Functions > Statistics > Probability Distributions > Example: Cauchy Distribution
Example: Cauchy Distribution
1. Show the definition of the Cauchy distribution:
Where:
l is the location parameter (mean)
s is the scale parameter (square-root of variance), s > 0
2. Define three sets of location and scale parameters, then calculate the amplitude, or height, of the curve with location and scale parameters l0 and s0:
 l0 0 l1 2 l2 -2 s0 1 s1 1 s2 1
3. Use the dcauchy function to get the probability density for value x using different values of location parameters and a fixed scale parameter:
Different values of location parameters shift the curve along the x-axis.
4. Plot the dcauchy function using a fixed location parameter and different values of scale parameters:
 l0 0 l1 0 l2 0 s0 1 s1 2 s2 3
Different values of scale parameters change the height of the curve.
5. Plot the dcauchy function using different values of location parameters and scale parameters:
 l0 0 l1 2 l2 4 s0 1 s1 2 s2 3
Different values of scale and location parameters shift the curves and change their height.
6. Plot the pcauchy function using different values of location parameters and a fixed scale parameter:
Different values of location parameters shift the curve along the x-axis.
All y values of pcauchy are between 0 and 1.
7. Plot the pcauchy function using a fixed location parameter and different values of scale parameters:
Different values of scale parameters flatten the curve horizontally, but all curves cross at y=0.5.
All y values of pcauchy fall between 0 and 1.
8. Plot the qcauchy function using different values of location parameters and a fixed scale parameter:
Different values of location parameters shift the curve along the y-axis.
All x values of qcauchy fall between 0 and 1.
9. Calculate the rcauchy function using fixed location and scale parameters:
Function rcauchy returns a vector of m random numbers having the Cauchy distribution.
10. Plot the random numbers returned by the rcauchy function.
Recalculating the worksheet causes function rcauchy to return a new set of random numbers, and the plot gets updated accordingly.