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| -rw-r--r-- | Doc/library/random.rst | 56 |
1 files changed, 26 insertions, 30 deletions
diff --git a/Doc/library/random.rst b/Doc/library/random.rst index 82e900d..291eca3 100644 --- a/Doc/library/random.rst +++ b/Doc/library/random.rst @@ -425,29 +425,28 @@ Simulations:: >>> def trial(): ... return choices('HT', cum_weights=(0.60, 1.00), k=7).count('H') >= 5 ... - >>> sum(trial() for i in range(10000)) / 10000 + >>> sum(trial() for i in range(10_000)) / 10_000 0.4169 >>> # Probability of the median of 5 samples being in middle two quartiles >>> def trial(): - ... return 2500 <= sorted(choices(range(10000), k=5))[2] < 7500 + ... return 2_500 <= sorted(choices(range(10_000), k=5))[2] < 7_500 ... - >>> sum(trial() for i in range(10000)) / 10000 + >>> sum(trial() for i in range(10_000)) / 10_000 0.7958 Example of `statistical bootstrapping <https://en.wikipedia.org/wiki/Bootstrapping_(statistics)>`_ using resampling -with replacement to estimate a confidence interval for the mean of a sample of -size five:: +with replacement to estimate a confidence interval for the mean of a sample:: # http://statistics.about.com/od/Applications/a/Example-Of-Bootstrapping.htm from statistics import fmean as mean from random import choices - data = 1, 2, 4, 4, 10 - means = sorted(mean(choices(data, k=5)) for i in range(20)) + data = [41, 50, 29, 37, 81, 30, 73, 63, 20, 35, 68, 22, 60, 31, 95] + means = sorted(mean(choices(data, k=len(data))) for i in range(100)) print(f'The sample mean of {mean(data):.1f} has a 90% confidence ' - f'interval from {means[1]:.1f} to {means[-2]:.1f}') + f'interval from {means[5]:.1f} to {means[94]:.1f}') Example of a `resampling permutation test <https://en.wikipedia.org/wiki/Resampling_(statistics)#Permutation_tests>`_ @@ -463,7 +462,7 @@ between the effects of a drug versus a placebo:: placebo = [54, 51, 58, 44, 55, 52, 42, 47, 58, 46] observed_diff = mean(drug) - mean(placebo) - n = 10000 + n = 10_000 count = 0 combined = drug + placebo for i in range(n): @@ -476,32 +475,29 @@ between the effects of a drug versus a placebo:: print(f'The one-sided p-value of {count / n:.4f} leads us to reject the null') print(f'hypothesis that there is no difference between the drug and the placebo.') -Simulation of arrival times and service deliveries in a single server queue:: +Simulation of arrival times and service deliveries for a multiserver queue:: + from heapq import heappush, heappop from random import expovariate, gauss from statistics import mean, median, stdev average_arrival_interval = 5.6 - average_service_time = 5.0 - stdev_service_time = 0.5 - - num_waiting = 0 - arrivals = [] - starts = [] - arrival = service_end = 0.0 - for i in range(20000): - if arrival <= service_end: - num_waiting += 1 - arrival += expovariate(1.0 / average_arrival_interval) - arrivals.append(arrival) - else: - num_waiting -= 1 - service_start = service_end if num_waiting else arrival - service_time = gauss(average_service_time, stdev_service_time) - service_end = service_start + service_time - starts.append(service_start) - - waits = [start - arrival for arrival, start in zip(arrivals, starts)] + average_service_time = 15.0 + stdev_service_time = 3.5 + num_servers = 3 + + waits = [] + arrival_time = 0.0 + servers = [0.0] * num_servers # time when each server becomes available + for i in range(100_000): + arrival_time += expovariate(1.0 / average_arrival_interval) + next_server_available = heappop(servers) + wait = max(0.0, next_server_available - arrival_time) + waits.append(wait) + service_duration = gauss(average_service_time, stdev_service_time) + service_completed = arrival_time + wait + service_duration + heappush(servers, service_completed) + print(f'Mean wait: {mean(waits):.1f}. Stdev wait: {stdev(waits):.1f}.') print(f'Median wait: {median(waits):.1f}. Max wait: {max(waits):.1f}.') |