Fitting a distribution to a histogram

Question

I have some data which I've plotted using sns.distplot The x axis is the number of days a certain player is injured for:

I want to get the cdf for this distribution. It does not have to be extremely accurate but I want to run some simulations and effectively I want to have the distribution for this data, call it X. Then I want to run

X.rvs(1000)

which would give me an array of 1000 random numbers which represent the number of days players are injured. eg if it returns

array(2,35,140,3,4,6,7,23,55,63,...,87)

Those should represent the number of days players are injured.

Really not sure how to do this as all I have to go on is the data behind this histogram which is simply plotted with sns.distplot(data,kde=True)

Hope someone can help

data:

data = pd.DataFrame([78,
58,
124,
62,
30,
46,
31,
34,
94,
15,
41,
18,
63,
15,
63,
31,
35,
23,
19,
19,
47,
154,
113,
29,
35,
58,
62,
93,
93,
93,
37,
31,
16,
17,
16,
17,
62,
31,
145,
116,
183,
183,
183,
93,
148,
183,
13,
160,
183,
183,
68,
15,
183,
57,
91,
183,
86,
133,
20,
183,
89,
183,
43,
30,
183,
183,
136,
183,
183,
12,
183,
60,
161,
67,
183,
40,
121,
52,
58,
183,
183,
9,
151,
183,
183,
183,
116,
9,
95,
183,
27,
16,
183,
52,
167,
12,
183,
183,
94,
65,
183,
30,
183,
19,
14,
183,
54,
37,
183,
152,
33,
22,
67,
183,
40,
17,
183,
50,
7,
183,
106,
72,
183,
183,
22,
80,
183,
183,
58,
183,
183,
183,
183,
183,
15,
183,
183,
183,
183,
127,
156,
183,
26,
183,
183,
59,
9,
183,
183,
55,
183,
183,
183,
28,
18,
51,
18,
11,
18,
26,
77,
65,
61,
19,
61,
61,
61,
30,
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21,
182,
37,
27,
49,
26,
7,
16,
14,
19,
33,
30,
4,
28,
60,
15,
162,
40,
39,
14,
22,
7,
47,
121,
40,
39,
15,
8,
30,
13,
150,
16,
7,
78,
30,
41,
26,
21,
65,
155,
54,
44,
85,
54,
72,
19,
21,
26,
127,
17,
4,
75,
23,
69,
44,
71,
102,
23,
21,
17,
61,
155,
27,
38,
27,
30,
107,
33,
24,
103,
61,
98,
6,
60,
22,
51,
]

Answer 1

Given the raw data it's fairly easy to provide a reasonable approximation.

from scipy import stats

p_data = [1, 1, 2, 4, 3, 8, 19, 11, 12, 7, 11, 12, 16, 7, 176, 62, 55, 44, 38, 48, 29, 28, 29, 35, 22, 32, 30, 36, 22, 33, 30, 30, 35, 20, 24, 33, 22, 28, 27, 32, 28, 13, 20, 9, 11, 12, 21, 13, 12, 18, 18, 16, 14, 12, 10, 15, 8, 14, 11, 19, 14, 11, 14, 12, 10, 12, 8, 7, 7, 7, 8, 5, 3, 10, 8, 10, 10, 8, 4, 6, 5, 3, 2, 8, 8, 8, 3, 8, 5, 7, 9, 2, 12, 5, 4, 3, 1, 9, 5, 3, 4, 4, 2, 5, 5, 5, 2, 1, 5, 6, 4, 2, 2, 1, 6, 3, 2, 6, 4, 5, 3, 2, 1, 2, 5, 3, 6, 3, 2, 1, 4, 1, 5, 4, 1, 2, 1, 2, 2, 2, 8, 2, 2, 4, 6, 1, 4, 3, 3, 6, 2, 4, 1, 4, 3, 3, 5, 3, 3, 4, 4, 5, 3, 2, 1, 2, 3, 3, 1, 1, 1, 4, 3, 3, 5, 4, 4, 4, 1, 148]
thesum=sum(p_data)

p_data = [_/thesum for _ in p_data]

x_k = range(1, 1+len(p_data))
custom = stats.rv_discrete(name='custm', values=(x_k, p_data))

R = custom.rvs(size=1000)

print (R[:20])

First I used Counter from itertools to count how many times each duration occurred. As might be expected, some durations do not occur in the data and were represented as zero counts. Bearing in mind the operative word 'approximate' I felt justified in replacing the few zero values with numbers that are close to the neighbouring values. The results are what you see in p_data . Then I normalise (to make values sum to one as probabilities).

There was a dribble of values at the right end, from about 180 days on up. I put all this mass at 180 days. There was no mass at zero days. This explains why x_k runs from one through 180 inclusive.

Finally I use the rv_discrete object whose rvs method proves to be reasonably fast.