hamza9559 / poisson_distribution

Fitting Poisson distribution

NAME: HAMZA FAROOQUE

REG. NO: 212223040054

Aim :

To fit poisson distribution for the arrival of objects per minute from the feeder

Software required :

Python and Visual component tool

Theory:

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.

Conditions for Poisson Distribution:

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 :

Experiment :

Program :

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 :

Results

The Poisson distribution is fitted for the objects arrived from feeder per minute and the data is tested using Chi-square test.