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Type of probability distribution
the same probability space, the joint probability distribution or multivariate probability distribution for X,Y,… is a probability distribution that gives
Joint probability distribution
Joint_probability_distribution
Probability that random variable X is less than or equal to x
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution
Cumulative distribution function
Cumulative_distribution_function
Description of continuous random distribution
In probability theory, a probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function
Probability_density_function
Topics referred to by the same term
Probability distribution function may refer to: Probability distribution, a function that gives the probabilities of occurrence of possible outcomes for
Probability distribution function
Probability_distribution_function
Discrete-variable probability distribution
In probability and statistics, a probability mass function (PMF), discrete probability density function, probability function, or frequency function is
Probability_mass_function
Mathematical function for the probability a given outcome occurs in an experiment
a probability distribution tells us how likely different results are. Formally, it is a probability measure: a function that assigns probabilities to
Probability_distribution
Statistical function that defines the quantiles of a probability distribution
In probability and statistics, the quantile function of a probability distribution is the inverse of its cumulative distribution function. That is, the
Quantile_function
Smooth approximation of one-hot arg max
softmax function, also known as softargmax or normalized exponential function, converts a tuple of K real numbers into a probability distribution over K
Softmax_function
Topics referred to by the same term
Probability function may refer to: Probability distribution Probability axioms, which define a probability function Probability measure, a real-valued
Probability_function
Fourier transform of the probability density function
In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If
Characteristic function (probability theory)
Characteristic_function_(probability_theory)
Conditional probability used in Bayesian statistics
The two are related as follows: Given a prior belief that a probability distribution function is p ( θ ) {\displaystyle p(\theta )} and that the observations
Posterior_probability
Probability theory and statistics concept
In probability theory and statistics, the conditional probability distribution is a probability distribution that describes the probability of an outcome
Conditional probability distribution
Conditional_probability_distribution
Uniform distribution on an interval
that it is contained in the distribution's support. The probability density function of the continuous uniform distribution is f ( x ) = { 1 b − a for
Continuous uniform distribution
Continuous_uniform_distribution
Discrete probability distribution
probability theory and statistics, the Poisson distribution (US: /pwɑːˈsɒn/ pwahss-ON, UK: /ˈpwɑːsɒn, ˈpwæsɒn/ PWA(H)SS-on) is a discrete probability
Poisson_distribution
Continuous probability distribution
In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the
Logistic_distribution
Concept in probability theory and statistics
In probability theory and statistics, the moment generating function of a real-valued random variable is a generating function that provides an alternative
Moment_generating_function
Many probability distributions that are important in theory or applications have been given specific names. The Bernoulli distribution, which takes value
List of probability distributions
List_of_probability_distributions
Probability distribution
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes
Binomial_distribution
Probability distribution
form of its probability density function is f(x)=12πσ2exp(−(x−μ)22σ2). The parameter μ is the mean or expectation of the distribution (and also its
Normal_distribution
Probability distribution
probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: The probability distribution of
Geometric_distribution
Probability distribution
probability theory and statistics, Student's t distribution (or simply the t distribution) t ν {\displaystyle t_{\nu }} is a continuous probability distribution
Student's_t-distribution
Topics referred to by the same term
Distribution function may refer to Cumulative distribution function, a basic concept of probability theory Distribution function (physics), a function
Distribution_function
Probability distribution
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance
Exponential_distribution
Probability distribution of energy states of a system
a Boltzmann distribution (also called Gibbs distribution) is a probability distribution or probability measure that gives the probability that a system
Boltzmann_distribution
Function related to statistics and probability theory
and continuous probability distributions (a more general definition is discussed below). Given a probability density or mass function x ↦ f ( x ∣ θ )
Likelihood_function
Property of having a unique mode or maximum value
with the same probability. Figure 2 and Figure 3 illustrate bimodal distributions. Other definitions of unimodality in distribution functions also exist
Unimodality
Probability distribution
multiple variables is called a Dirichlet distribution. The probability density function (PDF) of the beta distribution, for 0 ≤ x ≤ 1 {\displaystyle 0\leq
Beta_distribution
Probability distribution
In probability theory and statistics, the negative binomial distribution, also called a Pascal distribution, is a discrete probability distribution that
Negative binomial distribution
Negative_binomial_distribution
Power series derived from a discrete probability distribution
In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of
Probability generating function
Probability_generating_function
Continuous probability distribution
In probability theory and statistics, the Weibull distribution /ˈwaɪbʊl/ is a continuous probability distribution. It models a broad range of random variables
Weibull_distribution
Probability distribution
few stable distributions with a probability density function that can be expressed analytically, the others being the normal distribution and the Lévy
Cauchy_distribution
Probability distribution
In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes
Laplace_distribution
Probability distribution
The Cantor distribution is the probability distribution whose cumulative distribution function is the Cantor function. This distribution has neither a
Cantor_distribution
Probability distribution of the sum of random variables
convolution/sum of probability distributions arises in probability theory and statistics as the operation in terms of probability distributions that corresponds
Convolution of probability distributions
Convolution_of_probability_distributions
Distribution function associated with the empirical measure of a sample
distribution function is an estimate of the cumulative distribution function that generated the points in the sample. It converges with probability 1
Empirical distribution function
Empirical_distribution_function
Probability of survival beyond any specified time
{\displaystyle T} has cumulative distribution function F ( t ) {\displaystyle F(t)} and probability density function f ( t ) {\displaystyle f(t)} on the
Survival_function
Type of probability distribution
unchanged when its probability density function (for continuous probability distribution) or probability mass function (for discrete random variables) is
Symmetric probability distribution
Symmetric_probability_distribution
Type of probability distribution
In probability theory, the arcsine distribution is the probability distribution whose cumulative distribution function involves the arcsine and the square
Arcsine_distribution
Probability distribution modeling a coin toss which need not be fair
In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution
Bernoulli_distribution
Probability distribution
The Pareto distribution, named after the Italian polymath Vilfredo Pareto, is a probability distribution in the form of a power law that is used to describe
Pareto_distribution
Mathematical concept
Probability distribution fitting or simply distribution fitting is the fitting of a probability distribution to a series of data concerning the repeated
Probability distribution fitting
Probability_distribution_fitting
Probability distribution
inverse-gamma distribution and a stable distribution. The probability density function of the Lévy distribution over the domain x ≥ μ {\displaystyle x\geq
Lévy_distribution
Probability distribution in physics
stable distribution for which a closed form expression of the probability density function is known. However, its probability density function is not
Holtsmark_distribution
Probability distribution
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally
Log-normal_distribution
Probability distribution
In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails
Heavy-tailed_distribution
Probability distribution used to model household income
called the "generalized log-logistic distribution". The Burr (Type XII) distribution has probability density function: f ( x ; c , k ) = c k x c − 1 ( 1
Burr_distribution
Probability distribution
In probability theory and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to
Skew_normal_distribution
Statistical distribution
distribution. It is characterised by its probability density function, within the support of the distribution, being proportional to the reciprocal of
Reciprocal_distribution
Probability distribution and special case of gamma distribution
In probability theory and statistics, the χ 2 {\displaystyle \chi ^{2}} -distribution with k {\displaystyle k} degrees of freedom is the distribution of
Chi-squared_distribution
Family of continuous probability distributions
beta distribution, but much simpler to use especially in simulation studies since its probability density function, cumulative distribution function and
Kumaraswamy_distribution
Specific probability distribution function, important in physics
mechanics), the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and
Maxwell–Boltzmann distribution
Maxwell–Boltzmann_distribution
Probability distribution
In probability theory and statistics, the gamma distribution is a versatile two-parameter family of continuous probability distributions. The exponential
Gamma_distribution
Aspect of probability and statistics
In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the
Marginal_distribution
Continuous probability distribution for a non-negative random variable
In probability and statistics, the log-logistic distribution (known as the Fisk distribution in economics) is a continuous probability distribution for
Log-logistic_distribution
Probability distribution with more than one mode
the probability density function, as shown in Figures 1 and 2. Categorical, continuous, and discrete data can all form multimodal distributions. Among
Multimodal_distribution
Probability distribution
random variable equal to a with probability 1. This is a special case of a discrete distribution; its probability mass function equals 1 in a and 0 everywhere
Degenerate_distribution
Statistics function
Q-function is the tail distribution function of the standard normal distribution. In other words, Q ( x ) {\displaystyle Q(x)} is the probability that
Q-function
Concept in statistics
probability and statistics, a compound probability distribution (also known as a mixture distribution or contagious distribution) is the probability distribution
Compound probability distribution
Compound_probability_distribution
Conditional distribution in statistics
distribution is a conditional distribution that results from restricting the domain of some other probability distribution. Truncated distributions arise
Truncated_distribution
Table of probabilities related to the normal distribution
the values of Φ, the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic is observed below
Standard_normal_table
Type of probability distribution
and its probability density function is sometimes referred to as a mixture density. The cumulative distribution function (and the probability density
Mixture_distribution
Continuous probability distribution
In probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and
Hyperbolic secant distribution
Hyperbolic_secant_distribution
Statistical distribution for dependence between random variables
In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each
Copula_(statistics)
Discrete probability distribution
In probability theory and statistics, a categorical distribution (also called a generalized Bernoulli distribution, multinoulli distribution) is a discrete
Categorical_distribution
Class of statistical models
x ≠ 0 ( x ) {\displaystyle p_{x\neq 0}(x)} is a truncated probability distribution function, truncated at 0. Hurdle models were introduced by John G.
Hurdle_model
Probability distribution in mathematics
In probability theory and statistics, the zeta distribution is a discrete probability distribution. If X is a zeta-distributed random variable with parameter
Zeta_distribution
Type of probability distribution
characteristic function of any infinitely divisible distribution is then called an infinitely divisible characteristic function. More rigorously, the probability distribution
Infinite divisibility (probability)
Infinite_divisibility_(probability)
Two-parameter family of continuous probability distributions
inverse gamma distribution differently, as a scaled inverse chi-squared distribution. The inverse gamma distribution's probability density function is defined
Inverse-gamma_distribution
Discrete probability distribution
In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete
Logarithmic_distribution
Algorithm
in Monte Carlo simulations by using a known or approximate probability distribution function to concentrate the search in those areas of the integrand
VEGAS_algorithm
Generalized function whose value is zero everywhere except at zero
Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized function on the real
Dirac_delta_function
Continuous function that is not absolutely continuous
positive probability to some interval to which this distribution assigns probability zero. In particular, as Vitali (1905) pointed out, the function is not
Cantor_function
Wigner distribution function in physics as opposed to in signal processing
Schrödinger equation to a probability distribution in phase space. It is a generating function for all spatial autocorrelation functions of a given quantum-mechanical
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
Fundamental theorem in probability theory and statistics
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample
Central_limit_theorem
Theoretical framework
statistical model is a probability distribution function proposed as generating data. In a parametric model, the probability distribution function has variable
Conceptual_model
Logarithm of probabilities, useful for calculations
unwrapping the exponent. For example, the log probability of the normal distribution's probability density function is − ( ( x − m x ) / σ m ) 2 + C {\displaystyle
Log_probability
Probability distribution of only one random variable
probability mass function for discrete variables, probability density function for continuous variables, or their cumulative distribution function, which applies
Univariate_distribution
Notions of probabilistic convergence, applied to estimation and asymptotic analysis
in distribution tells us about the limit distribution of a sequence of random variables. This is a weaker notion than convergence in probability, which
Convergence of random variables
Convergence_of_random_variables
Distribution of an uncertain quantity
A prior probability distribution (often simply called the prior probability, prior distribution, or prior) of an uncertain quantity is its assumed probability
Prior_probability
Probability theory operation
can reasonably be modelled as arising from a specified distribution. Specifically, the probability integral transform is applied to construct an equivalent
Probability integral transform
Probability_integral_transform
Average uncertainty in variable's states
needed to describe the state of the variable, considering the distribution of probabilities across all potential states. Given a discrete random variable
Entropy_(information_theory)
Extension of the factorial function
factorial function do exist, but the gamma function is the most popular and useful. It appears as a factor in various probability-distribution functions and
Gamma_function
Family of probability distributions
In probability theory and statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within
Generalized extreme value distribution
Generalized_extreme_value_distribution
Particular case of the generalized extreme value distribution
In probability theory and statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution
Gumbel_distribution
Observed value of a random variable
model are often called "empirical", as in empirical distribution function or empirical probability. Conventionally, to avoid confusion, upper case letters
Realization_(probability)
Function in statistics
cumulative distribution function (CDF) of a probability distribution. In fact, the logit is the quantile function of the logistic distribution, while the
Logit
Set of different models of the climate system
in the model. Any prior assumptions about distribution can influence the probability distribution function produced. There are at least five different
Climate_ensemble
Probability distribution
In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to
Rayleigh_distribution
Continuous probability distribution, named after Benjamin Gompertz
distributed according to the Gompertz distribution. The probability density function of the Gompertz distribution is: f ( x ; η , b ) = b η exp ( η +
Gompertz_distribution
Mathematical function having a characteristic "bell"-shaped curve
bell-shaped function is typically a sigmoid function. Bell shaped functions are also commonly symmetric. Many common probability distribution functions are bell
Bell-shaped_function
Generalized expected utility model of choice under uncertainty
transformations to be applied to the cumulative probability distribution function, rather than to individual probabilities (Quiggin, 1982, 1993). The central idea
Rank-dependent expected utility
Rank-dependent_expected_utility
Branch of mathematics concerning probability
event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which
Probability_theory
Probability distribution
In probability and statistics, the inverse-chi-squared distribution (or inverted-chi-square distribution) is a continuous probability distribution of
Inverse-chi-squared distribution
Inverse-chi-squared_distribution
Behavioral model of risky decision-making
to the cumulative probability distribution function, as in rank-dependent expected utility theory but not applied to the probabilities of individual outcomes
Cumulative_prospect_theory
Measure for evaluating probabilistic forecasts
predictions of the whole probability distribution F {\displaystyle F} of the outcome. On the other hand, scoring functions assess point predictions,
Scoring_rule
Concept in probability theory
In Bayesian probability theory, if, given a likelihood function p ( x ∣ θ ) {\displaystyle p(x\mid \theta )} , the posterior distribution p ( θ ∣ x )
Conjugate_prior
Information-theoretic measure
In information theory, the cross-entropy between two probability distributions p and q, over the same underlying set of events, measures the average number
Cross-entropy
Distribution of variables which satisfies a stability property under linear combinations
In probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same
Stable_distribution
Variable representing a random phenomenon
and its distribution is a discrete probability distribution, i.e. can be described by a probability mass function that assigns a probability to each value
Random_variable
Probability distribution
In probability theory and statistics, the triangular distribution is a continuous probability distribution with lower limit a, upper limit b, and mode
Triangular_distribution
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PROBABILITY DISTRIBUTION-FUNCTION
PROBABILITY DISTRIBUTION-FUNCTION
PROBABILITY DISTRIBUTION-FUNCTION
PROBABILITY DISTRIBUTION-FUNCTION
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