Modified random distribution: Difference between revisions
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modifier(x) = (y = 2x - 1; y < 0 ? -y : y) |
modifier(x) = (y = 2x - 1; y < 0 ? -y : y) |
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modrands(rands1, rands2) = [x for (i, x) in enumerate(rands1) if rands2[i] < modifier(x)] |
modrands(rands1, rands2) = [x for (i, x) in enumerate(rands1) if rands2[i] < modifier(x)] |
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histogram(modrands(rand( |
histogram(modrands(rand(50000), rand(50000)), nbins = 20) |
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</lang>{{out}} |
</lang>{{out}} |
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<pre> |
<pre> |
Revision as of 04:18, 26 February 2021
Given a random number generator, (rng), generating numbers in the range 0.0 .. 1.0 called rgen, for example; and a function modifier(x) taking an number in the same range and generating the probability that the input should be generated, in the same range 0..1; then implement the following algorithm for generating random numbers to the probability given by function modifier:
while True: random1 = rgen() random2 = rgen() if random2 < modifier(random1): answer = random1 break endif endwhile
- Task
- Create a modifier function that generates a 'V' shaped probability of number generation using something like, for example:
modifier(x) = 2*(0.5 - x) if x < 0.5 else 2*(x - 0.5)
- Create a generator of random numbers with probabilities modified by the above function.
- Generate >= 10,000 random numbers subject to the probability modification.
- Output a textual histogram with from 11 to 21 bins showing the distribution of the random numbers generated.
Show your output here, on this page.
Julia
<lang>using UnicodePlots
modifier(x) = (y = 2x - 1; y < 0 ? -y : y) modrands(rands1, rands2) = [x for (i, x) in enumerate(rands1) if rands2[i] < modifier(x)] histogram(modrands(rand(50000), rand(50000)), nbins = 20)
</lang>
- Output:
┌ ┐ [0.0 , 0.05) ┤▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 2412 [0.05, 0.1 ) ┤▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 2164 [0.1 , 0.15) ┤▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1850 [0.15, 0.2 ) ┤▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1652 [0.2 , 0.25) ┤▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1379 [0.25, 0.3 ) ┤▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1121 [0.3 , 0.35) ┤▇▇▇▇▇▇▇▇▇▇▇▇▇ 903 [0.35, 0.4 ) ┤▇▇▇▇▇▇▇▇▇▇ 695 [0.4 , 0.45) ┤▇▇▇▇▇▇ 407 [0.45, 0.5 ) ┤▇▇ 118 [0.5 , 0.55) ┤▇▇ 126 [0.55, 0.6 ) ┤▇▇▇▇▇ 358 [0.6 , 0.65) ┤▇▇▇▇▇▇▇▇▇ 639 [0.65, 0.7 ) ┤▇▇▇▇▇▇▇▇▇▇▇▇ 837 [0.7 , 0.75) ┤▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1121 [0.75, 0.8 ) ┤▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1332 [0.8 , 0.85) ┤▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1608 [0.85, 0.9 ) ┤▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1920 [0.9 , 0.95) ┤▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 2204 [0.95, 1.0 ) ┤▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 2348 └ ┘ Frequency
Python
<lang python>import random from typing import List, Callable, Optional
def modifier(x: float) -> float:
""" V-shaped, modifier(x) goes from 1 at 0 to 0 at 0.5 then back to 1 at 1.0 .
Parameters ---------- x : float Number, 0.0 .. 1.0 .
Returns ------- float Target probability for generating x; between 0 and 1.
""" return 2*(.5 - x) if x < 0.5 else 2*(x - .5)
def modified_random_distribution(modifier: Callable[[float], float],
n: int) -> List[float]: """ Generate n random numbers between 0 and 1 subject to modifier.
Parameters ---------- modifier : Callable[[float], float] Target random number gen. 0 <= modifier(x) < 1.0 for 0 <= x < 1.0 . n : int number of random numbers generated.
Returns ------- List[float] n random numbers generated with given probability.
""" d: List[float] = [] while len(d) < n: r1 = prob = random.random() if random.random() < modifier(prob): d.append(r1) return d
if __name__ == '__main__':
from collections import Counter
data = modified_random_distribution(modifier, 50_000) bins = 15 counts = Counter(d // (1 / bins) for d in data) # mx = max(counts.values()) print(" BIN, COUNTS, DELTA: HISTOGRAM\n") last: Optional[float] = None for b, count in sorted(counts.items()): delta = 'N/A' if last is None else str(count - last) print(f" {b / bins:5.2f}, {count:4}, {delta:>4}: " f"{'#' * int(40 * count / mx)}") last = count</lang>
- Output:
BIN, COUNTS, DELTA: HISTOGRAM 0.00, 6326, N/A: ######################################## 0.07, 5327, -999: ################################# 0.13, 4487, -840: ############################ 0.20, 3495, -992: ###################### 0.27, 2601, -894: ################ 0.33, 1744, -857: ########### 0.40, 914, -830: ##### 0.47, 225, -689: # 0.53, 899, 674: ##### 0.60, 1783, 884: ########### 0.67, 2623, 840: ################ 0.73, 3566, 943: ###################### 0.80, 4383, 817: ########################### 0.87, 5422, 1039: ################################## 0.93, 6205, 783: #######################################