
FRECHET PLOTName:
The Frechet plot is formed by
If the data come from a 2parameter Frechet distribution, then the points on this plot should be approximately linear. If you fit a line to the points on this plot, the intercept can be used as an estimate of the scale parameter and the slope can be used as an estimate of the shape parameter. However, the plot is generally used to determine if a 2parameter Frechet is appropriate. If the plot is approximately linear, then parameter estimates would usually be determined by maximum likelihood using the command
Maximum likelihood estimates would generally be preferred over the Frechet plot estimates since its statistical properties are better understood. Currently, this plot is supported for the maximum version of the Frechet distribution. It is also only supported for the case with no censoring. It is also not supported for grouped data. The characteristics of these components are controlled through the LINE and CHARACTER commands. This is demonstrated in the program examples below. If you have groups in the data, you can specify a "highlight" option to draw the points in the different groups with different attributes. For example, this can be used to draw outliers in a different color. This is demonstrated in the second program example below.
where <y> is a response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
<SUBSET/EXCEPT/FOR qualification> where <y> is a response variable; <x> is a groupid variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
HIGHLIGHT FRECHET PLOT Y1 X
The percent point estimates are computed by using the estimates of scale (SCAL) and shape (SHAPE) obtained from the plot and plugging these values into the Frechet percent point function.
. Step 1: Read the data . skip 25 read frechet.dat y skip 0 . . Step 2: Set plot control features . label case asis title case asis title offset 2 character X blank line blank solid title Frechet Plot for FRECHET.DAT y1label LN(LN(P(i))) x1label LN(y(i)) x2label P(i) = (i  0.3)/(n + 0.4) . . Step 3: Generate the plot . frechet plot yProgram 2: . Demonstrate the HIGHLIGHT option . . Step 1: Read the data . skip 25 read frechet.dat y skip 0 let n = size y let x = 0 for i = 1 1 n let x = 1 subset y > 22 let x = 1 subset y < 14 . . Step 2: Set plot control features . label case asis title case asis title offset 2 character circle circle blank character hw 1 0.75 all character fill on on character color black red line blank blank solid title Frechet Plot for FRECHET.DAT y1label LN(LN(P(i))) x1label LN(y(i)) x2label P(i) = (i  0.3)/(n + 0.4) . . Step 3: Generate the plot . highlight frechet plot y x  
Date created: 01/31/2015 Last updated: 12/04/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 