Question

Suppose that the true distribution function F(x) and the fitted distribution function of  are the same. For what distribution F(x) will the Q-Q and P-P plots be essentially the same if the sample size n is large?

Answer 1

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Answer:

For normal distribution F(x) will be the Q-Q and P-P plots be essentially same if the sample size is large.

Reason:

The probability-probability plot is a graph of the empirical CDF values plotted against the theoretical (fitted) CDF values. It is used to determine how well a specific distribution fits to the observed data. The P-P plot will be approximately linear if the specified theoretical distribution is the correct model.

The quantile-quantile plot is a graph of the input data values plotted against the quantiles (inverse CDF values) of the fitted distribution.

The interpretation of the Q-Q plot is similar to the P-P plot: if the distribution you are testing is the correct model, the graph points will lie on an approximately straight line.