In probability theory and statistics the probit function is the inverse cumulative distribution function, or quantile function of the normal distribution. It has been suggested that this article or section be merged with Probability axioms. ... Template:Otherusescccc A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... In mathematics, an inverse function is in simple terms a function which does the reverse of a given function. ... In probability theory, the cumulative distribution function (abbreviated cdf) completely describes the probability distribution of a real-valued random variable, X. For every real number x, the cdf is given by where the right-hand side represents the probability that the random variable X takes on a value less than... This article or section does not adequately cite its references or sources. ... The normal distribution, also called Gaussian distribution by scientists (named after Carl Friedrich Gauss due to his rigorous application of the distribution to astronomical data (Havil, 2003)) is a probability distribution of great importance in many fields. ...

The probit function is often denoted as Φ ^{− 1} and is of type:

Plot of probit function

Like the logit (log odds) function, it may be used to transform a variable p ranging over the interval (0,1) into a derived quantity Φ ^{− 1}(p) ranging over the real numbers. This has applications in probit models, which are generalized linear models. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... In mathematics, especially as applied in statistics, the logit (pronounced with a long o and a soft g, IPA ) of a number p between 0 and 1 is This function is used in logistic regression. ... In mathematics, interval is a concept relating to the sequence and set-membership of one or more numbers. ... In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ... The probit model is a popular specification of a binary regression model, using a probit link function. ... In statistics, the generalized linear model (GLM) is a useful generalization of ordinary least squares regression. ...

The probit function may be expressed in terms of the inverse of the error function: Plot of the error function In mathematics, the error function (also called the Gauss error function) is a non-elementary function which occurs in probability, statistics and partial differential equations. ...

The idea of probit was published in 1934 by Chester Ittner Bliss (1899-1979) in an article in Science on how to treat data such as the percentage of a pest killed by a pesticide. Bliss proposed transforming the percentage killed into a "probability unit" (or "probit") which was linearly related to the modern definition (he defined it arbitrarily as equal to 0 for 0.0001 and 1 for 0.9999). He included a table to aid other researchers to convert their kill percentages to his probit, which they could then plot against the logarithm of the dose and thereby, it was hoped, obtain a more or less straight line. Science is the journal of the American Association for the Advancement of Science (AAAS). ... A cropduster spreading pesticide. ...

A popular alternative to probit is the logit model, named by analogy to the probit function but based on the logistic function. It also maps the interval from 0 to 1 into the whole real line. In mathematics, especially as applied in statistics, the logit (pronounced with a long o and a soft g, IPA ) of a number p between 0 and 1 is This function is used in logistic regression. ... Logistic curve, specifically the sigmoid function A logistic function or logistic curve models the S-curve of growth of some set P. The initial stage of growth is approximately exponential; then, as competition arises, the growth slows, and at maturity, growth stops. ... In mathematics, the real line is simply the set of real numbers. ...

See also

• Rankit analysis, also developed by Chester Bliss.

In statistics, the rankits of the data points in a data set consisting simply of a list of scalars are expected values of order statistics of the standard normal distribution corresponding to data points in a manner determined by the order in which the data points appear. ...

Reference

• Bliss, C. I., (1934), The method of probits. Science 79:38-39.