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normal-dist.dm42
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normal-dist.dm42
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// Normal distribution functions
//
// Im trying to only use my dm42 for my statistics class (bad idea probally),
// hoping we don't end up needing any more complacated functions...
// Refrences:
// - Winitzki, Sergei. "A handy approximation for the error function and its inverse." A lecture note obtained through private communication (2008).
// - https://en.wikipedia.org/wiki/Cumulative_distribution_function
// - https://stackoverflow.com/questions/457408/is-there-an-easily-available-implementation-of-erf-for-python
// Normal cumulative distribution function
//
// (1 + erf((x - mu) / sigma / sqrt(2))) / 2
export def cdf {
MVAR "X"
MVAR "MU"
MVAR "SIGMA"
VARMENU cdf
STOP
RCL "X"
RCL "MU"
-
RCL "SIGMA"
/
2
SQRT
/
erf()
1, +
2, /
exit()
}
// Inverse normal cumulative distribution function
//
// mu + sigma * sqrt(2) * inv_erf(2 * x - 1)
export def icdf {
MVAR "X"
MVAR "MU"
MVAR "SIGMA"
VARMENU icdf
STOP
2
RCL "X"
*
1
-
inv_erf()
2
SQRT
*
RCL "SIGMA"
*
RCL "MU"
+
exit()
}
def exit {
CLMENU
if { FS? 03 } {
SF 27
}
}
// Error function
//
// sign = signum(x)
// x = abs(x)
//
// a1 = 0.254829592
// a2 = -0.284496736
// a3 = 1.421413741
// a4 = -1.453152027
// a5 = 1.061405429
// p = 0.3275911
//
// t = 1.0/(1.0 + p*x)
// y = 1.0 - (((((a5*t + a4)*t) + a3)*t + a2)*t + a1) * t * e^(-x^2)
// sign*y
def erf {
// Take the absolute value of x
// also save the sign of x for later
DUP
ABS
STO 00 // |X| in 00
DROP
SIGN
STO 01 // sign(X) in 01
DROP
// Calculate t
0.3275911 // p
RCL 00
*
1,+
1/X
STO 02 // t in 02
DROP
// Calculate y
1
1.061405429 // a5
RCL 02, *
-1.453152027 // a4
+
RCL 02, *
1.421413741 // a3
+
RCL 02, *
-0.284496736 // a2
+
RCL 02, *
0.254829592 // a1
+
RCL 02, *
// * e^(-x^2)
RCL 00
X↑2
+/-
E↑X
*
-
// Return sign
RCL 01
*
}
// Inverse error function
//
// s = signum(x)
// x = abs(x)
//
// a = (8 * (pi - 3)) / (3 * pi * (4 - pi)) # ~0.140012
// s * sqrt(sqrt((2 / (pi * a) + (log(1 - x ** 2)) / 2) ** 2 - log(1 - x ** 2) / a) - (2 / (pi * a) + log(1 - x ** 2) / 2))
def inv_erf {
DUP
ABS
STO 00 // |X| in 00
DROP
SIGN
STO 01 // sign(X) in 01
DROP
// Calculate of a
8
PI
3
-
*
4
PI
-
PI
*
3
*
/
STO 02 // a in 02
DROP
// Calculate
2
PI
RCL 02
*
/
1
RCL 00
X↑2
-
LN
2
/
+
X↑2
1
RCL 00
X↑2
-
LN
RCL 02
/
-
SQRT
2
PI
RCL 02
*
/
1
RCL 00
X↑2
-
LN
2
/
+
-
SQRT
// Restore sign
RCL 01
*
}