More about Discovery Process Models
89
overcome this disadvantage, the ˆ
F estimated is approximated by various probability distributions. Then the best fi t among the distributions
is judged using the informal graphic procedure.
The Procedure
Suppose that ˆ
F is an estimate and is being tested to determine whether
it is equal to a hypothesized distribution F 0 . A number of graphic
methods can be applied to test the hypothesis. The percent–percent
(P–P) plot is checked to determine whether it falls along a straight line
through the origin with a slope of one. However, the P–P plot has two
disadvantages. First, it only allows one to check the adequacy of completely specifi ed distributions. In practice, it would be used more to
determine the shape of the distribution, such as lognormality. Second,
if the plot is nonlinear, it becomes diffi cult to determine which alternative shapes one should consider.
The Q–Q plot, on the other hand, is designed to overcome the drawbacks inherited from P–P plots and can be used to assess the adequacy
of a hypothesis whether a data set comes from a family F 0 [ y2m/s ] for
an unknown location parameter µ and scale σ
2 . If we consider that the
data set is from a distribution with shape F 0 , the data will follow a linear confi guration. So one needs only look for linearity without having to
estimate values for µ and σ
2 . If linearity does exist, then the intercept of the
line is an estimation of µ, and the slope is an estimation of σ
2 . Departures
from the straight line in the theoretical Q–Q plot clearly indicate that the
observed and theoretical distributions do not match. When data points
do not show a straight line on a plot, then they may indicate the nature of
the mismatch, such as (1) presence of outliers at either end; (2) curvature
at both ends, indicating long or short tails at both ends; (3) convex or concave curvature, related to symmetry; and (4) plateaus. The signifi cance
of these mismatches (Chambers et al., 1983) will be discussed later.
Interpretation
Outliers
Samples of geological populations often contain outliers. When they
are encountered in a set of data, it is prudent to examine the source of
the data, if possible, to verify the values. If the values are in error, they
can be corrected or set aside, but if they really belong to the population,
they might be the most important observation in the sample.
89
overcome this disadvantage, the ˆ
F estimated is approximated by various probability distributions. Then the best fi t among the distributions
is judged using the informal graphic procedure.
The Procedure
Suppose that ˆ
F is an estimate and is being tested to determine whether
it is equal to a hypothesized distribution F 0 . A number of graphic
methods can be applied to test the hypothesis. The percent–percent
(P–P) plot is checked to determine whether it falls along a straight line
through the origin with a slope of one. However, the P–P plot has two
disadvantages. First, it only allows one to check the adequacy of completely specifi ed distributions. In practice, it would be used more to
determine the shape of the distribution, such as lognormality. Second,
if the plot is nonlinear, it becomes diffi cult to determine which alternative shapes one should consider.
The Q–Q plot, on the other hand, is designed to overcome the drawbacks inherited from P–P plots and can be used to assess the adequacy
of a hypothesis whether a data set comes from a family F 0 [ y2m/s ] for
an unknown location parameter µ and scale σ
2 . If we consider that the
data set is from a distribution with shape F 0 , the data will follow a linear confi guration. So one needs only look for linearity without having to
estimate values for µ and σ
2 . If linearity does exist, then the intercept of the
line is an estimation of µ, and the slope is an estimation of σ
2 . Departures
from the straight line in the theoretical Q–Q plot clearly indicate that the
observed and theoretical distributions do not match. When data points
do not show a straight line on a plot, then they may indicate the nature of
the mismatch, such as (1) presence of outliers at either end; (2) curvature
at both ends, indicating long or short tails at both ends; (3) convex or concave curvature, related to symmetry; and (4) plateaus. The signifi cance
of these mismatches (Chambers et al., 1983) will be discussed later.
Interpretation
Outliers
Samples of geological populations often contain outliers. When they
are encountered in a set of data, it is prudent to examine the source of
the data, if possible, to verify the values. If the values are in error, they
can be corrected or set aside, but if they really belong to the population,
they might be the most important observation in the sample.