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In statistics, a univariate distribution is a probability distribution of only one random variable. This is in contrast to a multivariate distribution , the probability distribution of a random vector (consisting of multiple random variables).
Univariate is a term commonly used in statistics to describe a type of data which consists of observations on only a single characteristic or attribute. A simple example of univariate data would be the salaries of workers in industry. [ 1 ]
The Cauchy distribution, an example of a distribution which does not have an expected value or a variance. In physics it is usually called a Lorentzian profile, and is associated with many processes, including resonance energy distribution, impact and natural spectral line broadening and quadratic stark line broadening.
In statistics, a univariate distribution characterizes one variable, although it can be applied in other ways as well. For example, univariate data are composed of a single scalar component. In time series analysis, the whole time series is the "variable": a univariate time series is the series of values over time of a single quantity ...
The normal distribution is an important example where the inverse transform method is not efficient. However, there is an exact method, the Box–Muller transformation , which uses the inverse transform to convert two independent uniform random variables into two independent normally distributed random variables.
HOS are particularly used in the estimation of shape parameters, such as skewness and kurtosis, as when measuring the deviation of a distribution from the normal distribution. In statistical theory, one long-established approach to higher-order statistics, for univariate and multivariate distributions is through the use of cumulants and joint ...
In particular, the bootstrap is useful when there is no analytical form or an asymptotic theory (e.g., an applicable central limit theorem) to help estimate the distribution of the statistics of interest. This is because bootstrap methods can apply to most random quantities, e.g., the ratio of variance and mean.
A probability distribution whose sample space is one-dimensional (for example real numbers, list of labels, ordered labels or binary) is called univariate, while a distribution whose sample space is a vector space of dimension 2 or more is called multivariate.