# What does heavy tailed Q-Q plot mean?

## What does heavy tailed Q-Q plot mean?

The tails of the histogram are “extermely heavy” at each end of the histogram. In the Normal Q-Q Plot, the plot curves away from the line at each end, again in opposite directions, only this time they curve away extremely quickly, due to the “heavy tails” at the each end of the histogram.

What does a light tailed Q-Q plot mean?

Left skewed qqplot: Left-skew is also known as negative skew. Light tailed qqplot: meaning that compared to the normal distribution there is little more data located at the extremes of the distribution and less data in the center of the distribution.

What does right skewed Q-Q plot mean?

Right-skewed data Below is an example of data (150 observations) that are drawn from a distribution that is right-skewed (in this case it is the exponential distribution). Right-skew is also known as positive skew. On a Q-Q plot right-skewed data appears curved.

### What happens if Q-Q plot is not normal?

A normal probability plot, or more specifically a quantile-quantile (Q-Q) plot, shows the distribution of the data against the expected normal distribution. If the data is non-normal, the points form a curve that deviates markedly from a straight line.

What are QQ plots used for?

The quantile-quantile (q-q) plot is a graphical technique for determining if two data sets come from populations with a common distribution. A q-q plot is a plot of the quantiles of the first data set against the quantiles of the second data set.

What happens if QQ plot is not normal?

## How can you tell if data is normally distributed?

You may also visually check normality by plotting a frequency distribution, also called a histogram, of the data and visually comparing it to a normal distribution (overlaid in red). In a frequency distribution, each data point is put into a discrete bin, for example (-10,-5], (-5, 0], (0, 5], etc.

How does a fat tail Q-Q plot work?

The distribution with a fat tail will have both the ends of the Q-Q plot to deviate from the straight line and its center follows a straight line, whereas a thin-tailed distribution will form a Q-Q plot with a very less or negligible deviation at the ends thus making it a perfect fit for the Normal Distribution. How much data should do we need?

What does a QQ plot look like on average?

This allows us to spot a heavy tail or a light tail and hence, skewness greater or smaller than the theoretical distribution, and so on. Here’s what QQ-plots look like (for particular choices of distribution) on average:

### Where are the quantiles on a QQ plot?

With a QQ-plot, the quantiles of the sample data are on the vertical axis, and the quantiles of a specified probability distribution are on the horizontal axis. The plot consists of a series of points that show the relationship between the actual data and the specified probability distribution.

Which is an example of a Q-Q plot?

The theoretical distribution in the following examples is the Gaussian (Normal) distribution with mean 0 and standard deviation 1. In a Q-Q plot each data point in your dataset is put in its own quantile, then a data point is generated from the corresponding theoretical quantile.