Through the Cumulative Probability Function (CPF) or Cumulative Distribution Function (CDF), we can visually see the probability accumulation below each data point in the dataset, which helps us understand the distribution characteristics of the data, such as whether the data is skewed, whether there are outliers, etc.
1. CDF is particularly useful in uncertainty analysis. For example, when the expected NPV is relatively low, we can further understand how likely it is that the economic benefit of a project will occur in a certain interval by calculating the sum of the probabilities of all possible values within a given interval (i.e., the cumulative probability).
2. CDF can also be used for data visualization. For example, CDF is more effective than histograms or kernel density estimation when it comes to representing the cumulative distribution of data. This is because CDF can show the probability distribution of all data less than or equal to the current data value, which is very helpful in representing the probability of a data point occurring within a certain interval.
3. CDF can help us better understand the distribution of data. In probability theory, probability distributions are the way in which a random variable is likely to be valued. If we can get the cumulative probability function of a random variable, we can know the probability that the value of that random variable will be in any particular interval. This helps us better understand the distribution characteristics of the data, such as the concentration trend of the data, how discrete it is, and so on.
4. CDF has an important application in hypothesis testing. In statistics, hypothesis testing is a method of inferring characteristics of a population based on sample data. The cumulative probability function can be used to calculate the probability of an observation, which can help us determine if the sample data deviates significantly from the expected distribution or parameters. For example, when testing whether the mean of a normally distributed population is equal to a particular value, we can calculate the probability of the observed data from the cumulative probability function, and then judge whether the sample data is statistically significant based on this probability.
5. CDF is also related to confidence intervals. A confidence interval is a way of estimating the range of possible values for a population parameter. When we make an estimate of the population parameter, we get an estimate and the corresponding confidence interval. The cumulative probability function can be used to calculate the confidence level of the confidence interval, which is the probability that the population parameter will take its value within the confidence interval. This probability helps us understand how well we grasp the overall parameters, i.e., how likely our estimate is to be correct.
Therefore, in data analysis, we should make full use of the advantages and characteristics of the cumulative probability function in order to better process and analyze the data.