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## Parameter Estimation

• 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 jth class interval, is the midpoint of the jth interval, and c is the number of class intervals.
• Example 10.6 on page 369

• 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.

Next: Goodness-of-Fit Tests Up: Identifying the Distribution with Previous: Quantile-Quantile Plots
Meng Xiannong 2002-10-18