Generating N random numbers that probability distribution fits to any given function curve.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 | # Generating N random numbers that probability distribution
# fits to any given function curve
# FB - 201006137
import math
import random
# define any function here!
def f(x):
return math.sin(x)
# f(x) = 1.0 : for uniform probability distribution
# f(x) = x : for triangular probability distribution
# (math.sqrt(random.random()) would also produce triangular p.d. though.)
# f(x) = math.exp(-x*x/2.0)/math.sqrt(2.0*math.pi) : for std normal p.d.
# (taking average of (last) 2,3,... random.random() values would also
# produce normal probability distributions though.)
# define any xmin-xmax interval here! (xmin < xmax)
xmin = 0.0
xmax = math.pi
# find ymin-ymax
numSteps = 1000000 # bigger the better but slower!
ymin = f(xmin)
ymax = ymin
for i in range(numSteps):
x = xmin + (xmax - xmin) * float(i) / numSteps
y = f(x)
if y < ymin: ymin = y
if y > ymax: ymax = y
n = 10 # how many random numbers to generate
for i in range(n):
while True:
# generate a random number between 0 to 1
xr = random.random()
yr = random.random()
x = xmin + (xmax - xmin) * xr
y = ymin + (ymax - ymin) * yr
if y <= f(x):
print xr
break
|
A better and faster way to compute random number with arbitrary distribution is to draw a number x between 0 and 1 and return cdf^{-1}(x), where cdf^{-1} is the inverse cumulative distribution function of 'f'.
The problem w/ that is how to find that function for any given arbitrary probability distribution function. I still think this way is much simpler and practical.