0

I have found this curve on a paper

I have achieved to get some points on this curve thanks to the app' automeris, however, now that I have the coordinates of several points, how can I create a distribution with them and pick (in Python if possible) randomly within my created distribution ?

Cheers, Eddie

Data

45.0, 0.263

47.3, 0.470

51.5, 1.34

53.0, 1.86

54.3, 2.35

55.1, 2.84

55.8, 3.39

56.1, 3.88

56.6, 4.36

57.4, 5.41

57.1, 4.89

57.9, 6.41

57.6, 5.90

58.4, 7.46

58.1, 6.97

58.6, 8.49

58.6, 7.98

59.1, 10.1

59.1, 9.52

59.1, 8.99

59.9, 11.6

59.6, 11.1

59.6, 10.6

60.1, 13.1

60.1, 12.6

60.1, 12.1

60.9, 14.7

60.6, 14.2

60.7, 13.7

61.4, 15.7

61.2, 15.2

61.7, 16.7

61.7, 16.2

62.4, 17.8

62.2, 17.2

62.9, 18.7

62.7, 18.3

63.7, 19.3

64.7, 19.8

67.3, 19.8

68.3, 19.3

69.4, 18.8

70.4, 18.3

71.5, 17.8

72.8, 17.3

74.0, 16.8

75.6, 16.4

77.2, 15.9

78.2, 15.4

79.7, 14.9

81.3, 14.4

82.9, 13.9

84.7, 13.4

86.0, 13.0

87.3, 12.5

89.1, 12.0

90.1, 11.5

91.7, 11.0

92.9, 10.5

94.2, 9.99

95.8, 9.52

96.8, 9.04

98.4, 8.54

99.9, 8.03 

101, 7.59 

103, 7.08 

105, 6.61 

107, 6.13 

109, 5.66 

111, 5.24 

112, 4.74 

117, 3.92 

122, 3.32 

124, 3.12 

128, 2.63 

130, 2.46 

135, 2.10

138, 1.94 

142, 1.73 

146, 1.52 

150, 1.34 

154, 1.18 

163, 0.910 

172, 0.712 

180, 0.592
Bharti Rawat
  • 1,949
  • 21
  • 32
Eddie
  • 179
  • 1
  • 1
  • 7
  • Do you want to pick one of the specific points or generate a random variable within the x-bounds according to that distribution (i.e. discrete selection or continuous interpolation)? – a_guest Feb 06 '19 at 08:52
  • What have you tried so far? – Tobias Brösamle Feb 06 '19 at 09:02
  • I want to recreate a distribution given by the data I have picked from a paper. The data give the x,y coordinates of the outline of the distribution (it looks somewhat like an F distribution), with the first column giving my y coordinates and the second giving my x coordinates. – Eddie Feb 06 '19 at 09:09
  • Possible duplicate of [Create a continuous distribution in python](https://stackoverflow.com/questions/17676710/create-a-continuous-distribution-in-python) – Peter O. Feb 06 '19 at 21:46

2 Answers2

0

I will create a dataframe with that data. and use a function to pick randomly say a row randomly. See a mockup below:

import pandas as pd 
import matplotlib.pyplot as plt
df = pd.DataFrame([
[45.0, 0.263],
[47.3, 0.470],
[51.5, 1.34],
[53.0, 1.86],
[54.3, 2.35],
[55.1, 2.84],
[55.8, 3.39],
[56.1, 3.88],
[56.6, 4.36],
[57.4, 5.41],
[57.1, 4.89],
[57.9, 6.41],
[57.6, 5.90],
[58.4, 7.46],
[58.1, 6.97],
[58.6, 8.49],
[58.6, 7.98],
[59.1, 10.1],
[59.1, 9.52],
[59.1, 8.99],
[59.9, 11.6],
[59.6, 11.1],
[59.6, 10.6],
[60.1, 13.1],
[60.1, 12.6],
[60.1, 12.1],
[60.9, 14.7],
[60.6, 14.2],
[60.7, 13.7],
[61.4, 15.7],
[61.2, 15.2],
[61.7, 16.7],
[61.7, 16.2],
[62.4, 17.8],
[62.2, 17.2],
[62.9, 18.7],
[62.7, 18.3],
[63.7, 19.3],
[64.7, 19.8],
[67.3, 19.8],
[68.3, 19.3],
[69.4, 18.8],
[70.4, 18.3],
[71.5, 17.8],
[72.8, 17.3],
[74.0, 16.8],
[75.6, 16.4],
[77.2, 15.9],
[78.2, 15.4],
[79.7, 14.9],
[81.3, 14.4],
[82.9, 13.9],
[84.7, 13.4],
[86.0, 13.0],
[87.3, 12.5],
[89.1, 12.0],
[90.1, 11.5],
[91.7, 11.0],
[92.9, 10.5],
[94.2, 9.99],
[95.8, 9.52],
[96.8, 9.04],
[98.4, 8.54],
[99.9, 8.03], 
[101, 7.59], 
[103, 7.08], 
[105, 6.61],
[107, 6.13], 
[109, 5.66], 
[111, 5.24], 
[112, 4.74],
[117, 3.92], 
[122, 3.32], 
[124, 3.12], 
[128, 2.63],
[130, 2.46], 
[135, 2.10],
[138, 1.94],
[142, 1.73],
[146, 1.52], 
[150, 1.34], 
[154, 1.18], 
[163, 0.910],
[172, 0.712],
[180, 0.592] 
], columns=["Col_A", "Col_B"])

plt.plot(df['Col_A'],df['Col_B']);

Plotting the points on a graph, we get:

enter image description here

To get a random value, I have created this function:

import random

def RandomSample(data, samplecount):
    return data.iloc[random.sample(data.index, samplecount)]

RandomSample(df,1)

The result below: this is a random row.

Col_A   Col_B
38  64.7    19.8

Another easy way to get a sample is to just use df.sample(n=1), where n is the number of samples needed.

MEdwin
  • 2,940
  • 1
  • 14
  • 27
0

The below code buckets the distribution between the provided samples, and then randomly selects a bucket according to said distribution. It then linearly interpolates between the sample to either side, to determine the point to select between them. You could view it as a trapezoidal approximation to the integral (representing the cumulative probability distribution).

from bisect import bisect_left
from random import uniform

def make_lookup(data):
    keys = sorted(data.keys())
    lookup = dict()
    total = 0
    for lkey, hkey in zip(keys, keys[1:]):
        lval, hval = data[lkey], data[hkey]
        total += (lval + hval) * (hkey - lkey) // 2
        lookup[total] = lkey
    return lookup

def draw_number(cprobs, lookup):
    rand = uniform(0, cprobs[-1])
    index = bisect_left(cprobs, rand) - 1
    lo, hi = cprobs[index], cprobs[index+1]
    lkey, hkey = lookup[lo], lookup[hi]
    return lkey + (rand - lo) * (hkey - lkey) / (hi - lo)

def main():
    data = {128.0: 2.63, 130.0: 2.46, 107.0: 6.13, 98.4: 8.54, 135.0: 2.1, 138.0: 1.94, 87.3: 12.5, 142.0: 1.73, 60.7: 13.7, 61.4: 15.7, 150.0: 1.34, 117.0: 3.92, 154.0: 1.18, 111.0: 5.24, 60.1: 12.1, 90.1: 11.5, 99.9: 8.03, 163.0: 0.91, 146.0: 1.52, 62.9: 18.7, 172.0: 0.712, 45.0: 0.263, 47.3: 0.47, 51.5: 1.34, 180.0: 0.592, 57.1: 4.89, 54.3: 2.35, 55.1: 2.84, 56.6: 4.36, 57.9: 6.41, 58.4: 7.46, 59.6: 10.6, 60.6: 14.2, 61.2: 15.2, 62.7: 18.3, 53.0: 1.86, 64.7: 19.8, 67.3: 19.8, 68.3: 19.3, 69.4: 18.8, 70.4: 18.3, 71.5: 17.8, 72.8: 17.3, 74.0: 16.8, 75.6: 16.4, 77.2: 15.9, 78.2: 15.4, 79.7: 14.9, 56.1: 3.88, 82.9: 13.9, 58.6: 7.98, 84.7: 13.4, 86.0: 13.0, 57.4: 5.41, 89.1: 12.0, 57.6: 5.9, 91.7: 11.0, 92.9: 10.5, 58.1: 6.97, 94.2: 9.99, 95.8: 9.52, 96.8: 9.04, 62.4: 17.8, 59.1: 8.99, 101.0: 7.59, 81.3: 14.4, 60.9: 14.7, 103.0: 7.08, 109.0: 5.66, 61.7: 16.2, 112.0: 4.74, 59.9: 11.6, 62.2: 17.2, 105.0: 6.61, 55.8: 3.39, 122.0: 3.32, 63.7: 19.3, 124.0: 3.12}

    lookup = make_lookup(data)
    cprobs = sorted(lookup.keys())

    num = draw_number(cprobs, lookup)
    print(num)

if __name__ == "__main__":
    main()

Its also pretty fast- so if you need lots of samples, it shouldn't pose any issues.

Dillon Davis
  • 6,679
  • 2
  • 15
  • 37