python隨機數學習筆記

  1 #coding:utf-8
  2 import  random
  3 
  4 # random.randint(1,10)產生1，10的隨機整數
  5 for i in range(1,5):
  6     ranint = random.randint(1,10)
  7     print(ranint, end=" ")
  8 print()
  9 
 10 #random.random()產生0，1之間的隨機數
 11 for j in range(1,5):
 12     ran_1 = random.random()
 13     print(ran_1,end=" ")
 14 print()
 15 #random.uniform(10,20)產生指定區間的隨機符點數
 16 for a in range(1,5):
 17     ran_2 = random.uniform(10,20)
 18     print(ran_2,end=" ")
 19 print()
 20 
 21 #random.randrange(10,20,2)在指定區間上以特定步長產生隨機數
 22 for b in range(1,5):
 23     ran_3 = random.randrange(10,20,2)
 24     print(ran_3,end=" ")
 25 print()
 26 for c in range(1,5):
 27     ran_4 = random.choice(range(10,20,2))
 28     print(ran_4,end=" ")
 29 print()
 30 
 31 #random.choice從序列中獲取一個隨機元素
 32 ran_5 = random.choice(['a','b','c','d'])
 33 print(ran_5)
 34 
 35 #random.shuffle(x[, random])，用於將一個列表中的元素打亂
 36 p = ['I','love','you','and','do','you','hate','me']
 37 ran_6 = random.shuffle(p)
 38 print(p)
 39 
 40 #random.sample(sequence, k)，從指定序列中隨機獲取指定長度的片段。sample函數不會修改原有序列。
 41 
 42 list = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
 43 slice = random.sample(list, 5)  #從list中隨機獲取5個元素，做爲一個片段返回
 44 print(slice)
 45 print(list)  #原有序列並無改變。
 46 
 47 #random.sample(population, k)產生指定序列的指定長度的隨機數,可利用此方法產生10位隨機密碼
 48 #列表轉字符串方法：「」.join(list)
 49 #字符串轉列表方法：list(str)
 50 ran_7 = random.sample('abcdefghijklmnopqrstuvwxyz1234567890!@#$%^&*():"?><',10)
 51 print("".join(ran_7))
 52 
 53 #random.triangular(low, high, mode)
 54 # random.triangular（低，高，模式）
 55 # 返回一個隨機浮點數N，以便在這些邊界之間使用指定的模式。該低和高界默認的0和1。
 56 # 所述模式參數默認爲邊界之間的中點，給人一種對稱分佈。low <= N <= high
 57 ran_8 = random.triangular(10,20)
 58 print(ran_8)
 59 
 60 # random.betavariate（alpha，beta ）
 61 # Beta分發。參數的條件是和 。返回值的範圍介於0和1之間。alpha > 0beta > 0
 62 ran_9 = random.betavariate(2,9)
 63 print(ran_9)
 64 
 65 # random.expovariate（lambd ）
 66 # 指數分佈。 lambd是1.0除以所需的平均值。它應該是非零的。
 67 # （該參數將被稱爲「拉姆達」，可是這是在Python保留字。）
 68 # 返回值的範圍從0到正無窮大若是lambd爲正，且從負無窮大到0，若是lambd爲負。
 69 for i in [0.01,0.2,1,33,-0.02,-0.99,-22,-88]:
 70     ran_10 = random.expovariate(i)
 71     print(ran_10,end=" ")
 72 
 73 # random.gammavariate（alpha，beta ）
 74 # Gamma分佈。（不是伽瑪函數！）參數的條件是和。alpha > 0beta > 0
 75 #
 76 # 機率分佈函數是：
 77 #
 78 #           x ** (alpha - 1) * math.exp(-x / beta)
 79 # pdf(x) =  --------------------------------------
 80 #             math.gamma(alpha) * beta ** alpha
 81 # random.gauss（mu，sigma ）
 82 # 高斯分佈。 mu是平均值，sigma是標準誤差。這比normalvariate()下面定義的函數稍快。
 83 #
 84 # random.lognormvariate（mu，sigma ）
 85 # 記錄正態分佈。若是你採用這個分佈的天然對數，你將得到具備平均μ和標準誤差西格瑪的正態分佈。 mu能夠有任何值，sigma必須大於零。
 86 #
 87 # random.normalvariate（mu，sigma ）
 88 # 正態分佈。 mu是平均值，sigma是標準誤差。
 89 #
 90 # random.vonmisesvariate（mu，kappa ）
 91 # mu是平均角度，以弧度表示，介於0和2 * pi之間，kappa 是濃度參數，必須大於或等於零。若是 kappa等於零，則該分佈在0到2 * pi的範圍內減少到均勻的隨機角度。
 92 #
 93 # random.paretovariate（alpha ）
 94 # 帕累託分佈。 alpha是形狀參數。
 95 #
 96 # random.weibullvariate（alpha，beta ）
 97 # 威布爾分佈。 alpha是scale參數，beta是shape參數。
 98 
 99 # 基本示例：
100 #
101 # >>>
102 # >>> random()                             # Random float:  0.0 <= x < 1.0
103 # 0.37444887175646646
104 #
105 # >>> uniform(2.5, 10.0)                   # Random float:  2.5 <= x < 10.0
106 # 3.1800146073117523
107 #
108 # >>> expovariate(1 / 5)                   # Interval between arrivals averaging 5 seconds
109 # 5.148957571865031
110 #
111 # >>> randrange(10)                        # Integer from 0 to 9 inclusive
112 # 7
113 #
114 # >>> randrange(0, 101, 2)                 # Even integer from 0 to 100 inclusive
115 # 26
116 #
117 # >>> choice(['win', 'lose', 'draw'])      # Single random element from a sequence
118 # 'draw'
119 #
120 # >>> deck = 'ace two three four'.split()
121 # >>> shuffle(deck)                        # Shuffle a list
122 # >>> deck
123 # ['four', 'two', 'ace', 'three']
124 #
125 # >>> sample([10, 20, 30, 40, 50], k=4)    # Four samples without replacement
126 # [40, 10, 50, 30]
127 # 模擬：
128 #
129 # >>>
130 # >>> # Six roulette wheel spins (weighted sampling with replacement)
131 # >>> choices(['red', 'black', 'green'], [18, 18, 2], k=6)
132 # ['red', 'green', 'black', 'black', 'red', 'black']
133 #
134 # >>> # Deal 20 cards without replacement from a deck of 52 playing cards
135 # >>> # and determine the proportion of cards with a ten-value
136 # >>> # (a ten, jack, queen, or king).
137 # >>> deck = collections.Counter(tens=16, low_cards=36)
138 # >>> seen = sample(list(deck.elements()), k=20)
139 # >>> seen.count('tens') / 20
140 # 0.15
141 #
142 # >>> # Estimate the probability of getting 5 or more heads from 7 spins
143 # >>> # of a biased coin that settles on heads 60% of the time.
144 # >>> trial = lambda: choices('HT', cum_weights=(0.60, 1.00), k=7).count('H') >= 5
145 # >>> sum(trial() for i in range(10000)) / 10000
146 # 0.4169
147 #
148 # >>> # Probability of the median of 5 samples being in middle two quartiles
149 # >>> trial = lambda : 2500 <= sorted(choices(range(10000), k=5))[2]  < 7500
150 # >>> sum(trial() for i in range(10000)) / 10000
151 # 0.7958
152 # 使用從新取樣和替換來估計大小爲5的樣本的均值的置信區間的統計自舉的示例：
153 #
154 # # http://statistics.about.com/od/Applications/a/Example-Of-Bootstrapping.htm
155 # from statistics import mean
156 # from random import choices
157 #
158 # data = 1, 2, 4, 4, 10
159 # means = sorted(mean(choices(data, k=5)) for i in range(20))
160 # print(f'The sample mean of {mean(data):.1f} has a 90% confidence '
161 #       f'interval from {means[1]:.1f} to {means[-2]:.1f}')
162 # 從新採樣置換測試的示例， 以肯定藥物與安慰劑的效果之間觀察到的差別的統計顯着性或p值：
163 #
164 # # Example from "Statistics is Easy" by Dennis Shasha and Manda Wilson
165 # from statistics import mean
166 # from random import shuffle
167 #
168 # drug = [54, 73, 53, 70, 73, 68, 52, 65, 65]
169 # placebo = [54, 51, 58, 44, 55, 52, 42, 47, 58, 46]
170 # observed_diff = mean(drug) - mean(placebo)
171 #
172 # n = 10000
173 # count = 0
174 # combined = drug + placebo
175 # for i in range(n):
176 #     shuffle(combined)
177 #     new_diff = mean(combined[:len(drug)]) - mean(combined[len(drug):])
178 #     count += (new_diff >= observed_diff)
179 #
180 # print(f'{n} label reshufflings produced only {count} instances with a difference')
181 # print(f'at least as extreme as the observed difference of {observed_diff:.1f}.')
182 # print(f'The one-sided p-value of {count / n:.4f} leads us to reject the null')
183 # print(f'hypothesis that there is no difference between the drug and the placebo.')
184 # 模擬單個服務器隊列中的到達時間和服務交付：
185 #
186 # from random import expovariate, gauss
187 # from statistics import mean, median, stdev
188 #
189 # average_arrival_interval = 5.6
190 # average_service_time = 5.0
191 # stdev_service_time = 0.5
192 #
193 # num_waiting = 0
194 # arrivals = []
195 # starts = []
196 # arrival = service_end = 0.0
197 # for i in range(20000):
198 #     if arrival <= service_end:
199 #         num_waiting += 1
200 #         arrival += expovariate(1.0 / average_arrival_interval)
201 #         arrivals.append(arrival)
202 #     else:
203 #         num_waiting -= 1
204 #         service_start = service_end if num_waiting else arrival
205 #         service_time = gauss(average_service_time, stdev_service_time)
206 #         service_end = service_start + service_time
207 #         starts.append(service_start)
208 #
209 # waits = [start - arrival for arrival, start in zip(arrivals, starts)]
210 # print(f'Mean wait: {mean(waits):.1f}.  Stdev wait: {stdev(waits):.1f}.')
211 # print(f'Median wait: {median(waits):.1f}.  Max wait: {max(waits):.1f}.')
212 # 也能夠看看 「黑客統計」 是Jake Vanderplas 關於統計分析的視頻教程， 僅使用了一些基本概念，包括模擬，抽樣，改組和交叉驗證。
213 # 經濟模擬Peter Norvig對 市場的模擬 ，顯示了該模塊提供的許多工具和分佈的有效使用（高斯，均勻，樣本，beta變量，選擇，三角和randrange）。
214 #
215 # 具體的機率介紹（使用Python）Peter Norvig 的教程，涵蓋了機率論的基礎知識，如何編寫模擬，以及如何使用Python進行數據分析。
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