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@sachinsdate
Created October 27, 2019 17:29
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A simulation of the Poisson process
import random
import math
import statistics
import matplotlib.pyplot as plt
_lambda = 5
_num_events = 100
_event_num = []
_inter_event_times = []
_event_times = []
_event_time = 0
print('EVENT_NUM,INTER_EVENT_T,EVENT_T')
for i in range(_num_events):
_event_num.append(i)
#Get a random probability value from the uniform distribution's PDF
n = random.random()
#Generate the inter-event time from the exponential distribution's CDF using the Inverse-CDF technique
_inter_event_time = -math.log(1.0 - n) / _lambda
_inter_event_times.append(_inter_event_time)
#Add the inter-event time to the running sum to get the next absolute event time
_event_time = _event_time + _inter_event_time
_event_times.append(_event_time)
#print it all out
print(str(i) +',' + str(_inter_event_time) + ',' + str(_event_time))
#plot the inter-event times
fig = plt.figure()
fig.suptitle('Times between consecutive events in a simulated Poisson process')
plot, = plt.plot(_event_num, _inter_event_times, 'bo-', label='Inter-event time')
plt.legend(handles=[plot])
plt.xlabel('Index of event')
plt.ylabel('Time')
plt.show()
#plot the absolute event times
fig = plt.figure()
fig.suptitle('Absolute times of consecutive events in a simulated Poisson process')
plot, = plt.plot(_event_num, _event_times, 'bo-', label='Absolute time of event')
plt.legend(handles=[plot])
plt.xlabel('Index of event')
plt.ylabel('Time')
plt.show()
_interval_nums = []
_num_events_in_interval = []
_interval_num = 1
_num_events = 0
print('INTERVAL_NUM,NUM_EVENTS')
for i in range(len(_event_times)):
_event_time = _event_times[i]
if _event_time <= _interval_num:
_num_events += 1
else:
_interval_nums.append(_interval_num)
_num_events_in_interval.append(_num_events)
print(str(_interval_num) +',' + str(_num_events))
_interval_num += 1
_num_events = 1
#print the mean number of events per unit time
print(statistics.mean(_num_events_in_interval))
#plot the number of events in consecutive intervals
fig = plt.figure()
fig.suptitle('Number of events occurring in consecutive intervals in a simulated Poisson process')
plt.bar(_interval_nums, _num_events_in_interval)
plt.xlabel('Index of interval')
plt.ylabel('Number of events')
plt.show()
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