关于改进机器状态监控的Box-Cox稀疏度措施的调查

Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This...

A standard box and whisker plot informs us about the spread of the data in a given sample. One can identify the minimum value, maximum value, first quartile value, second quartile or median value, and third quartile.
However, the box plot does not tell the reader about outliers - values that lie far from the center of the data. We can modify the standard box and whisker plot to identify the outliers and visualize the actual spread of the data in a sample.
Initially, we calculate the adjusted...

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n)  to the number of categories (k).

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...

In signal processing, signals are classified based on various characteristics: continuous-time versus discrete-time, periodic versus aperiodic, analog versus digital, and causal versus noncausal. Each category highlights distinct properties crucial for understanding and manipulating signals.
A continuous-time signal holds a value at every instant in time, representing information seamlessly. In contrast, a discrete-time signal holds values only at specific moments, often denoted as x(n), where...

The coefficient of variation measures the dispersion of the data points or distribution around the mean. Using the coefficient of variation, we can compare two data series with drastically different means or different units of measurement. The coefficient of variation for a sample and a population is expressed as a percentage of the ratio of standard deviation to the mean.
The coefficient of variation is a practical statistical tool in finance. It allows investors to assess the volatility or...