68–95–99.7 ruleIn statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively. In mathematical notation, these facts can be expressed as follows, where Pr() is the probability function, Χ is an observation from a normally distributed random variable, μ (mu) is the mean of the distribution, and σ (sigma) is its standard deviation: The usefulness of this heuristic especially depends on the question under consideration.
Data setA data set (or dataset) is a collection of data. In the case of tabular data, a data set corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the data set in question. The data set lists values for each of the variables, such as for example height and weight of an object, for each member of the data set. Data sets can also consist of a collection of documents or files.
Censoring (statistics)In statistics, censoring is a condition in which the value of a measurement or observation is only partially known. For example, suppose a study is conducted to measure the impact of a drug on mortality rate. In such a study, it may be known that an individual's age at death is at least 75 years (but may be more). Such a situation could occur if the individual withdrew from the study at age 75, or if the individual is currently alive at the age of 75. Censoring also occurs when a value occurs outside the range of a measuring instrument.
Winsorized meanA winsorized mean is a winsorized statistical measure of central tendency, much like the mean and median, and even more similar to the truncated mean. It involves the calculation of the mean after winsorizing -- replacing given parts of a probability distribution or sample at the high and low end with the most extreme remaining values, typically doing so for an equal amount of both extremes; often 10 to 25 percent of the ends are replaced.
Trimmed estimatorIn statistics, a trimmed estimator is an estimator derived from another estimator by excluding some of the extreme values, a process called truncation. This is generally done to obtain a more robust statistic, and the extreme values are considered outliers. Trimmed estimators also often have higher efficiency for mixture distributions and heavy-tailed distributions than the corresponding untrimmed estimator, at the cost of lower efficiency for other distributions, such as the normal distribution.
Huber lossIn statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. A variant for classification is also sometimes used. The Huber loss function describes the penalty incurred by an estimation procedure f. Huber (1964) defines the loss function piecewise by This function is quadratic for small values of a, and linear for large values, with equal values and slopes of the different sections at the two points where .
