 ```! QQ Plots: Quantile-Quantile plots provide a graphical way of comparing a sample from an unknown distribution with a stratified sample of the same size from a hypothesized known distribution. Method: The sample of unknown distribution is sorted into increasing order. Each observation from the unknown distribution is assumed to be from a quantile of the distribution. Each observation is paired with an observation from the corresponding quantile of the known distribution. If the two samples are in fact from the same distribution, except for a shift and a scale factor, then the scatter plot of pairs should appear as approximately a straight line. ; ! Keywords: QQ plot, Scatter plot, Distribution identification; SETS: OBS: X, Y, POSN; ENDSETSDATA: ! A sample of some price change data from an unknown distribution; X = 6.63720 5.25590 5.30745 5.39319 7.48938 5.49371 5.50063 5.59790 5.61768 5.70234 7.53937 7.94979 8.02154 8.64716 10.0878 1.90635 3.42523 3.90875 4.05281 4.32659 4.52476 4.74702 4.75941 4.89041 5.01090 5.76529 5.83823 5.88315 5.93804 5.99352 6.02313 6.08731 6.14521 6.20736 6.25867 5.21009 6.95652 7.08109 7.22246 7.25855 6.30321 6.37623 6.40571 6.44752 6.55521 6.57048 6.77461 6.79741 6.86744 5.12348 ; ENDDATA CALC: @SET('TERSEO',2); ! Turn off default output; nobs = @SIZE( OBS); ! Get the position of each observation in the sort order; POSN = @RANK( X); ! Generate a Y(i) from the matching quantile of a hypothesized distribution; @FOR(OBS(i): ! Normal distribution; Y(i) = @PNORMINV( 0, 1, POSN(i)/(nobs+1)); ! Symmetric Triangular distribution; ! Y(i) = @PTRIAINV( -1, +1, 0, POSN(i)/(nobs+1)); ! Exponential distribution; ! Y(i) = @PEXPOINV( 1, POSN(i)/(nobs+1)); ! Cauchy distribution; ! Y(i) = @PCACYINV( 0, 1, POSN(i)/(nobs+1)); ! Student t with 4 degrees of freedom; ! Y(i) = @PSTUTINV( 4, POSN(i)/(nobs+1)); ); ! Generate the QQ - Scatter plot of the pairs; @CHARTSCATTER( ' QQ Plot', 'Actual observations', 'Hypothesized distribution', 'Paired points', X, Y); ENDCALC ```