ABSTRACT
This chapter introduces the concept and characteristics of the probability distribution and the use of the probability distribution characteristics to identify certain univariate data patterns. A list of software packages for identifying the probability distribution characteristics of univariate data is provided along with references for applications. Many specific data patterns of univariate data can be identified through their corresponding types of probability distribution. The probability distributions of time series data with the spike, random fluctuation, step change, and steady change patterns have special characteristics. Time series data with multiple step changes create multiple clusters of data points with their different centroids and thus a multimodal distribution. A normal distribution and a skewed distribution are examples of unimodal distributions with only one mode, in contrast to multimodal distributions with multiple modes. A uniform distribution has no significant mode since data are evenly distributed and are not formed into clusters.
