e1071::skewness
时间: 2024-06-27 15:01:03 浏览: 6
e1071是一个R语言包,主要用于统计学习中的数据处理和预处理。skewness函数是该包中的一个统计计算工具,它用于计算数据分布的偏度(skewness)。偏度是衡量数据分布对称性的指标,当偏度为正时,数据分布呈现出右偏(即尾部较长在右侧),而偏度为负则表示左偏(尾部较长在左侧)。如果是0,则表示数据分布是对称的。
具体来说,e1071::skewness函数接受一个向量或数据框中的数值列作为输入,然后返回该列数值的偏度系数。在进行数据分析、异常检测或特征工程时,理解并计算偏度可以帮助我们更好地理解数据的分布形状,从而选择合适的模型或进行数据变换。
相关问题
r语言没有skewness函数
在R语言中,确实没有名为“skewness”的内置函数。但是,你可以使用“e1071”包中的“skewness”函数来计算偏度。你需要先安装该包并通过以下命令加载它:
```R
install.packages("e1071")
library(e1071)
```
然后,你可以使用以下命令计算偏度:
```R
x <- c(1, 2, 3, 4, 5)
skewness(x)
```
这里的“x”是一个数值向量,它包含您想要计算偏度的数据。这将返回该向量的偏度。
Daily foreign exchange rates (spot rates) can be obtained from the Federal Reserve Bank in St Louis (FRED). The data are the noon buying rates in New York City certified by the Federal Reserve Bank of New York. Consider the exchange rates between the U.S. dollar and the Euro from January 4, 1999 to March 8, 2013. See the file d-exuseu.txt. (a) Compute the daily log return of the exchange rate. (b) Compute the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of the log returns of the exchange rate. (c) Obtain a density plot of the daily long returns of Dollar-Euro exchange rate. (d) Test H0 : µ = 0 versus Ha : µ ̸= 0, where µ denotes the mean of the daily log return of Dollar-Euro exchange rate.
(a) The daily log return of the exchange rate can be calculated using the following formula:
log return = ln(price[t]) - ln(price[t-1])
where price[t] represents the exchange rate at time t and price[t-1] represents the exchange rate at time t-1.
Using the data in the file d-exuseu.txt, we can calculate the daily log returns as follows (assuming the data is stored in a variable called "exchange_rate"):
```python
import numpy as np
log_returns = np.log(exchange_rate[1:]) - np.log(exchange_rate[:-1])
```
The first element of "exchange_rate" is excluded from the calculation because there is no previous price to compare it to.
(b) The sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of the log returns can be calculated using the following code:
```python
mean = np.mean(log_returns)
std_dev = np.std(log_returns)
skewness = stats.skew(log_returns)
kurtosis = stats.kurtosis(log_returns, fisher=False)
minimum = np.min(log_returns)
maximum = np.max(log_returns)
print("Sample mean:", mean)
print("Standard deviation:", std_dev)
print("Skewness:", skewness)
print("Excess kurtosis:", kurtosis - 3) # convert to excess kurtosis
print("Minimum:", minimum)
print("Maximum:", maximum)
```
This code requires the "scipy.stats" module to be imported at the beginning of the script. The output will show the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of the log returns.
(c) To obtain a density plot of the daily log returns, we can use the following code:
```python
import matplotlib.pyplot as plt
plt.hist(log_returns, bins=50, density=True)
plt.xlabel("Daily log return")
plt.ylabel("Density")
plt.show()
```
This code will create a histogram of the log returns with 50 bins and normalize it to create a density plot. The output will show the density plot of the log returns.
(d) To test the hypothesis H0 : µ = 0 versus Ha : µ ̸= 0, where µ denotes the mean of the daily log return of Dollar-Euro exchange rate, we can use a t-test. The null hypothesis states that the mean log return is equal to zero, while the alternative hypothesis states that the mean log return is not equal to zero.
```python
from scipy.stats import ttest_1samp
t_stat, p_value = ttest_1samp(log_returns, 0)
print("t-statistic:", t_stat)
print("p-value:", p_value)
```
This code uses the "ttest_1samp" function from the "scipy.stats" module to calculate the t-statistic and the p-value. The output will show the t-statistic and the p-value of the test. If the p-value is less than the significance level (e.g., 0.05), we can reject the null hypothesis and conclude that the mean log return is significantly different from zero.
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