Page 425 - Contributed Paper Session (CPS) - Volume 6

CPS2008 Syafrina A.H et al.
() = ∑ log [( |)]
=1

Goodness of Fit (GOF) tests
The null and alternative hypotheses of the goodness of fit tests are the
data follow a specified distribution and the data do not follow the specified
distribution, respectively.
i. Cramer-von Mises (CvM) test
This test is an alternative to K-S test for testing the hypothesis that a set of
data comes from a specified continuous distribution. This test was introduced
by Cramér in 1928 and von Mises in 1931. The CvM statistic is used in testing
the goodness of fit of a probability distribution compared to a given empirical
distribution function. This test statistic is based on the squared summation of
the difference between the Empirical Distribution Function being tested.
According to Deidda and Puliga (2007), the CvM test statistic can be computed
as:
2
2
= 1 + ∑ [( ) − 2−1 ]

12 =1 2 (2.7)
where F is the cumulative distribution function of the specified or
hypothesized distribution while xi is the ordered data in ascending order and
n is the number of sample size.
ii. Kolmogorov-Smirnov (K-S) test
Kolmogorov-Smirnov is one of the GOF test which is usually used to decide
if a sample comes from a population with a specific distribution. This test is
based on the empirical distribution function. Given n is the sample size and
is the data points in ascending order, 1,2, … , . The K-S statistic is
given by,
− 1
= max (( ) − , − ( ) )

1≤≤
(2.8)
where F is the theoretical cumulative distribution of the distribution being
tested which must be a continuous distribution (Sharma & Singh, 2010).

3. Result
A summary of daily rainfall amount at Penang International Airport is
provided in Table 3.1. Based on Table 3.1, the results showed that the standard
deviation for the station is large due to several large values in the dataset
which possibly be affected by the extreme values as shown in Figure 3.1. This
explains the shape of the rainfall distribution for the station that is skewed to
the right as shown in Figure 3.2. In addition, the mean rainfall amount is near
to zero value, which is 0.249. This shows that Penang International Airport
received low mean rainfall amount. The irregularity of the daily rainfall data of
the station can be represented by the coefficient of variation (CV) which is
evident in all cases that the 100% is clearly exceeded with amount of variability

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