Methods for Testing Normality of Hydrologic Time Series - Hydrologic Time Series Analysis: Theory and Practice - page 38

to lower left, creating an S-shape. Figure 3.5, as an example, shows a 'ranked
data plot' of the right-skewed time series data.
Ranked data plots can be created as follows: consider a hydrologic time
series X 1 , X 2 , ..., X n with n data points. Arrange the time series data in ascending
order and let X (i) , for i = 1 to n , be the data listed in order from smallest to
largest such that X (1) is the smallest, X (2) is the second smallest, and X (n) is the
largest data point. Then, plot the ordered X (i) values at equally spaced intervals
along the horizontal axis to generate a ranked data plot. The entire procedure
can be executed easily using MS-Excel software.
3.1.5 Quantile Plot
A 'quantile plot' is a graph of the quantiles of the data (Fig. 3.6). It is very
similar to the 'ranked data plot' and makes no assumptions about a model for
the data. It is not subjective and displays every data point of a time series
instead of a summary of the data. The basic quantile plot is visually identical
to a ranked data plot except for its horizontal axis, which varies from 0.0 to
1.0, with each point plotted according to the fraction of the points it exceeds
(Walpole and Myers, 1985; USEPA, 1996). This allows the addition of vertical
lines indicating the quartiles or, many other quantiles of interest. Quantile
plots can be generated as follows: consider a hydrologic time series X 1 , X 2 , ...,
X n with n data points. Arrange the time series data in ascending order and let
X (i) , for i = 1 to n , be the data listed in order from smallest to largest such that
X (1) is the smallest, X (2) is the second smallest, and X (n) is the largest data
point. For each i , compute the fraction F i = ( i - 0.5)/ n . The 'quantile plot' is
a plot of the pairs [ F i , X (i) ], with straight lines connecting consecutive points.
Fig. 3.6. Example of a quantile plot.
A 'quantile plot' can be used to evaluate the quantile information such as
the median, quartiles, and interquartile range of the data points. Also, it can be
used to know the density of the data points, i.e., are all the data points close
to the centre with relatively few values in the tails or are there a large amount
of data points in one tail with the rest evenly distributed? The density of the