TABLE OF CONTENTS Percentiles split the data into 100 parts. Let us consider the pdf of Figure 10.15 below.
The area to the left of point x a is a; we denote this area as a percentile p a. Typical percentile values are 0.05 or 5%, 0.10 or 10%, , 0.95 or 95%, and 0.99 or 99% and these are denoted as P 0.05, P 0.10, , P 0.95, or P 0.99 respectively.
For continuous functions, the jth percentile p j is defined as
Compute p 0.90, p 0.95, and p 0.99 for the cdf of the exponential distribution of Figure 10.16 if = 1/2.
Solution:
From (10.90) above,
or
Taking the natural log of both sides of the above expression, we obtain
or
Then,
For a pdf of the discrete type, we can obtain approximate values of percentiles, if we first arrange the sample in ascending order of magnitude; then, we compute the jth percentile p j, j = 1, 2, 99 from the relation
where n = number of samples.
If i in (10.91) above turns out to be an integer, the jth percentile is the average of the observations in positions i and i + 1 in the sampled data set starting at the bottom (lowest value) of the distribution. If i...
