Chapter 1-1. Quantile-Quantile Plot (Q-Q plot)
Higher category : 【Statistics】 Chapter 1. Basics of Statistics
1. overview
1. overview
⑴ (note) quantile
① quantile function: inverse function of cumulative distribution function Φ
○ domain :｛x | 0 ≤ x ≤ 1｝
○ range : statistics of the group of interest
② depending on the number of sections, there are percentages, quartiles, etc.
⑵ definition: a set of points (x, y) as follows
① ｛(x, y) | Φ = P(X ＜ x) = P(Y ＜ y)｝
② note that x is the statistic of the standard normal distribution and y is the statistic of the sample group
⑶ case study
① when the sample group follows a normal distribution: Q-Q plot is close to a straight line
② if the distribution of samples is skewed to the right
○ (note) skewness ＜ 0
○ idea : you can think of dragging each point to the right from the existing normal distribution
○ since the random variable of each point increases, each point on the Q-Q plot moves upward from the diagonal
③ if the distribution of samples is skewed to the left
○ (note) skewness ＞ 0
○ idea : you can think of dragging each point to the left from the existing normal distribution
○ since the random variable of each point decreases, each point on the Q-Q plot moves downward from the diagonal
Input : 2019.10.10 11:50