Function whose integral over a region describes the probability of an event occurring in that region
Box plot and probability density function of a normal distribution N(0, σ2).Geometric visualisation of the mode, median and mean of an arbitrary unimodal probability density function.[1]
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Probability density function" – news · newspapers · books · scholar · JSTOR(June 2022) (Learn how and when to remove this message)
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.[2][3] Probability density is the probability per unit length, in other words, while the absolute likelihood for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample.
In a more precise sense, the PDF is used to specify the probability of the random variable falling within a particular range of values, as opposed to taking on any one value. This probability is given by the integral of this variable's PDF over that range—that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range. The probability density function is nonnegative everywhere, and the area under the entire curve is equal to 1.
The terms probability distribution function and probability function have also sometimes been used to denote the probability density function. However, this use is not standard among probabilists and statisticians. In other sources, "probability distribution function" may be used when the probability distribution is defined as a function over general sets of values or it may refer to the cumulative distribution function, or it may be a probability mass function (PMF) rather than the density. "Density function" itself is also used for the probability mass function, leading to further confusion.[4] In general though, the PMF is used in the context of discrete random variables (random variables that take values on a countable set), while the PDF is used in the context of continuous random variables.
^"AP Statistics Review - Density Curves and the Normal Distributions". Archived from the original on 2 April 2015. Retrieved 16 March 2015.
^Grinstead, Charles M.; Snell, J. Laurie (2009). "Conditional Probability - Discrete Conditional" (PDF). Grinstead & Snell's Introduction to Probability. Orange Grove Texts. ISBN 978-1616100469. Archived (PDF) from the original on 2003-04-25. Retrieved 2019-07-25.
^"probability - Is a uniformly random number over the real line a valid distribution?". Cross Validated. Retrieved 2021-10-06.
^Ord, J.K. (1972) Families of Frequency Distributions, Griffin. ISBN 0-85264-137-0 (for example, Table 5.1 and Example 5.4)
and 24 Related for: Probability density function information
In probability theory, a probabilitydensityfunction (PDF), densityfunction, or density of an absolutely continuous random variable, is a function whose...
is a continuous distribution, then its probabilitydensityfunction is known as the conditional densityfunction. The properties of a conditional distribution...
distribution for a real-valued random variable. The general form of its probabilitydensityfunction is f ( x ) = 1 σ 2 π e − 1 2 ( x − μ σ ) 2 {\displaystyle f(x)={\frac...
than that it is contained in the distribution's support. The probabilitydensityfunction of the continuous uniform distribution is f ( x ) = { 1 b − a...
cumulative distribution function, or by a multivariate probabilitydensityfunction together with a multivariate probability mass function. In the special case...
the area under the probabilitydensityfunction from negative infinity to x {\displaystyle x} . Cumulative distribution functions are also used to specify...
of an unobservable underlying probabilitydensityfunction. The unobservable densityfunction is thought of as the density according to which a large population...
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different...
}f_{X}(u){\mathcal {L}}_{X\mid Y=y}(u)\,du}}} gives the posterior probabilitydensityfunction for a random variable X {\displaystyle X} given the data Y =...
distribution is known, then the marginal probabilitydensityfunction can be obtained by integrating the joint probability distribution, f, over Y, and vice...
likelihood function (often simply called the likelihood) is the joint probability mass (or probabilitydensity) of observed data viewed as a function of the...
systems. The square of the modulus of this quantity represents a probabilitydensity. Probability amplitudes provide a relationship between the quantum state...
the normal, binomial, gamma, and Poisson distributions. The probabilitydensityfunction (pdf) of an exponential distribution is f ( x ; λ ) = { λ e −...
current (i.e. the probability current density) is related to the probabilitydensityfunction via a continuity equation. The probability current is invariant...
density estimation, i.e., a non-parametric method to estimate the probabilitydensityfunction of a random variable based on kernels as weights. KDE answers...
In probability and statistics, the quantile function outputs the value of a random variable such that its probability is less than or equal to an input...
a probabilitydensityfunction that can be expressed analytically, the others being the normal distribution and the Lévy distribution. A function with...
The survival function is a function that gives the probability that a patient, device, or other object of interest will survive past a certain time. The...
illustration involves a continuous probability distribution, for which the random variables have a probabilitydensityfunction. The second illustration, for...
controls the width of the "bell". Gaussian functions are often used to represent the probabilitydensityfunction of a normally distributed random variable...
Probability distribution function may refer to: Cumulative distribution functionProbability mass functionProbabilitydensityfunctionProbability distribution...
ideal gas (chi distribution with three degrees of freedom). The probabilitydensityfunction (pdf) of the chi-distribution is f ( x ; k ) = { x k − 1 e −...
Global Information
