如何绘制样本的PMF？(How to plot a PMF of a sample?)

如何绘制样本的PMF？(How to plot a PMF of a sample?)

是否有任何函数或库可以帮助我绘制样本的概率质量函数，就像绘制样本的概率密度函数一样？

例如，使用熊猫，绘制PDF就像调用一样简单：

sample.plot(kind="density")

如果没有简单的方法，我如何计算PMF，以便使用matplotlib进行绘图？

Is there any function or library that would help me to plot a probability mass function of a sample the same way there is for plotting the probability density function of a sample ?

For instance, using pandas, plotting a PDF is as simple as calling:

sample.plot(kind="density")

If there is no easy way, how can I compute the PMF so I could plot using matplotlib ?

最满意答案

如果ts是一个系列，您可以通过以下方式获得样本的PMF：

>>> pmf = ts.value_counts().sort_index() / len(ts)

并按以下方式绘制

>>> pmf.plot(kind='bar')

---

numpy唯一的解决方案可以使用np.unique完成：

>>> xs = np.random.randint(0, 10, 100) >>> xs array([5, 2, 2, 1, 2, 8, 6, 7, 5, 3, 2, 6, 4, 9, 7, 6, 4, 7, 6, 8, 7, 0, 6, 2, 9, 8, 7, 7, 2, 6, 2, 8, 0, 2, 5, 1, 3, 6, 7, 7, 2, 2, 0, 3, 8, 7, 4, 0, 5, 7, 5, 4, 4, 9, 5, 1, 6, 6, 0, 9, 4, 2, 0, 8, 7, 5, 1, 1, 2, 8, 3, 8, 9, 0, 0, 6, 8, 7, 2, 6, 7, 9, 7, 8, 8, 3, 3, 7, 8, 2, 2, 4, 4, 5, 3, 4, 1, 5, 5, 1]) >>> val, cnt = np.unique(xs, return_counts=True) >>> pmf = cnt / len(xs) >>> # values along with probability mass function >>> np.column_stack((val, pmf)) array([[ 0. , 0.08], [ 1. , 0.07], [ 2. , 0.15], [ 3. , 0.07], [ 4. , 0.09], [ 5. , 0.1 ], [ 6. , 0.11], [ 7. , 0.15], [ 8. , 0.12], [ 9. , 0.06]])

If ts is a series, you may obtain PMF of the sample by:

>>> pmf = ts.value_counts().sort_index() / len(ts)

and plot it by:

>>> pmf.plot(kind='bar')

---

numpy only solution can be done using np.unique:

>>> xs = np.random.randint(0, 10, 100) >>> xs array([5, 2, 2, 1, 2, 8, 6, 7, 5, 3, 2, 6, 4, 9, 7, 6, 4, 7, 6, 8, 7, 0, 6, 2, 9, 8, 7, 7, 2, 6, 2, 8, 0, 2, 5, 1, 3, 6, 7, 7, 2, 2, 0, 3, 8, 7, 4, 0, 5, 7, 5, 4, 4, 9, 5, 1, 6, 6, 0, 9, 4, 2, 0, 8, 7, 5, 1, 1, 2, 8, 3, 8, 9, 0, 0, 6, 8, 7, 2, 6, 7, 9, 7, 8, 8, 3, 3, 7, 8, 2, 2, 4, 4, 5, 3, 4, 1, 5, 5, 1]) >>> val, cnt = np.unique(xs, return_counts=True) >>> pmf = cnt / len(xs) >>> # values along with probability mass function >>> np.column_stack((val, pmf)) array([[ 0. , 0.08], [ 1. , 0.07], [ 2. , 0.15], [ 3. , 0.07], [ 4. , 0.09], [ 5. , 0.1 ], [ 6. , 0.11], [ 7. , 0.15], [ 8. , 0.12], [ 9. , 0.06]])