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Logistic regression is used in various fields, including machine learning, most medical fields, and social sciences. For example, the Trauma and Injury Severity Score (), which is widely used to predict mortality in injured patients, was originally developed by Boyd et al. using logistic regression. [6]
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
The resulting model is known as logistic regression (or multinomial logistic regression in the case that K-way rather than binary values are being predicted). For the Bernoulli and binomial distributions, the parameter is a single probability, indicating the likelihood of occurrence of a single event.
In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis).
The logit in logistic regression is a special case of a link function in a generalized linear model: it is the canonical link function for the Bernoulli distribution. More abstractly, the logit is the natural parameter for the binomial distribution; see Exponential family § Binomial distribution.
The formula can be understood as follows: p k q n−k is the probability of obtaining the sequence of n independent Bernoulli trials in which k ... Logistic regression;
In probability theory and statistics, the beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers arising when the probability of success in each of a fixed or known number of Bernoulli trials is either unknown or random.
IRLS is used to find the maximum likelihood estimates of a generalized linear model, and in robust regression to find an M-estimator, as a way of mitigating the influence of outliers in an otherwise normally-distributed data set, for example, by minimizing the least absolute errors rather than the least square errors.