF[100] = 3.090;
return(Null);
}
//Figure 22.5 Initialization of CDF
//--------------------------
A fairly detailed discussion about how to use it, including an example, is on pages 295 through 305 of my book -- Quantitative Trading Systems.
Thanks,
Howard
www.quantitativetradingsystems.com
On 5/30/07, vlanschot <vlanschot@xxxxxxxxx> wrote:
I have various functions for normal distributions, but for some reason
none seem to be able to replicate Excel's NORMDIST(x,mean,stdev,TRUE).
I've applied the Abramowitz & Stegun approximation to calculate the
cumulative normal function. However, the pdf agrees with Excel's
NORMDIST(x,mean,stdev,FALSE), but the cdf does not match its NORMDIST
(x,mean,stdev,TRUE).
I did read there have been criticisms expressed as to the accuracy of
XL's approximations, but doubt this is applicable in this case.
Any suggestions appreciated.
PS
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