#
# normal-dist.txt, 21 May 11

!msgpostfix \n

68.2689492 | Percentage inside one standard deviation
31.7310508 | Percentage outside one standard deviation
95.4499736 | Percentage inside two standard deviations
4.5500246  | Percentage outside two standard deviations
99.7300204 | Percentage inside three standard deviations
0.2699796  | Percentage outside three standard deviations
99.993666  | Percentage inside four standard deviations
0.006334   | Percentage outside four standard deviations


# Compute quantiles for standard normal distribution N(0, 1)
# Algorithm AS241  APPL. STATIST. (1988) VOL. 37, NO. 3, 477-484.

!msgpostfix Calculate quantile for standard normal distribution\n

!need all
3.3871328727963666080e0
1.3314166789178437745e+2
1.9715909503065514427e+3
1.3731693765509461125e+4
4.5921953931549871457e+4
6.7265770927008700853e+4
3.3430575583588128105e+4
2.5090809287301226727e+3

4.2313330701600911252e+1
6.8718700749205790830e+2
5.3941960214247511077e+3
2.1213794301586595867e+4
3.9307895800092710610e+4
2.8729085735721942674e+4
5.2264952788528545610e+3

1.42343711074968357734e0
4.63033784615654529590e0
5.76949722146069140550e0
3.64784832476320460504e0
1.27045825245236838258e0
2.41780725177450611770e-1 
2.27238449892691845833e-2 
7.74545014278341407640e-4 

2.05319162663775882187e0
1.67638483018380384940e0
6.89767334985100004550e-1
1.48103976427480074590e-1
1.51986665636164571966e-2
5.47593808499534494600e-4
1.05075007164441684324e-9

6.65790464350110377720e0
5.46378491116411436990e0
1.78482653991729133580e0
2.96560571828504891230e-1
2.65321895265761230930e-2
1.24266094738807843860e-3
2.71155556874348757815e-5
2.01033439929228813265e-7

5.99832206555887937690e-1
1.36929880922735805310e-1
1.48753612908506148525e-2
7.86869131145613259100e-4
1.84631831751005468180e-5
1.42151175831644588870e-7
2.04426310338993978564e-15

# 0.425

# home.online.no/~pjacklam/notes/invnorm

!msgpostfix Inverse of the Normal cdf, quantile function or probit function (pjackman)\n

!need all
-3.969683028665376e+01
 2.209460984245205e+02
-2.759285104469687e+02
 1.383577518672690e+02
-3.066479806614716e+01
 2.506628277459239e+00

-5.447609879822406e+01
 1.615858368580409e+02
-1.556989798598866e+02
 6.680131188771972e+01
-1.328068155288572e+01

-7.784894002430293e-03
-3.223964580411365e-01
-2.400758277161838e+00
-2.549732539343734e+00
 4.374664141464968e+00
 2.938163982698783e+00

 7.784695709041462e-03
 3.224671290700398e-01
 2.445134137142996e+00
 3.754408661907416e+00


# Odeh RE & Evans JO (1974) The percentage points of the normal distribution.
# Applied Statistics 22: 96-97 (AS70)

!msgpostfix Inverse of the Normal cdf, quantile function or probit function (Odeh & Evans)\n

!need all
-0.322232431087751
# -1.0
-0.342242088547343
-0.204231210245003e-1
-0.453642210147524e-4

 0.993484626059901e-1
 0.588581570494926
 0.531103462366099
 0.103537752849707
 0.385607006339815e-2


# Statistical computing, page 90
# W.J.Kennedy Jr and J.E.Gentle, 1980. 

!msgpostfix Normal cumulative distribution function (0 < x <= 0.5)\n

!need all
 2.4266795523053175e2
 2.1979261618294152e1
 6.9963834886191355
-3.5609843701815385e-2

 2.1505887586986120e2
 9.1164905404514901e1
 1.5082797630407787e1
# 1.0


!msgpostfix Normal cumulative distribution function (0.46875 < x <= 4.0)\n

!need all
 3.004592610201616005e2
 4.519189537118729422e2
 3.393208167343436870e2
 1.529892850469404039e2
 4.316222722205673530e1
 7.211758250883093659e0
 5.641955174789739711e-1
-1.368648573827167067e-7
   
 3.004592609569832933e2
 7.909509253278980272e2
 9.313540948506096211e2
 6.389802644656311665e2
 2.775854447439876434e2
 7.700015293522947295e1
 1.278272731962942351e1
# 1.0


!msgpostfix Normal cumulative distribution function (4.0 < x)\n

!need all
-2.99610707703542174e-3
-4.94730910623250734e-2
-2.26956593539686930e-1
-2.78661308609647788e-1
-2.23192459734184686e-2

 1.06209230528467918e-2
 1.91308926107829841e-1
 1.05167510706793207e0
 1.98733201817135256e0
# 1.0


# Rational approximation to inverse Gaussian distribution.

!msgpostfix Inverse of the Normal cdf, quantile function or probit function (error < 4.5e-4, Abramowitz and Stegun 26.2.23)\n

!need all
2.515517
0.802853
0.010328

1.000000
1.432788
0.189269
0.001308


# The percentage points of the Normal distribution
# JD Beasley and SG Springer
# Applied Statistics, 1977 vol 26 pp 118-121
# Algorithm AS211

!msgpostfix Inverse of the Normal cdf, quantile function or probit function (Beasley-Springer-Moro)\n

!need all
  2.50662823884
-18.61500062529
 41.39119773534
-25.44106049637

- 8.47351093090
 23.08336743743
-21.06224101826
  3.13082909833

  0.3374754822726147
  0.9761690190917186
  0.1607979714918209
  0.0276438810333863
  0.0038405729373609
  0.0003951896511919
  0.0000321767881768
  0.0000002888167364
  0.0000003960315187

