均勻分布

• 概念
• a與b的影響

概念

在概率論和統計學中，均勻分布也叫矩形分布，它是對稱概率分布，在相同長度間隔的分布概率是等可能的。 均勻分布由兩個參數a和b定義，它們是數軸上的最小值和最大值，通常縮寫為U（a，b）。

# 加載功能包 import numpy as np import scipy.stats as stats import matplotlib.pyplot as plt import matplotlib.style as style from IPython.core.display import HTML# 指定大小 %matplotlib inline style.use('fivethirtyeight') plt.rcParams['figure.figsize']=(14,7) plt.figure(dpi=100)# PDF 概率密度函數 plt.plot(np.linspace(-4,4,100),stats.uniform.pdf(np.linspace(-4,4,100))) # linspace選擇取值；uniform為均勻分布 plt.fill_between(np.linspace(-4,4,100),stats.uniform.pdf(np.linspace(-4,4,100)),alpha=.15) # 進行圖像填充# CDF累計概率密度函數 plt.plot(np.linspace(-4,4,100),stats.uniform.cdf(np.linspace(-4,4,100)))# 補充圖設置：LEGEND、TICKS與TITLE plt.text(x=-1.5, y=0.7, s="PDF(normed)", rotation=65, alpha = 75, weight="bold", color="#008fd5") plt.text(x=0.5, y=0.5, s="CDF", rotation=55, alpha = 75, weight="bold", color="#fc4f30") plt.tick_params(axis = 'both', which ='major', labelsize = 18) plt.axhline(y = 0, color ='black', linewidth = 1.3, alpha = 7) plt.text(x = -5, y = 1.055, s = "Normal Distribution - Overview", fontsize = 26, weight = 'bold', alpha = .75)

a與b的影響

plt.figure(dpi=100)# PDF loc=0, scale=1 plt.plot(np.linspace(-8,8,100),stats.uniform.pdf(np.linspace(-8,8,100),loc=0,scale=1)) plt.fill_between(np.linspace(-8,8,100),stats.uniform.pdf(np.linspace(-8,8,100),loc=0,scale=1),alpha=.15)# PDF loc=0, scale=2 plt.plot(np.linspace(-8,8,100),stats.uniform.pdf(np.linspace(-8,8,100),loc=0,scale=2)) plt.fill_between(np.linspace(-8,8,100),stats.uniform.pdf(np.linspace(-8,8,100),loc=0,scale=2),alpha=.15)# PDF loc=-3, scale=3 plt.plot(np.linspace(-8,8,100),stats.uniform.pdf(np.linspace(-4,4,100),loc=-3,scale=3)) plt.fill_between(np.linspace(-8,8,100),stats.uniform.pdf(np.linspace(-4,4,100),loc=-3,scale=3),alpha=.15)# LEGEND TICKS TITLE plt.text(x=-1.5, y=0.65, s="loc=0,scale=1", rotation=65, alpha = 75, weight="bold", color="#008fd5") plt.text(x=2, y=0.65, s="loc=0,scale=2", rotation=65, alpha = 75, weight="bold", color="#fc4f30") plt.text(x=-3.5, y=0.65, s="loc=-3,scale=3", rotation=65, alpha = 75, weight="bold", color="#e5ae38") plt.tick_params(axis = 'both', which ='major', labelsize = 18) plt.axhline(y = 0, color ='black', linewidth = 1.3, alpha = 7) plt.text(x = -5, y = 1.1, s = "Normal Distribution - loc and scale", fontsize = 26, weight = 'bold', alpha = .75)

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