def example_stats():
number_of_experiments = 500
number_of_prisoners = 50
results = monte_carlo(number_of_experiments, number_of_prisoners)
#Calculate some statistics:
minimum = min(results)
maximum = max(results)
median = (maximum - minimum)/2.0 + minimum
mean = np.mean(results)
string = "The simulation with {} results took an average of {} days \
or {} months or {} years to finish."
print(string.format(number_of_experiments, mean, mean/12, mean/365.0))
#what's the spread?
print "max:", maximum
print "min:", minimum
#where does the mean fall within that spread?
print "mean:", mean
print "median:", median
print "distance from mean to median:", mean - median
#how broad is the peak?
standard_deviation = np.std(results)
print "standard deviation:", standard_deviation
#Plot a histogram
histogram_data = plt.hist(results, bins=30)
plt.vlines(
median,
0,
max(histogram_data[0]),
linestyles='dashed',
lw = 4,
label = "median",
color='red')
plt.vlines(
mean,
0,
max(histogram_data[0]),
linestyles='dashed',
lw = 4,
label = "mean",
color='orange')
plt.title("Prisoner Escape Riddle Historgram, n={}".format(number_of_experiments))
plt.xlabel("Number of days to escape")
plt.ylabel("Frequency")
plt.legend()
plt.show()
def example_stats():
number_of_experiments = 500
number_of_prisoners = 50
results = monte_carlo(number_of_experiments, number_of_prisoners)
#Calculate some statistics:
minimum = min(results)
maximum = max(results)
median = (maximum - minimum) / 2.0 + minimum
mean = np.mean(results)
string = "The simulation with {} results took an average of {} days \
or {} months or {} years to finish."
print(string.format(number_of_experiments, mean, mean / 12, mean / 365.0))
#what's the spread?
print "max:", maximum
print "min:", minimum
#where does the mean fall within that spread?
print "mean:", mean
print "median:", median
print "distance from mean to median:", mean - median
#how broad is the peak?
standard_deviation = np.std(results)
print "standard deviation:", standard_deviation
#Plot a histogram
histogram_data = plt.hist(results, bins=30)
plt.vlines(median,
0,
max(histogram_data[0]),
linestyles='dashed',
lw=4,
label="median",
color='red')
plt.vlines(mean,
0,
max(histogram_data[0]),
linestyles='dashed',
lw=4,
label="mean",
color='orange')
plt.title("Prisoner Escape Riddle Historgram, n={}".format(
number_of_experiments))
plt.xlabel("Number of days to escape")
plt.ylabel("Frequency")
plt.legend()
plt.show()
label = "mean",
color='orange')
plt.title("Prisoner Escape Riddle Historgram, n={}".format(number_of_experiments))
plt.xlabel("Number of days to escape")
plt.ylabel("Frequency")
plt.legend()
plt.show()
#How quickly does the mean converge as number_of_experiments increases?
x_values = [] # number_of_experiments
y_values = [] # average value at each number_of_experiments
number_of_prisoners = 50
for n in range(1,51):
print n
x_values.append(n)
mean = np.mean(monte_carlo(n, number_of_prisoners))
y_values.append(mean)
plt.scatter(x_values, y_values)
plt.title("Convergence of Mean Value, number_of_prisoners = {}".format(number_of_prisoners))
plt.xlabel("Number of experiments")
plt.ylabel("Days to prisoner release")
#plt.savefig("convergence.png")
def line(slope, intercept, x):
a = intercept
b = slope
y = a + b * x
return y
slope, intercept, r_value, p_value, std_err = stats.linregress(x_values,y_values)
x_line_points = np.arange(1,51,1)
plt.title("Prisoner Escape Riddle Historgram, n={}".format(
number_of_experiments))
plt.xlabel("Number of days to escape")
plt.ylabel("Frequency")
plt.legend()
plt.show()
#How quickly does the mean converge as number_of_experiments increases?
x_values = [] # number_of_experiments
y_values = [] # average value at each number_of_experiments
number_of_prisoners = 50
for n in range(1, 51):
print n
x_values.append(n)
mean = np.mean(monte_carlo(n, number_of_prisoners))
y_values.append(mean)
plt.scatter(x_values, y_values)
plt.title("Convergence of Mean Value, number_of_prisoners = {}".format(
number_of_prisoners))
plt.xlabel("Number of experiments")
plt.ylabel("Days to prisoner release")
#plt.savefig("convergence.png")
def line(slope, intercept, x):
a = intercept
b = slope
y = a + b * x
return y
