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**Example text**

N . If the data has a similar distribution as the reference distribution then the qqplot is approximately linear. e. from the associated location-scale family Fµ,σ (x) = F ((x−µ)/σ). Thus, the qq-plot enables us to come up with a suitable class of distributions that fits the data and then we may estimate the location and scale parameters. The qq-plot is particularly useful for studying the tails of the distribution. Given a reference distribution F , if F has heavier tails than the data then the plot will curve down at the left and/or up at the right and the opposite if the reference distribution has too light tails.

5 −2 0 2 1 3 2 1 0 −1 −2 −3 −4 4 Figure 21: Simulation from a spherical distribution using the stochastic representation. First we simulate independently n times from the uniform distribution on the unit sphere to obtain s1 , . . , sn (above). Then, we simulate r1 , . . , rn from the distribution of R. Finally we put xk = rk sk for k = 1, . . , n (below). It follows immediately from the definition that elliptical distributed random vectors have the following stochastic representation. X ∼ Ed (µ, Σ, ψ) if and only if d there exist S, R, and A such that X = µ+RAS with S uniformly distributed on the unit sphere, R ≥ 0 a random variable independent of S, A ∈ Rd×k a matrix with AAT = Σ and µ ∈ Rd .

E. from the associated location-scale family Fµ,σ (x) = F ((x−µ)/σ). Thus, the qq-plot enables us to come up with a suitable class of distributions that fits the data and then we may estimate the location and scale parameters. The qq-plot is particularly useful for studying the tails of the distribution. Given a reference distribution F , if F has heavier tails than the data then the plot will curve down at the left and/or up at the right and the opposite if the reference distribution has too light tails.