The normal distribution, a very common probability density, useful because of the central limit theorem.
The normal distribution, a very common probability density, useful because of the central limit theorem.
Scatter plots are used in descriptive statistics to show the observed relationships between different variables, here using the Iris flower data set.
Gerolamo Cardano, a pioneer on the mathematics of probability.
Karl Pearson, a founder of mathematical statistics.
A least squares fit: in red the points to be fitted, in blue the fitted line.
Confidence intervals: the red line is true value for the mean in this example, the blue lines are random confidence intervals for 100 realizations.
In this graph the black line is probability distribution for the test statistic, the critical region is the set of values to the right of the observed data point (observed value of the test statistic) and the p-value is represented by the green area.
The confounding variable problem: X and Y may be correlated, not because there is causal relationship between them, but because both depend on a third variable Z. Z is called a confounding factor.
gretl, an example of an open source statistical package

Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component.

- Estimation theory

These inferences may take the form of answering yes/no questions about the data (hypothesis testing), estimating numerical characteristics of the data (estimation), describing associations within the data (correlation), and modeling relationships within the data (for example, using regression analysis).

- Statistics
The normal distribution, a very common probability density, useful because of the central limit theorem.

2 related topics

Alpha

Estimator

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished.

Estimation theory is concerned with the properties of estimators; that is, with defining properties that can be used to compare different estimators (different rules for creating estimates) for the same quantity, based on the same data.

400 px

Expected value

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400 px

For a different example, in statistics, where one seeks estimates for unknown parameters based on available data, the estimate itself is a random variable.

To empirically estimate the expected value of a random variable, one repeatedly measures observations of the variable and computes the arithmetic mean of the results.