sdutils

sdist.plt

set term svg
set output 'sdist_under.svg'
set xrange [-4:4]
set yrange [0:0.45]
set samples 1000
plot \
     x < 1 ? exp(-x*x/2)/sqrt(6.283185307179586) : 1/0 with filledcurves x1 lc rgb "grey", \
     exp(-x*x/2)/sqrt(6.283185307179586) lw 2 lc rgb "black"
     
set output 'sdist_inside.svg'
plot \
     abs(x) < 1 ? exp(-x*x/2)/sqrt(6.283185307179586) : 1/0 with filledcurves x1 lc rgb "grey", \
     exp(-x*x/2)/sqrt(6.283185307179586) lw 2 lc rgb "black"

sdutils.py

import math
import scipy.special as sp

SQRT2 = math.sqrt(2)

'''
See https://i.imgur.com/UqmxwuF.png for visualisation of these probabilities
'''

'''find P(value < μ + arg*σ), or area to the left of certain value'''
def sdu(arg):
    return (sp.erf(arg / SQRT2) + 1) / 2

'''find P(μ + a*σ < value < μ + b*σ), or area between cetain values'''
def sdr(a, b):
    return (sp.erf(b / SQRT2) - sp.erf(a / SQRT2)) / 2

'''find P(abs(value - μ) < arg*σ), or area within certain distance from mean'''
def sdi(arg):
    return sp.erf(arg / SQRT2)

'''find x such that P(value < μ + xσ) = p'''
def sdu_inv(p):
    return sp.erfinv(p * 2 - 1) * SQRT2

'''find x such that P(abs(value - μ) < xσ) = p'''
def sdi_inv(p):
    return sp.erfinv(p) * SQRT2