## Test for Distribution

You can test that the data are from a specific
family of distributions, such as the normal,
lognormal, exponential, or Weibull distributions.
You do not need to specify the distribution parameters
except the threshold parameters for the lognormal,
exponential, and Weibull distributions.
The Kolmogorov statistic assesses the discrepancy
between the empirical distribution and the estimated
hypothesized distribution *F*.
For a test of normality, the hypothesized distribution is
a normal distribution function with parameters and
estimated by the sample mean and standard deviation.
The probability of a larger test statistic is obtained
by linear interpolation within the range of simulated
critical values given by Stephens (1974).
For a test of whether the data are from a lognormal
distribution, the hypothesized distribution is a
lognormal distribution function with a given parameter
and parameters and estimated
from the sample after the logarithmic transformation
of the data, .The sample mean and standard deviation of the
transformed sample are used as the parameter estimates.
The test is therefore equivalent to the test
of normality on the transformed sample.
For a test of exponentiality, the hypothesized
distribution is an exponential distribution function
with a given parameter and a parameter
estimated by .The probability of a larger test statistic is obtained
by linear interpolation within the range of simulated
critical values given by Stephens (1974).
For a test of whether the data are from a Weibull
distribution, the hypothesized distribution is a
Weibull distribution function with a given parameter
and parameters *c* and estimated
by the maximum-likelihood method.
The probability of a larger test statistic is obtained by
linear interpolation within the range of simulated critical
values given by Chandra, Singpurwalla, and Stephens (1981).
You specify the distribution in the cumulative distribution
options dialog or in the **Test for Distribution** dialog
after choosing **Curves:Test for Distribution** from the menu,
as shown in Figure 38.33.
You can also specify a threshold parameter other than zero
for lognormal, exponential, and Weibull distributions.

**Figure 38.33:** Test for Distribution Dialog

The default tests that the data are from a normal distribution.
A test for normality and a test for lognormal distribution
with = 30 are given in Figure 38.34.
You can use the **Mean/Theta** slider to adjust
the threshold parameter, , for lognormal,
exponential, and Weibull distributions.

**Figure 38.34:** Tests for Distribution

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