Probability plot overview
A probability plot is a graphical technique to assess whether a dataset follows a particular probability distribution (e.g., normal, exponential, Weibull). It helps visualize how well data fits a theoretical distribution. There are different types of probability plot.
Q-Q Plot (Quantile-Quantile Plot)
- Compares data quantiles to theoretical quantiles.
- Straight Line → Data follows the chosen distribution.
- Curved or S-shaped → Data deviates from the distribution.
P-P Plot (Probability-Probability Plot)
- Compares cumulative probabilities of data vs. theoretical distribution.
- Less sensitive to tail differences than a Q-Q plot.
- Probability Paper
- Traditional probability paper has a specially designed scale (e.g., normal, log-normal, Weibull) so that data following the target distribution appears as a straight line when plotted.
Application | Description |
Assessing Distribution Fit | Check whether data come from a specific distribution (for example, normal or exponential). Good for hypothesis testing, statistical modeling, and transformation. |
Finding Deviations | Shows where observed data do not come from a theoretical distribution. Any point(s) away from the straight line suggests a location where the distribution is incorrect, perhaps skewness or heavy tails. |
Diagnostics | Tests assumptions for statistical tests, such as assuming a certain type of distribution for statistical tests (such as normality in regression or ANOVA). |
Understanding Data Behavior | Provides information about the data's spread, skewness, kurtosis, and tails in relation to the theoretical distribution. |
Reference: Some of the text in this article has been generated using AI tools such as ChatGPT and edited for content and accuracy.
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