## Chapter 8. Estimation

The code for this chapter is in `estimation.py`

. For information about downloading
and working with this code, see Using the Code.

## The Estimation Game

Let’s play a game. I think of a distribution, and you have to guess what it is. I’ll give you two hints: it’s a normal distribution, and here’s a random sample drawn from it:

```
[-0.441, 1.774, -0.101, -1.138, 2.975,
-2.138]
```

What do you think is the mean parameter, μ, of this distribution?

One choice is to use the sample mean, , as an estimate of μ.
In this example, is 0.155, so it would be reasonable to guess μ = 0.155. This process is called **estimation**, and the
statistic we used (the sample mean) is called an **estimator**.

Using the sample mean to estimate μ is so obvious that it is hard to imagine a reasonable alternative. But suppose we change the game by introducing outliers.

*I’m thinking of a distribution.* It’s a normal
distribution, and here’s a sample that was collected by an unreliable
surveyor who occasionally puts the decimal point in the wrong place.

```
[-0.441, 1.774, -0.101, -1.138, 2.975,
-213.8]
```

Now what’s your estimate of μ? If you use the sample mean, your guess is -35.12. Is that the best choice? What are the alternatives?

One option is to identify and discard outliers, and then compute the sample mean of the rest. ...

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