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What is a Q-Q plot, and if given a set of realized values of a random...

What is a Q-Q plot, and if given a set of realized values of a random variable, how can a Q-Q plot be used to assess the distribution of the random variable?

math   Statistics-And-Probability   
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Answer #1

QQ plot stands for quantile quantile plot. It is graphical tools that helps us to check if a given set of random values come from a theoretical distribution such as Normal distribution or exponential distribution.

In a qqplot, a scatter diagram is created by plotting the quantiles of the theoritical distribution on the x axis and the quantiles of the sample data on the y axis. If the points form a straight, line we assume that the data sample follows the theoritical distribution.


To construct the a qqplot from a given dataset, follow the following steps.

1. Arrange the data in the ascending order.Let k be the rank of the data point. Also let n be number of datapoint. Hence the highest value of k is n

2. For each rank of the datapoint we find the following
p =(k-1/2)n
3. We then look up each value of p in the theoritical distribution and find the probability
4. Next we plot the probability on the x axis and the datapoints on the y axis and observe the line which is formed. If it is straight line we conclude that the data follows the theorictical distribution.
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