Nel 1898 il barone von Bortkewitch pubblicò un libro sulla distribuzione di Poisson in cui presentò varie collezioni di dati sperimentali che la seguivano. Ecco qui, ad esempio, i dati sugli incidenti mortali per calci di cavallo o mulo presso i 14 reparti della cavalleria prussiana nell'arco di 20 anni, dal 1875 al 1894.  Completando la seguente tabella confrontali con le frequenze attese secondo il modello di Poisson.

n° morti per anno per reparto	0	1	2	3	4	≥5
frequenza	144	?	?	?	?	0
frequenza attesa	?	?	?	?	?	?

Elaboro i dati con R, ma avrei potuto usare altro software.

caval = c(
0,0,0,0,0,0,0,1,1,0,0,0,1,0,
2,0,0,0,1,0,0,0,0,0,0,0,1,1,
2,0,0,0,0,0,1,1,0,0,1,0,2,0,
1,2,2,1,1,0,0,0,0,0,1,0,1,0,
0,0,0,1,1,2,2,0,1,0,0,2,1,0,
0,3,2,1,1,1,0,0,0,2,1,4,3,0,
1,0,0,2,1,0,0,1,0,1,0,0,0,0,
1,2,0,0,0,0,1,0,1,1,2,1,4,1,
0,0,1,2,0,1,2,1,0,1,0,3,0,0,
3,0,1,0,0,0,0,1,0,0,2,0,1,1,
0,0,0,0,0,0,1,0,0,2,0,1,0,1,
2,1,0,0,1,1,1,0,0,1,0,1,3,0,
1,1,2,1,0,0,3,2,1,1,0,1,2,0,
0,1,1,0,0,1,1,0,0,0,0,1,1,0,
0,0,1,1,0,1,1,0,0,1,2,2,0,2,
1,2,0,2,0,1,1,2,0,2,1,1,2,2,
0,0,0,1,1,1,0,1,1,0,3,3,1,0,
1,3,2,0,1,1,3,0,1,1,0,1,1,0,
0,1,0,0,0,1,0,2,0,0,1,3,0,0,
1,0,0,0,0,0,0,0,1,0,1,1,0,0)
N = length(caval); N
# 280
source("http://macosa.dima.unige.it/r.R")  # se non l'hai già caricato
range(caval)
#  0  4
M = mean(caval); M
# 0.7
BF=3; HF=3
Histo(caval, -0.5,4.5, 1)
P = dpois(0:7, lambda=0.7)
round(P*N,3)
# 139.044  97.331  34.066  7.949  1.391  0.195  0.023  0.002
segm(0:6,0, 0:6,P*100, "red")

Frequencies and percentage freq.: 
144,  91,  32,   11,  2
51.43,32.5,11.43,3.93,0.71

n° morti per anno per reparto	0	1	2	3	4	≥5
frequenza	144	91	32	11	2	0
frequenza attesa	139	97	34	8	1.4	0.2

Istogramma ottenuto con questo script online:

A = 0   B = 5   intervals = 5   their width = 1
n=280   min=0   max=4   mean=0.7
0,0,0,0,0,0,0,1,1,0,0,0,1,0, 2,0,0,0,1,0,0,0,0,0,0,0,1,1, 2,0,0,0,0,0,1,1,0,0,1,0,2,0, 1,2,2,1,1,0,0,0,0,0,1,0,1,0, 0,0,0,1,1,2,2,0,1,0,0,2,1,0, 0,3,2,1,1,1,0,0,0,2,1,4,3,0, 1,0,0,2,1,0,0,1,0,1,0,0,0,0, 1,2,0,0,0,0,1,0,1,1,2,1,4,1, 0,0,1,2,0,1,2,1,0,1,0,3,0,0, 3,0,1,0,0,0,0,1,0,0,2,0,1,1, 0,0,0,0,0,0,1,0,0,2,0,1,0,1, 2,1,0,0,1,1,1,0,0,1,0,1,3,0, 1,1,2,1,0,0,3,2,1,1,0,1,2,0, 0,1,1,0,0,1,1,0,0,0,0,1,1,0, 0,0,1,1,0,1,1,0,0,1,2,2,0,2, 1,2,0,2,0,1,1,2,0,2,1,1,2,2, 0,0,0,1,1,1,0,1,1,0,3,3,1,0, 1,3,2,0,1,1,3,0,1,1,0,1,1,0, 0,1,0,0,0,1,0,2,0,0,1,3,0,0, 1,0,0,0,0,0,0,0,1,0,1,1,0,0
%:   | 51.43 | 32.5 | 11.43 | 3.93 | 0.71 |

Il grafico della poissoniana posso ottenerelo facilmente con WolframAlpha introducendo  Poisson distribution mu = 0.7.

Posso verificare che c'è corrispondenza tra questi valori (0.51, 0.34, 0.12, 0.30) e quelli sperimentali.
 

Vedi Altre leggi di distrib. negli Oggetti Matematici.