- After a family of distribution has been selected such as
Poisson, Normal, Geometric ..., the next step is to estimate the
parameters of the distribution.
- Sample mean and sample variance can be used to estimate the
parameters in a distribution.
- Let
be the sample of size
*n*. - The sample mean is

- The sample variance is

- If the data are discrete and grouped in a frequency
distribution, then we can re-write the equations as

and

- Example 10.5 on page 368
- If the data are continuous, we ``discretize'' them and
estimate the mean

and the variance

where is the observed frequency in the*j*th class interval, is the midpoint of the*j*th interval, and*c*is the number of class intervals. - Example 10.6 on page 369

- Let
be the sample of size
- A few well-established, suggested estimators are listed in
Table 10.3 on page 370, followed by examples. They come from theory of
statistics.
- The examples include Poisson Distribution, Uniform Distribution,
Normal Distribution, Exponential Distribution, and Weibull Distribution.