Summary statisticsIn descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as simply as possible. Statisticians commonly try to describe the observations in a measure of location, or central tendency, such as the arithmetic mean a measure of statistical dispersion like the standard mean absolute deviation a measure of the shape of the distribution like skewness or kurtosis if more than one variable is measured, a measure of statistical dependence such as a correlation coefficient A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot.
Sampling biasIn statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample of a population (or non-human factors) in which all individuals, or instances, were not equally likely to have been selected. If this is not accounted for, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling.
Maximum likelihood estimationIn statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.
Convenience samplingConvenience sampling (also known as grab sampling, accidental sampling, or opportunity sampling) is a type of non-probability sampling that involves the sample being drawn from that part of the population that is close to hand. This type of sampling is most useful for pilot testing. Convenience sampling is not often recommended for research due to the possibility of sampling error and lack of representation of the population. But it can be handy depending on the situation. In some situations, convenience sampling is the only possible option.
Generalized extreme value distributionIn probability theory and statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within extreme value theory to combine the Gumbel, Fréchet and Weibull families also known as type I, II and III extreme value distributions. By the extreme value theorem the GEV distribution is the only possible limit distribution of properly normalized maxima of a sequence of independent and identically distributed random variables.
Fréchet distributionThe Fréchet distribution, also known as inverse Weibull distribution, is a special case of the generalized extreme value distribution. It has the cumulative distribution function where α > 0 is a shape parameter. It can be generalised to include a location parameter m (the minimum) and a scale parameter s > 0 with the cumulative distribution function Named for Maurice Fréchet who wrote a related paper in 1927, further work was done by Fisher and Tippett in 1928 and by Gumbel in 1958.
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.
Gumbel distributionIn probability theory and statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions. This distribution might be used to represent the distribution of the maximum level of a river in a particular year if there was a list of maximum values for the past ten years. It is useful in predicting the chance that an extreme earthquake, flood or other natural disaster will occur.
