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  • 虽然有一些博文已经介绍了一些方法,但是我在调研和绘制时发现,大部分的博文中都用了复杂的for循环语句来实现(可能是因为我太笨,看不懂for循环),并且大部分都不是针对DataFrame来做累计概率分布的,都是做简单...

    累积分布函数(Cumulative Distribution Function),又叫分布函数,是概率密度函数的积分,能完整描述一个实随机变量X的概率分布。在电子器件制造中常常用于描述器件失效分布,可以明显的表示出在特定数值下的器件概率分布占比;
    虽然有一些博文已经介绍了一些方法,但是我在调研和绘制时发现,大部分的博文中都用了复杂的for循环语句来实现(可能是因为我太笨,看不懂for循环),并且大部分都不是针对DataFrame来做累计概率分布的,都是做简单列表,在解决问题的过程中,我发现了自己认为更加简单,易用的代码实现方法,在这里与大家分享,希望对大家有所帮助;
    首先,介绍解决问题的思路
    众所周知,累计概率分布就是对于可选变量由小到大排列后,各个变量的累计概率形成的,因此:

    **1)将所要处理的数据的所有可能取值中的唯一值以及唯一值出现的频数得出来;

    2)所有数据的总数我们需要知道,因为每个数据出现频数除以数据总数才能获得该数据的概率;

    3)将数据列表从小到大排列,然后将每个数据出现的概率进行叠加,这里需要用到cumsum函数;

    4)绘制累计分布图**

    然后,就是具体的代码分组讲解:
    1)将所要处理的数据的所有可能取值中的唯一值以及唯一值出现的频数得出来;

    import pandas as pd
    import matplotlib.pyplot as plt
    import numpy as np
    

    这里是需要用到的模块,在程序最开始先调用,就像做菜准备好调料一样;
    紧接着是数据的读取,为了简便讲解,这里仅仅选用数据的一部分,所用的数据是长度为193的列表,格式为csv,因此,应用read_csv命令,

    #读取待处理数据
    data=pd.read_csv("c:\\Users\\dell\\Desktop\\1.csv",header=None)
    

    以下是运行代码的终端显示
    在这里插入图片描述
    数据类型为只有一列的dataframe格式;

    #获取数据的总数
    denominator=len(data[0])
    #将数据转换为Series
    Data=pd.Series(data[0])
    #利用value_counts方法进行分组频数计算
    Fre=Data.value_counts()
    #对获得的表格整体按照索引自小到大进行排序
    Fre_sort=Fre.sort_index(axis=0,ascending=True)
    

    得到的Fre_sort数据如下所示:
    在这里插入图片描述
    2)所有数据的总数我们需要知道,因为每个数据出现频数除以数据总数才能获得该数据的概率;

    #重置表格索引
    Fre_df=Fre_sort.reset_index()
    #将频数转换成概率
    Fre_df[0]=Fre_df[0]/denominator
    #将列表列索引重命名
    Fre_df.columns=['Rds','Fre']
    

    得到的列表输出如下所示:
    在这里插入图片描述
    3)将数据列表从小到大排列,然后将每个数据出现的概率进行叠加,这里需要用到cumsum函数;

    #利用cumsum函数进行概率的累加并按照顺序添加到表格中
    Fre_df['cumsum']=np.cumsum(Fre_df['Fre'])
    

    数据表格输出如下所示:
    在这里插入图片描述

    #创建画布
    plot=plt.figure()
    #只有一张图,也可以多张
    ax1=plot.add_subplot(1,1,1)
    #按照Rds列为横坐标,累计概率分布为纵坐标作图
    ax1.plot(Fre_df['Rds'],Fre_df['cumsum'])
    #图的标题
    ax1.set_title("CDF")
    #横轴名
    ax1.set_xlabel("Rds")
    #纵轴名
    ax1.set_ylabel("P")
    #横轴的界限
    ax1.set_xlim(0.1,0.5)
    #图片显示
    plt.show()
    

    4)绘制累计分布图
    图片输出如下所示:
    在这里插入图片描述
    完整代码如下所示:

    import pandas as pd
    import matplotlib.pyplot as plt
    import numpy as np
    data=[]
    data=pd.read_csv("c:\\Users\\dell\\Desktop\\1.csv",header=None)
    denominator=len(data[0])#分母数量
    Data=pd.Series(data[0])#将数据转换为Series利用分组频数计算
    Fre=Data.value_counts()
    Fre_sort=Fre.sort_index(axis=0,ascending=True)
    Fre_df=Fre_sort.reset_index()#将Series数据转换为DataFrame
    Fre_df[0]=Fre_df[0]/denominator#转换成概率
    Fre_df.columns=['Rds','Fre']
    Fre_df['cumsum']=np.cumsum(Fre_df['Fre'])
    plot=plt.figure()
    ax1=plot.add_subplot(1,1,1)
    ax1.plot(Fre_df['Rds'],Fre_df['cumsum'])
    ax1.set_title("CDF")
    ax1.set_xlabel("Rds")
    ax1.set_ylabel("P")
    ax1.set_xlim(0.1,0.5)
    plt.show()
    

    注意事项:
    1)在需要对数据进行频数计算时,需要用到pd.Series的value_counts方法,但是read_csv的数据格式是pd.DataFrame,因此,需要通过pd.Series方法对dataframe中的data[0]列进行转换,即

    Data=pd.Series(data[0])#将数据转换为Series利用分组频数计算
    Fre=Data.value_counts()
    

    2)在对Fre数据表格进行排序时,需要用到Series和DataFrame的sort_index函数,其中axis=0代表按照行索引进行排序,默认是升序,降序用ascending=False来限定,如果按照特定行或列,可以在by参数中进行陷定;

    Fre=Data.value_counts()
    Fre_sort=Fre.sort_index(axis=0,ascending=True)
    

    3)cumsum函数特别适合于进行CDF图绘制,与for循环相比,效率应该更高;

    Fre_df['cumsum']=np.cumsum(Fre_df['Fre'])
    

    4)图片的横坐标界限需要细化,否则,由于里面的个别异常点导致图像的可视化程度降低,也可以通过布尔索引,将异常值去掉;

    展开全文
  • excell中如何绘制正态分布图

    千次阅读 2012-02-27 12:01:40
    绘制正态分布图:首先计算有效数据样本的最大值、最小值、有效算术平均值、标准偏差。 确定统计样本有效数据的分布范围。 2、用正态分布涵数计算样本有效数据范围间数据的正态分布。NORMIDST(样本统计的范围,...

    正态分布函数为NORMDIST

    要绘制正态分布图:首先计算有效数据样本的最大值、最小值、有效算术平均值、标准偏差。

    确定统计样本有效数据的分布范围。

    2、用正态分布涵数计算样本有效数据范围间数据的正态分布。NORMIDST(样本统计的范围,有效样本算术平均值,有效样本的标准偏差,{10})第四参数如果是1,返回的是累计分布,0返回的是概率分布,根据自己对样本统计的需要选择!

    1.AVERAGE求平均值   0.0274

    2. STDEV 估算样本的标准偏差。标准偏差反映相对于平均值 (mean) 的离散程度

    0.995914

    1.AVERAGE求平均值

    2. STDEV 估算样本的标准偏差。标准偏差反映相对于平均值 (mean) 的离散程度

    正态分布函数的语法NORMDIST(xmeanstandard_devcumulative)cumulative为一逻辑值,如果为0则是密度函数,如果为1则是累积分布函数。如果画正态分布图,则为0

    例如均值10%标准值20%的正态分布,先在A1中敲入一个变量,假定-50,选中A列,点编辑-填充-序列,选择列,等差序列,步长值10,终止值70。然后在B1中敲入NORMDISTA110200),返回值为0.000222,选中B1,当鼠标在右下角变成黑十字时,下拉至B13,选中A1B13区域,点击工具栏上的图表向导-散点图,选中第一排第二个图,点下一步,默认设置,下一步,标题自己写,网格线中的勾去掉,图例中的勾去掉,点下一步,完成。图就初步完成了。下面是微调把鼠标在图的坐标轴上点右键,选 坐标轴格式,在刻度中填入你想要的最小值,最大值,主要刻度单位(x轴上的数值间隔),y轴交叉于(y0时,x多少)等等。确定后,正态分布图就大功告成了。

    制作标准正态分布图

    步骤一:输入数据。

    1.在单元格A1输入

    2.选定单元格A1A121

    3.选取编辑菜单下的填充”—“序列

    序列产生在框,选定选项;

    类型框,选定等差序列选项;

    步长值框,输入0.05

    终止值框,输入3

    4.单击确定

    5.在单元格B1中输入,回车得0.004432 ,即为 时的标准正态分布的概率密度函数值。

    6.把鼠标放在单元格B1上的单元格填充柄上,当鼠标变成十字时,向下拖曳鼠标至B121

    步骤二:作图。

    1.用鼠标左键拖曳选定作图所需的数据区域A1B121

    2.点击常用工具栏中的图表向导按钮。

    3.在弹出的图表向导的(4步骤之1)图表类型中,选择散点图,在子图表类型中选择第二排右侧第一个图(形为两条曲线相交),单击下一步

    4.在弹出的图表向导的(4步骤之2)图表数据源中,使用默认值,单击下一步

    5.在弹出的图表向导的(4步骤之3)图表选项中,

    标题选项卡中,图表标题方框中输入标准正态分布图

    网格线选项卡中,取消网格线;

    图例选项卡中,取消图例。

    6.点击下一步,得到图表向导的(4步骤之4)图表位置,使用默认值,点完成即可。适当调整字体和刻度,得到标准正态分布图。

    展开全文
  • 已知各数据的概率,想要画一张CDF,代码如下 from scipy import stats import matplotlib.pyplot as plt import numpy as np y = [] for i in range(42): y.append(1) for i in range(42,45): y....
  • 本文介绍了如何读取H5文件模型的权重,然后用MATLAB中绘制权重的概率密度图和分布图


    前言

      在keras框架中,CNN模型的权重存储在.H5文件中。对于模型压缩,如果我们可以直观地表示权重分布,则可以更好地压缩模型。

      源代码及测试模型:github


    一、.h5文件是什么?

      H5文件是层次数据格式第5代的版本(Hierarchical Data Format,HDF5),它是用于存储科学数据的一种文件格式和库文件。

     H5文件在内存占用、压缩、访问速度方面都有非常优秀的特性,在工业领域和科学领域都有很多运用。

     H5将文件结构简化成两个主要的对象类型:
      1、数据集,就是同一类型数据的多维数组。
      2、组,是一种容器结构,可以包含数据集和其他组。

     这导致了H5文件是一种真正的层次结构、文件系统式的数据类型。

    使用HDFview可以查看.h5文件数据:

    二、读取权重

      在keras框架下,权重存储在.h5文件里,但是会发现他是多维的数组,我们需要转化为一维的数组。

    读取权重代码如下(python)github里也给了示例模型数据:

    import h5py
    import numpy as np
    
    f = h5py.File("vgg_c10_weights.h5", 'r')
    weight=f['dense_2']['dense_2']['kernel:0'][:]
    arr=[*weight.flat]
    print(arr)
    
    

    三、画概率密度和概率分布图

    1、代码

    matlab代码如下:

    %Weight data
    y=[-0.07823358, 0.036483012, 0.023191258, -0.030578785, -0.066693835, -0.0854588, 0.08300646, 0.08942385, -0.11829137, -0.013333141, -0.07403876, 0.10446264, -0.0056504924, -0.07293615, 0.09306226, -0.02272057, 0.10528777, 0.0033772867, 0.05895922, 0.004327648, 0.007880116, -0.007982012, -0.02346343, -0.021149963, -0.14343587, 0.060619462, -0.017020343, 0.0466622, -0.0023637738, -0.1394115, -0.025693009, -0.045585092, 0.11406694, 0.06605256, 0.08267429, -0.032339267, -0.08646445, 0.023823919, -0.058365516, -0.06329959, 0.03088722, -0.0681865, 0.024144359, 0.018830607, 0.073954396, 0.062303334, -0.092773594, -0.024946135, -0.06477076, -0.10998212, 0.09022007, -0.008706043, -0.010750936, -0.092770554, -0.08854947, -0.04611184, 0.03377814, -0.06946026, -0.015279668, -0.09689598, 0.105069585, 0.06281916, 0.052788198, -0.04716059, -0.0050950465, -0.045496017, 0.036378097, -0.036254294, 0.01855796, 0.11275769, 0.080049716, -0.08884576, 0.085176334, -0.036098063, 0.08046631, 0.008654743, -0.052356284, -0.06148749, 0.045361444, -0.10486241, 0.026779855, -0.07999122, 0.11058479, 0.044780087, 0.025129262, 0.06437333, 0.04211642, -0.0101183, 0.05465461, -0.08255355, -0.06564422, 0.059500016, 0.011849151, -0.0030775864, -0.089061156, 0.04785844, 0.08207179, 0.008126591, 0.10400653, 0.0067659705, -0.0796457, 0.11147225, 0.058147557, 0.06509853, -0.06336494, -0.09358208, -0.013097775, -0.042526584, 0.032579888, 0.11175599, 0.059967287, 0.0031134244, -0.07826652, -0.103837244, -0.060524236, -0.06133329, -0.14628379, -0.00027663456, -0.007726543, 0.028311793, 0.062065877, -0.020515855, 0.07635802, -0.12706412, 0.06209806, 0.04437406, -0.05928555, -0.07670137, -0.02398678, 0.065054454, 0.0018625982, -0.13011803, -0.03246126, 0.00083278754, -0.05125616, 0.10150898, -0.017208248, 0.021759547, -0.12802114, -0.026744707, -0.05097659, 0.027193421, -0.0028606812, -0.08272114, 0.08111431, 0.03175934, -0.09664833, -0.052566092, -0.119504005, -0.121057525, -0.0025585445, 0.10065011, 0.043200996, -0.100719124, 0.084012456, -0.047567166, 0.03869142, -0.019688971, -0.01255515, 0.087166175, 0.024723971, -0.0183944, -0.0018622207, -0.08454035, 0.0724082, 0.020561479, -0.079297885, -0.099633135, 0.09083268, -0.026335834, 0.017297642, 0.07453839, 0.026781961, -0.035677906, -0.052836094, 0.098903574, 0.101426035, 0.08467944, -0.048275996, 0.10063886, 0.072023295, -0.0020786768, -0.08507581, -0.08312145, -0.082591616, -0.11272094, -0.11838837, -0.07308268, 0.02731154, 0.018327735, 0.0487386, -0.059277177, -0.0357025, 0.070758596, 0.04837331, 0.09040934, 0.04967485, 0.004220202, -0.13225341, 0.060381398, -0.029936474, -0.08929155, 0.06547212, -0.10580234, 0.05767494, 0.05627891, -0.01685736, -0.08883569, 0.063161716, 0.07510806, -0.088413574, -0.16631822, -0.013542988, -0.028250327, 0.016346216, -0.031058444, 0.041276153, 0.029487161, -0.13452686, -0.12862928, -0.073844016, -0.07946574, -0.060389776, 0.0005943128, -0.0844686, 0.07297822, -0.05023131, -0.04803074, 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    ymin=min(y);
    ymax=max(y);
    x=linspace(ymin,ymax,40);
    %The maximum and minimum interval is divided into 40 equal points (39 equal points), and then the number of each interval is calculated
      
    yy=hist(y,x);
    %Calculate the number of each interval
    yy=yy/length(y);
    %计算各个区间的个数;Calculate the number of each interval
    bar(x,yy)
    %画出概率密度分布图;Plot the probability density distribution
    s=0;
    for i=2:length(x)
        s=[s,trapz(x([1:i]),yy([1:i]))];
    end
    figure;
    plot(x,s,x,s,'*')
    

    2、结果

    请添加图片描述


    总结

    In the framework of keras, the weights of CNN model are stored in. H5 file. For model compression, if we can intuitively express the weight distribution, we can better compress the model

    Run w_ distribution.py File, you can read the weight in the. H5 file.Then run the weight distribution. M file in MATLAB to draw the probability density distribution of the weight

    展开全文
  • 可视化篇(四)——— python绘制双y轴、箱线图、概率分布三种图形及案例摘要绘制双y轴图形绘制箱线图绘制概率分布图 摘要 本文演示了如何通过python绘制双y轴、箱线图、概率分布三种图形,并给出了具体案例供读者...

    可视化篇(四)——— python绘制双y轴、箱线图、概率分布三种图形及案例

    摘要

    本文演示了如何通过python绘制双y轴、箱线图、概率分布三种图形,并给出了具体案例供读者参考。

    绘制双y轴图形

    效果图如下
    在这里插入图片描述
    代码如下

    import numpy as np
    import matplotlib.pyplot as plt
    from matplotlib.font_manager import FontProperties
    import datetime
    
    # 此设置为使图形能显示带特殊格式的字符
    plt.rcParams['axes.unicode_minus'] = False
    
    # 构建虚拟数据
    """
    x轴为日期
    左y轴为y1,y2
    右y轴为 y1-y2 及其均值
    """
    date = [(datetime.datetime.strptime("2019-12-08 00:00:00","%Y-%m-%d %H:%M:%S") + datetime.timedelta(days=i)).strftime("%Y-%m-%d%H:%M:%S")[:10] for i in range(300)]
    x = np.arange(300)
    x_ticks = [int(i) for i in np.linspace(0, (x.shape[0] - 1), 5)]
    y1 = np.random.randn(300) *2 + 75
    y2 = np.random.randn(300) *2 + 70
    
    # 设置字体
    font = FontProperties(fname="C:\Windows\Fonts\simsun.ttc", size=30)
    
    figure = plt.figure(figsize=[30, 16], dpi=72)
    
    ax1 = figure.add_subplot(111)
    
    fig1 = ax1.plot(x, y1, color="c", label="y1")
    fig2 = ax1.plot(x, y2, color="b", label="y2")
    plt.yticks(fontproperties=font)
    plt.xlabel("date", fontproperties=FontProperties(fname="C:\Windows\Fonts\simsun.ttc", size=45))
    plt.xticks(x_ticks, date, fontproperties=FontProperties(fname="C:\Windows\Fonts\simsun.ttc", size=30), rotation=15)
    ax1.set_ylim(40, 83)
    ax1.set_ylabel("y", fontproperties=FontProperties(fname="C:\Windows\Fonts\simsun.ttc", size=45))
    
    ax2 = ax1.twinx()
    
    fig3 = ax2.plot(x, y1-y2, color="m", label="y1-y2")
    fig4 = ax2.plot(x, [(y1-y2).mean()] * (x.shape[0]), color="g", linestyle="--", linewidth=5, label="mean of y1-y2")
    ax2.set_ylim(-5, 40)
    ax2.set_ylabel("y1-y2", fontproperties=FontProperties(fname="C:\Windows\Fonts\simsun.ttc", size=45))
    plt.yticks(fontproperties=font)
    
    # 显示均值
    ax2.text(x.shape[0], (y1-y2).mean() - 0.1, str((y1-y2).mean())[:4], fontdict={"size": 30, "color": "g"})
    
    # 设置图列
    legends = fig1 + fig2 + fig3 + fig4
    labels = [l.get_label() for l in legends]
    plt.legend(legends, labels, prop=font, loc=(0.8, 0.4))
    
    plt.show()
    

    绘制箱线图

    效果图如下
    在这里插入图片描述

    代码如下

    import numpy as np
    import matplotlib.pyplot as plt
    from matplotlib.font_manager import FontProperties
    import seaborn as sns
    import pandas as pd
    
    # 此设置为使图形能显示带特殊格式的字符
    plt.rcParams['axes.unicode_minus'] = False
    
    # 构建虚拟数据
    """
    绘制x1,x2,x3,x4四组数据的箱线图
    """
    x1 = np.random.randn(200)*2+5
    x2 = np.random.randn(200)*2+10
    x3 = np.random.randn(200)*2+15
    x4 = np.random.randn(200)*2+20
    data = np.array([x1,x2,x3,x4]).T
    df = pd.DataFrame(data,columns=["x1","x2","x3","x4"])
    
    font = FontProperties(fname = "C:\Windows\Fonts\simsun.ttc",size=30)
    figure = plt.figure(figsize=[16,12],dpi=72)
    
    # whis为异常值在上下四分位点差值的多少倍以外
    sns.boxplot(data = df, whis=3, orient="v", fliersize=15)
    plt.ylabel("Kpa", fontproperties=FontProperties(fname="C:\Windows\Fonts\simhei.ttf", size=45))
    plt.yticks(fontproperties=font)
    plt.xticks(fontproperties = FontProperties(fname = "C:\Windows\Fonts\simsun.ttc",size=45))
    plt.grid(linestyle="--", linewidth=1, alpha=0.5, axis="y")
    plt.show()
    

    绘制概率分布图

    效果图如下
    在这里插入图片描述
    代码如下

    import numpy as np
    import matplotlib.pyplot as plt
    from matplotlib.font_manager import FontProperties
    import seaborn as sns
    
    # 此设置为使图形能显示带特殊格式的字符
    plt.rcParams['axes.unicode_minus'] = False
    
    # 构建虚拟数据
    """
    绘制x的概率分布图
    """
    x = np.random.randn(1000)*2+100
    figure = plt.figure(figsize=[30,26],dpi=72)
    sns.distplot(x,bins=30,kde_kws={"color":"red"},color="c")
    plt.xticks(fontproperties=FontProperties(fname="C:\Windows\Fonts\simsun.ttc",size=30))
    plt.yticks(fontproperties=FontProperties( fname="C:\Windows\Fonts\simsun.ttc",size=30))
    plt.xlabel(xlabel="活化能",fontproperties = FontProperties( fname="C:\Windows\Fonts\simsun.ttc",size=45))
    plt.ylabel("概率密度",fontproperties = FontProperties( fname="C:\Windows\Fonts\simsun.ttc",size=45))
    
    plt.show()
    

    by CyrusMay 2021 01 25

    脱下长日的假面
    奔向梦幻的疆界
    南瓜马车的午夜
    换上童话的玻璃鞋
    ——————五月天(拥抱)——————

    展开全文
  • 现在人工智能越来越实用,甚至深入到千家万户,随之而来的就是...概率分布表示样本数据的模样,长的好不好看如果有图像展示出来就非常完美了,使用Python绘制频率分布直方非常简洁,因为用的频次非常高,这里记录...
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  • 直方是一种用于展示定量数据分布的常用图形。通过直方,用户可以很直观的看出数据分布的形状、中心位置以及数据的...在绘制时,直方是按照数值大小进行分组排列,前后顺序不可变更;柱状则是对分类对象进...
  • 我已经绘制了Matplotlib的直方,通过目视检查,这些值似乎是正态分布的:但是,我想验证这一点.我已经发现在 scipy.stats.mstats.normaltest下实施了一个正常测试,但结果另有说明.我得到这个输出:(masked_array(data...
  • matlab绘正态/卡方/t/F分布概率密度

    千次阅读 2020-07-16 18:02:13
    本博文源于上一篇博文的函数格式的应用,链接如下: 本博文就以例子方式讲解如何绘出分布概率密度绘制
  • 这篇文章主要介绍了python 生成正态分布数据,并绘图和解析,帮助大家更好的利用python进行数据分析,感兴趣的朋友可以了解下1、生成正态分布数据并绘制概率分布图importpandasaspdimportnumpyasnpimportmatplotlib....
  • 本文演示了如何通过python绘制双y轴、箱线图、概率分布三种图形,并给出了具体案例源代码供读者参考。绘制双y轴图形效果如下代码如下import numpy as npimport matplotlib.pyplot as pltfrom matplotlib.font_...
  • 本文主要总结如何绘制直方,以及常用的使用场景。 什么是直方:一个随机变量在各个取值区间有个概率分布,将其绘制出来:x轴为等间隔的取值区间(bins),y轴为该区间的频数(可归一化),即直方。 接口 Signature...
  • 上一次我们讲解了利用Python的2D绘图库matplotlib来绘制函数图像(用Python画函数图像),下面我们来讨论如何绘制带参数的函数图像。下面我们用正态分布概率密度在做例子(概率密度的图像为正态分布曲线),其概率...
  • 我的目标是绘制两个类的概率分布函数(pdf)。每一类都有高斯似然矩阵和等效协方差矩阵,但均值向量不同。我想要两个pdf在z轴的同一平面上,x和y轴包含pdf的投影。下面的代码(主要是从here)绘制了其中一个PDF:# Our 2...
  • 0x01描述性度量集中趋势离散程度偏态和峰度...频率直方每条频率*组距=每组概率面积与频率0x03茎叶 数据集为整数 数据高位为树茎,低位为树叶 树茎0,树叶3,7,9:存在数据3,7,9 树茎1,树叶456,存在数据:14...
  • 上一次我们讲解了利用Python的2D绘图库matplotlib来绘制函数图像(用Python画函数图像),下面我们来讨论如何绘制带参数的函数图像。下面我们用正态分布概率密度在做例子(概率密度的图像为正态分布曲线),其概率密度...

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