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  • I have a multivariate probability density function P(x,y,z), and I want to sample from it. Normally, I would use numpy.random.choice() for this sort of task, but this function only works for 1-dimensi...

    I have a multivariate probability density function P(x,y,z), and I want to sample from it. Normally, I would use numpy.random.choice() for this sort of task, but this function only works for 1-dimensional probability densities. Is there an equivalent function for multivariate pdfs?

    解决方案

    There a few different paths one can follow here.

    (1) If P(x,y,z) factors as P(x,y,z) = P(x) P(y) P(z) (i.e., x, y, and z are independent) then you can sample each one separately.

    (2) If P(x,y,z) has a more general factorization, you can reduce the number of variables that need to be sampled to whatever's conditional on the others. E.g. if P(x,y,z) = P(z|x, y) P(y | x) P(x), then you can sample x, y given x, and z given y and x in turn.

    (3) For some particular distributions, there are known ways to sample. E.g. for multivariate Gaussian, if x is a sample from a mean 0 and identity covariance Gaussian (i.e. just sample each x_i as N(0, 1)), then y = L x + m has mean m and covariance S = L L' where L is the lower-triangular Cholesky decomposition of S, which must be positive definite.

    (4) For many multivariate distributions, none of the above apply, and a more complicated scheme such as Markov chain Monte Carlo is applied.

    Maybe if you say more about the problem, more specific advice can be given.

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  • I have started to use python for analysis. I would like to do the following:Get the distribution of datasetGet the peaks in this distributionI used gaussian_kde from scipy.stats to make estimation for...

    I have started to use python for analysis. I would like to do the following:

    Get the distribution of dataset

    Get the peaks in this distribution

    I used gaussian_kde from scipy.stats to make estimation for kernel density function. Does guassian_kde make any assumption about the data ?. I am using data that are changed over time. so if data has one distribution (e.g. Gaussian), it could have another distribution later. Does gaussian_kde have any drawbacks in this scenario?. It was suggested in question to try to fit the data in every distribution in order to get the data distribution. So what's the difference between using gaussian_kde and the answer provided in question. I used the code below, I was wondering also to know is gaussian_kde good way to estimate pdf if the data will be changed over time ?. I know one advantage of gaussian_kde is that it calculate bandwidth automatically by a rule of thumb as in here. Also, how can I get its peaks?

    import pandas as pd

    import numpy as np

    import pylab as pl

    import scipy.stats

    df = pd.read_csv('D:\dataset.csv')

    pdf = scipy.stats.kde.gaussian_kde(df)

    x = np.linspace((df.min()-1),(df.max()+1), len(df))

    y = pdf(x)

    pl.plot(x, y, color = 'r')

    pl.hist(data_column, normed= True)

    pl.show(block=True)

    解决方案

    I think you need to distinguish non-parametric density (the one implemented in scipy.stats.kde) from parametric density (the one in the StackOverflow question you mention). To illustrate the difference between these two, try the following code.

    import pandas as pd

    import numpy as np

    import scipy.stats as stats

    import matplotlib.pyplot as plt

    np.random.seed(0)

    gaussian1 = -6 + 3 * np.random.randn(1700)

    gaussian2 = 4 + 1.5 * np.random.randn(300)

    gaussian_mixture = np.hstack([gaussian1, gaussian2])

    df = pd.DataFrame(gaussian_mixture, columns=['data'])

    # non-parametric pdf

    nparam_density = stats.kde.gaussian_kde(df.values.ravel())

    x = np.linspace(-20, 10, 200)

    nparam_density = nparam_density(x)

    # parametric fit: assume normal distribution

    loc_param, scale_param = stats.norm.fit(df)

    param_density = stats.norm.pdf(x, loc=loc_param, scale=scale_param)

    fig, ax = plt.subplots(figsize=(10, 6))

    ax.hist(df.values, bins=30, normed=True)

    ax.plot(x, nparam_density, 'r-', label='non-parametric density (smoothed by Gaussian kernel)')

    ax.plot(x, param_density, 'k--', label='parametric density')

    ax.set_ylim([0, 0.15])

    ax.legend(loc='best')

    d29f1a3030b08e6d1b5e4b1ae10b717d.png

    From the graph, we see that the non-parametric density is nothing but a smoothed version of histogram. In histogram, for a particular observation x=x0, we use a bar to represent it (put all probability mass on that single point x=x0 and zero elsewhere) whereas in non-parametric density estimation, we use a bell-shaped curve (the gaussian kernel) to represent that point (spreads over its neighbourhood). And the result is a smoothed density curve. This internal gaussian kernel has nothing to do with your distributional assumption on the underlying data x. Its sole purpose is for smoothing.

    To get the mode of non-parametric density, we need to do an exhaustive search, as the density is not guaranteed to have uni-mode. As shown in the example above, if you quasi-Newton optimization algo starts between [5,10], it is very likely to end up with a local optimal point rather than the global one.

    # get mode: exhastive search

    x[np.argsort(nparam_density)[-1]]

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  • I have the following code below that prints the PDF graph for a particular mean and standard deviation.Now I need to find the actual probability, of a particular value. So for example if my mean is 0,...

    I have the following code below that prints the PDF graph for a particular mean and standard deviation.

    Now I need to find the actual probability, of a particular value. So for example if my mean is 0, and my value is 0, my probability is 1. This is usually done by calculating the area under the curve. Similar to this:

    I am not sure how to approach this problem

    import numpy as np

    import matplotlib

    import matplotlib.pyplot as plt

    def normal(power, mean, std, val):

    a = 1/(np.sqrt(2*np.pi)*std)

    diff = np.abs(np.power(val-mean, power))

    b = np.exp(-(diff)/(2*std*std))

    return a*b

    pdf_array = []

    array = np.arange(-2,2,0.1)

    print array

    for i in array:

    print i

    pdf = normal(2, 0, 0.1, i)

    print pdf

    pdf_array.append(pdf)

    plt.plot(array, pdf_array)

    plt.ylabel('some numbers')

    plt.axis([-2, 2, 0, 5])

    plt.show()

    print

    解决方案

    Unless you have a reason to implement this yourself. All these functions are available in scipy.stats.norm

    I think you asking for the cdf, then use this code:

    from scipy.stats import norm

    print(norm.cdf(x, mean, std))

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  • plt.suptitle('Gaussian PDF', fontsize=16) plt.tight_layout() plt.show() 以上这篇python高斯分布概率密度函数的使用详解就是小编分享给大家的全部内容了,希望能给大家一个参考,也希望大家多多支持我们。...

    如下所示:

    import matplotlib.pyplot as plt

    import numpy as np

    from scipy import stats

    from matplotlib import style

    style.use('fivethirtyeight')

    mu_params = [-1, 0, 1]

    sd_params = [0.5, 1, 1.5]

    x = np.linspace(-7, 7, 100)

    f, ax = plt.subplots(len(mu_params), len(sd_params), sharex=True, sharey=True, figsize=(12,8))

    for i in range(3):

    for j in range(3):

    mu = mu_params[i]

    sd = sd_params[j]

    y = stats.norm(mu, sd).pdf(x)

    ax[i, j].plot(x, y)

    ax[i, j].plot(0,0, label='mu={:3.2f}\nsigma={:3.2f}'.format(mu,sd), alpha=0)

    ax[i, j].legend(fontsize=10)

    ax[2,1].set_xlabel('x', fontsize=16)

    ax[1,0].set_ylabel('pdf(x)', fontsize=16)

    plt.suptitle('Gaussian PDF', fontsize=16)

    plt.tight_layout()

    plt.show()

    20190710095735.jpg

    以上这篇python高斯分布概率密度函数的使用详解就是小编分享给大家的全部内容了,希望能给大家一个参考,也希望大家多多支持我们。

    本文标题: python高斯分布概率密度函数的使用详解

    本文地址: http://www.cppcns.com/jiaoben/python/265117.html

    展开全文
  • matlab作概率密度函数很简单,但是本人学的python,因此想用python作图,从txt文本中读取数据,然后用python概率密度函数图像,
  • 今天小编就为大家分享一篇python高斯分布概率密度函数的使用详解,具有很好的参考价值,希望对大家有所帮助。一起跟随小编过来看看吧
  • 今天小编就为大家分享一篇python实现beta分布概率密度函数的方法,具有很好的参考价值,希望对大家有所帮助。一起跟随小编过来看看吧
  • 计算概率分布的相关参数时,一般使用 scipy 包,常用的函数包括以下几个:pdf:连续随机分布的概率密度函数pmf:离散随机分布的概率密度函数cdf:累计分布函数百分位函数(累计分布函数的逆函数)生存函数的逆函数...
  • 目录1、scipy库中各分布对应的方法2、stats中各分布的常用方法及其功能3、正态分布的概率密度函数及其图象1)正态分布的概率密度函数及其图象2)python绘制正态分布的概率密度函数图象4、卡方分布的概率密度函数及其...
  • 我查看了this维基百科文章和Numpy源代码,发现了这个randomkit.c文件,它实现了函数rk_gauss(它实现了Box-Muller变换)、rk_double和{}(它实现了模拟均匀分布随机变量的Mersenne Twister随机数生成器,由Box-...
  • python 服从正态分布下概率密度函数

    千次阅读 2019-10-11 00:13:40
    python 服从正态分布下概率密度函数和累积密度函数 服从正太分布下,概率密度函数公式 公式解释: f(x): 是某样本(样本以数值形式表现)为某数值时发生的概率 0<f(x)<1 x: 是随机抽样的数值,取值范围从负...
  • # python 服从正太分布下概率密度函数 利用input()函数输入均值和标准差, 多次绘制概率密度函数图形并将图像曲线放置在同一张图中 代码块: """ 绘制正太分布函数曲线图 """ import matplotlib.pyplot as plt import...
  • 二维高斯分布概率密度函数数据集实战优化坐标轴与图像优化图像再次优化 概率密度函数 大家肯定都有听说过正态分布,其实正态分布只是概率密度分布的一种,正态分布的概率密度函数均值为μ ,标准差σ是高斯函数的一...
  • python 服从正太分布 离散情况 下 的概率密度函数 scipy.stats库是分布函数库, 包含正太分布,泊松分布,卡方分布等 导入scipy.stats库以后, 应用函数norm生成服从正太分布的概率密度函数, 具体法是: scipy...
  • python高斯分布概率密度函数

    万次阅读 2018-07-18 21:02:34
    import matplotlib.pyplot as plt import numpy as np from scipy import stats from matplotlib import style style.use('fivethirtyeight') mu_params = [-1, 0, 1] sd_params = [0.5, 1, 1.5] ...
  • 关于使用Excel画出t分布的概率密度函数图表的问题,试答如下:使用excel绘制t分布的概率密度函数,需要两列:1)自变量X,2)计算自变量X对应的t分布的概率密度函数。由于Excel中TDIST函数计算的是概率累积密度,不...
  • 1.概率密度函数  1.1. 定义  如果对于随机变量X的分布函数F(x),存在非负函数f(x),使得对于任意实数有  则称X为连续型随机变量,其中F(x)称为X的概率密度函数,简称概率密度。(f(x)>=0,若f(x)在点x处连续则F...
  • python实现beta分布概率密度函数

    万次阅读 2018-07-18 21:28:03
    beta分布的最大特点是其多样性, 从下图可以看出, beta分布具有各种形态, 有U形, 类似正态分布的形状, 类似uniform分布的形状等, 正式这一特质使beta分布在共轭先验的计算中起到重要作用: import matplotlib.pyplot ...
  • 二维高斯分布概率密度函数数据集实战优化坐标轴与图像优化图像再次优化 概率密度函数 大家肯定都有听说过正态分布,其实正态分布只是概率密度分布的一种,正态分布的概率密度函数均值为μ ,标准差σ是高斯函数的一...
  • 如何在Python中计算PDF(概率密度函数)?现在我需要找到实际的概率的特殊价值。例如,如果我的意思是0,而我的值是0,那么我的概率就是1.这通常是通过计算曲线下的面积来完成的。与此相似:我不知道如何除非你有...
  • Python计算一组数据的PDF(概率密度函数)方法 公式如下: python实现: 第一种方法: import scipy.stats as st st.norm.pdf([一组数据]) 第二种方法: def pdf(x, mean, var): return exp(-(x - mean) ** 2 / ...
  • 高斯分布以及概率密度函数Python)(持续更新)前言一、高斯分布二、概率密度函数 前言 项目上需要用到高斯分布、正太分布以及概率密度函数。我对这部分知识点产生了一些疑问,上网查资料发现很少有人在我这个点...
  • pdf:连续随机分布的概率密度函数 pmf:离散随机分布的概率密度函数 cdf:累计分布函数 百分位函数(累计分布函数的逆函数) 生存函数的逆函数(1 - cdf 的逆函数) 函数里面不仅能跟一个数据,还能跟一个数组。...
  • 这篇文章通俗地解释了概率论的两个基石函数:概率分布函数、概率密度函数,建议不熟悉的同学,认真阅读。1先从离散型随机变量和连续性随机变量说起对于如何分辨离散型随机变量和...

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