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Exponential pdf: 'epdf(x) = EXP(-x/β)/β'
Exponential cdf: 'ecdf(x) = 1 - EXP(-x/β)'
Weibull pdf: 'Wpdf(x) = α*β*x^(β-1)*EXP(-α*x^β)'
Weibull cdf: 'Wcdf(x) = 1 - EXP(-α*x^β)'
Use function DEFINE to define all these functions. Next, enter the values of α
and
β, e.g., 1K~‚a` 2K ~‚b`
Finally, for the cdf for Gamma and Beta cdf’s, you need to edit the program
definitions to add NUM to the programs produced by function DEFINE. For
example, the Gamma cdf, i.e., the function gcdf, should be modified to read: «
x 'NUM( ∫ (0,x,gpdf(t),t))' » and stored back into @gcdf
. Repeat
the procedure for
βcdf. Use RPN mode to perform these changes.
Unlike the discrete functions defined earlier, the continuous functions defined in
this section do not include their parameters (
α and/or β) in their definitions.
Therefore, you don't need to enter them in the display to calculate the functions.
However, those parameters must be previously defined by storing the
corresponding values in the variables
α and β. Once all functions and the
values
α and β have been stored, you can order the menu labels by using
function ORDER. The call to the function will be the following:
ORDER({‘
α’,’β’,’gpdf’,’gcdf’,’βpdf’,’βcdf’,’epdf’,’ecdf’,’Wpdf’,’Wcdf’})
Following this command the menu labels will show as follows (Press L to
move to the second list. Press L once more to move to the first list):
Some examples of application of these functions, for values of
α = 2, β = 3, are
shown below. Notice the variable IERR that shows up in the second screen shot.
This results from a numerical integration for function gcdf.