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The UserFormula facility enables the user to insert formulas
for plotting curves, generating or transforming data and transforming
parameters in the EV/GP models. The user can define his own
functions which then become available in nearly every edit field.
A calculator for evaluating formulas is also provided.
More general mechanisms are available by means of the built-in programming
language StatPascal. UserFormula (UFO)
Introduction Calculator Plot Curve Generate Data Transform Data Transform Parameters
Ufo: Further Examples
Ufo: Predefined Functions
Ufo: Syntax of Formulas
Introduction
A formula specified by the user may be plotted by entering its definition in the edit
field f(x,p). Xtremes plots the functions x -> f(x,p) where p may be
varied using the up and down arrow.
Moreover, data sets may be transformed or generated by giving an explicit formula.
In the first case the transformation T(x) is applied a to every point of the active
univariate date set. In the latter case a quantile transformation is applied to i.i.d
random variables generated according to the uniform distribution on [0,1].
The syntax for formulas is simular to that in programming languages; operators and
predefined functions may be combined in the usual way. For example, enter the
term
1/sqrt(2*3.1415)*exp(-(x-p)**2/2)
to plot a normal density with varying location parameter.
You may also define your own functions in the Calculator
by typing the
name of the function and its parameters followed by the definition. The functions you
define may call each other, but exercise caution to provide a correct termination
condition when defining direct or indirect recursive calls. Note that each function
must be entered on a separate line. The definitions are saved in the text file
FORMULA.TXT in the directory where the program file XTREMES.EXE is located.
For example, if you enter the definition
norm(x,mu) = 1/(sqrt(2*3.1315)) * exp(-(x-mu)**2/2)
you may plot normal densities with varying location parameter by evaluating the term
norm(x,p) .
Calculator
The calculator evaluates formulas entered in the upper edit
field. Simply enter expressions like 5+2*3 and press
gauss(x,m,s)=gaussiandensity((x-m)/s)/s
to define the function gauss. Formulas defined
in this edit field are available in other UFO-dialog boxes.
Click the Copy button to copy the results of a calculation
to the clipboard. The = button is used to evaluate
an expression, while the OK parses the user defined functions
and closes the dialog box.
Plot Curve
Univariate
Multivariate
Plot Curve (Univariate mode)
One can plot the graph of a function f(x) or f(x,p), where p is
an additional parameter that can be changed interactively using
the Parameter Varying Tool in
the Toolbar.
Examples for valid functions are:
3*x+5
paretodensity(p,x)
You can enter any name for the destination window in the
field Select window. If the window does not exist,
a new one is created.
Plot Curve (Multivariate mode)
One can plot the graph of a function f(x,y), where the
range of x and y is defined by the values entered
under Support of function. Xtremes displays
a Surface Plot of
the function.
Generate Data
A univariate data set is generated by applying a
quantile transformation Qf(x) to
independent data generated under the uniform distribution
on [0,1).
Transform Data
Univariate
Time Series
Multivariate
Transform Data (Univariate)
A transformation T(x) is applied to the points of the
active univariate data set.
Transform Data (Time Series)
Specify two functions T1(t, x) and T2(t, x) to transform the
active time series
(t[i], x[i])
to the time series
(T1(t[i], x[i]), T2(t[i], x[i])).
Real-valued times are allowed.
Transform Data (Multivariate)
Specify transformations T1, T2, ... Tk to obtain the transformed
data set (T1(x), T2(x), ... Tk(x)) where x is the
vector containing the rows of the active multivariate data set.
The left-hand side of the dialog box displays the column names
of the multivariate data sets and assigns variable
names x1, x2, ... to the columns. On the right-hand side,
the user defines the names of the columns of the
transformed data set as well as a transformation. The arrow
button provides a template of the transformation T(x) = x.
Example:
If the active data set contains three columns
labeled x, y and z, then on the
left-hand size of the dialog box the following is displayed:
x: x1
y: x2
z: x3
To obtain a data set with the columns Col1 and Col2,
where Col1 is set to 2*x and Col2 is set
to y+z, one defines the following transformation on
the right-hand side:
Col1: 2*x1
Col2: x2+x3
Demo B.3 of Statistical Analysis contains a complete
example.
Transform Parameters (EV/GP)*
Recall that two different parametrizations are possible in the
EV/GP models, namely, the alpha and gamma parametrization
(see Statistical Analysis, Sections 1.3 and 1.4). A dialog
box allows to transform parameters from one mode into the other
one.
© 2005 Xtremes Group
· updated Jun 21, 2005