Probability density function of the Cauchy distribution
This functionality does not run in MATLAB.
stats::cauchyPDF(a, b) returns a procedure representing the probability density function
of the Cauchy distribution with median a and scale parameter b > 0.
The procedure f := stats::cauchyPDF(a, b) can be called in the form f(x) with arithmetical expressions x. The return value of f(x) is either a floating-point number or a symbolic expression:
If x is a floating-point number and a and b can be converted to suitable floating-point numbers, then f(x) returns a floating-point number.
In all other cases, the symbolic expression b/PI * 1/((x-a)^2 + b^2)) is returned.
Numerical values of a and b are only accepted if they are real and b is positive.
The function is sensitive to the environment variable DIGITS which determines the numerical working precision.
We calculate the Cauchy density with a = 2 and at various points:
f := stats::cauchyPDF(2, 3/4): f(-infinity), f(9/10), f(0.9), f(2), f(infinity)
We use symbolic arguments:
f := stats::cauchyPDF(a, b): f(x), f(2), f(2.0)
When a and b evaluate to numbers, the function f starts to produce numerical values:
a := PI: b:= 1/8: f(2), f(2.0)
delete f, a, b:
The median: an arithmetical expression representing a real value
The scale parameter: an arithmetical expression representing a positive real value