difference between parameter and estimator

A parameter is a value that describes a characteristic of an entire population. It is a fixed value, but in practice, we often do not know its actual value. Examples of parameters include the population mean (μ) and the population standard deviation (σ).

On the other hand, an estimator is a statistic (a function of the data) that is used to infer the value of an unknown parameter in a statistical model. The estimator provides an estimated value of the parameter. For example, the sample mean (x̄) is an estimator of the population mean (μ), and the sample standard deviation (s) is an estimator of the population standard deviation (σ).

In summary, a parameter is a fixed but unknown value that we want to estimate, and an estimator is a function of the sample data that we use to estimate the parameter.

A parameter is a numerical characteristic of a population. For example, the mean and standard deviation are parameters of a population. Parameters are usually unknown because we cannot measure the entire population.

An estimator, on the other hand, is a statistic (a function of the data) that is used to infer the value of an unknown parameter in a statistical model. For example, the sample mean and sample standard deviation are estimators of the population mean and standard deviation, respectively.

The main difference between a parameter and an estimator is that a parameter is a fixed value that describes a population, while an estimator is a variable that is based on sample data and is used to estimate a population parameter.