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 # Fitting Poisson  distribution
 # Aim : 
-
 To fit poisson distribution for the arrival of objects per minute from the feeder
 
 # Software required :  
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 Python and Visual component tool
 
 # Theory:
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 The Poisson distribution is the discrete probability distribution of the number of events occurring in a given time period, given the average number of times the event occurs over that time period.
 
 ![image](https://user-images.githubusercontent.com/104613195/166248326-fd042076-8b0b-40c4-8b11-1d8e8fcb74db.png)
 
  Conditions for Poisson Distribution:
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 1. An event can occur any number of times during a time period.
 2. Events occur independently. I
 3. The rate of occurrence is constant.
 4. The probability of an event occurring is proportional to the length of the time period. 
- 
-# Procedure :
-
+ # Procedure :
 ![image](https://user-images.githubusercontent.com/104613195/166251988-d0c53205-6080-4f7b-ae4c-398178586637.png)
-
 # Experiment :
-
 ![image](https://user-images.githubusercontent.com/103921593/230282876-f4a5afbf-cac1-4648-a1b0-c78840638a8e.png)
-
 # Program :
-
- 
-
-# Output : 
-
-
-
+~~~
+Developed By: RAKSHITHA K
+Register No: 23003887
+import numpy as np
+import math
+import scipy.stats
+L=[int(i) for i in input().split()]
+N=len(L); M=max(L) 
+X=list();f=list()
+for i in range (M+1):
+    c = 0
+    for j in range(N):
+        if L[j]==i:
+            c=c+1
+    f.append(c)
+    X.append(i)
+sf=np.sum(f)
+p=list()
+for i in range(M+1):
+    p.append(f[i]/sf) 
+mean=np.inner(X,p)
+p=list();E=list();xi=list()
+print("X P(X=x) Obs.Fr Exp.Fr xi")
+print("--------------------------")
+for x in range(M+1):
+    p.append(math.exp(-mean)*mean**x/math.factorial(x))
+    E.append(p[x]*sf)
+    xi.append((f[x]-E[x])**2/E[x])
+    print("%2.2f %2.3f %4.2f %3.2f %3.2f"%(x,p[x],f[x],E[x],xi[x]))
+print("--------------------------")
+cal_chi2_sq=np.sum(xi)
+print("Calculated value of Chi square is %4.2f"%cal_chi2_sq)
+table_chi2=scipy.stats.chi2.ppf(1-.01,df=M)
+print("Table value of chi square at 1 level is %4.2f"%table_chi2)
+if cal_chi2_sq<table_chi2:
+    print("The given data can be fitted in poisson Distribution at 1% LOS")
+else:
+    print("The given data cannot be fitted in Poisson Distribution at 1% LOS")
+# Output :
+![image](https://github.com/ramjan1729/Poisson_distribution/assets/139336455/7df7652e-225c-467e-9e6f-3df8b127fb5f)
 # Results
-
 The Poisson distribution is fitted for the objects arrived from feeder per minute and the data is tested using Chi-square test.