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Discrete-variable probability distribution
In probability and statistics, a probability mass function (sometimes called probability function or frequency function) is a function that gives the
Probability_mass_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
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
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
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
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
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)
Probability distribution
The probability of getting exactly k successes in n independent Bernoulli trials (with the same rate p) is given by the probability mass function: f (
Binomial_distribution
Probability theory and statistics concept
is a continuous distribution, then its probability density function is known as the conditional density function. The properties of a conditional distribution
Conditional probability distribution
Conditional_probability_distribution
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
Function related to statistics and probability theory
components of a vector. For a probability function (or probability density function) Pr[x | θ] that gives the probability (or probability density) of data x for
Likelihood_function
Type of probability distribution
joint probability distribution can be expressed in terms of a joint cumulative distribution function and either in terms of a joint probability density
Joint probability distribution
Joint_probability_distribution
Branch of mathematics concerning probability
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations
Probability_theory
Mathematical concept
in the sample space. A probability function, P {\displaystyle P} , which assigns, to each event in the event space, a probability, which is a number between
Probability_space
Measure of total value one, generalizing probability distributions
In mathematics, a probability measure is a real-valued function defined on a set of events in a σ-algebra that satisfies measure properties such as countable
Probability_measure
Smooth approximation of one-hot arg max
The softmax function, also known as softargmax or normalized exponential function, converts a tuple of K real numbers into a probability distribution over
Softmax_function
Discrete probability distribution
In probability theory and statistics, the Poisson distribution (/ˈpwɑːsɒn/) is a discrete probability distribution that expresses the probability of a
Poisson_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
Sigmoid shape special function
2/{\sqrt {\pi }}} . This nonelementary integral is a sigmoid function that occurs often in probability, statistics, and partial differential equations. In statistics
Error_function
Probability of survival beyond any specified time
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
Survival_function
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
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
Conditional probability used in Bayesian statistics
The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood
Posterior_probability
The Dirac delta function, although not strictly a probability distribution, is a limiting form of many continuous probability functions. It represents
List of probability distributions
List_of_probability_distributions
Complex number whose squared absolute value is a probability
proposed by Max Born, in 1926. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum
Probability_amplitude
Mathematical description of quantum state
transition probabilities to inner products. The Schrödinger equation determines how wave functions evolve over time, and a wave function behaves qualitatively
Wave_function
Probability distribution
to multiple variables is called a Dirichlet distribution. The probability density function (PDF) of the beta distribution, for 0 ≤ x ≤ 1 {\displaystyle
Beta_distribution
Probabilistic optimization technique and metaheuristic
{\displaystyle s_{\mathrm {new} }} is specified by an acceptance probability function P ( e , e n e w , T ) {\displaystyle P(e,e_{\mathrm {new} },T)}
Simulated_annealing
PIL are compatible, so no prior probability function exists that satisfies them all. Some prior probability functions however are distinguished through
Pure_inductive_logic
Chances of card combinations in poker
the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands. Probability and
Poker_probability
Procedure that can be infinitely repeated, with a well-defined set of outcomes
more outcomes. The assignment of probabilities to the events—that is, a function P mapping from events to probabilities. An outcome is the result of a single
Experiment (probability theory)
Experiment_(probability_theory)
Number measuring the chance an event occurs
Probability concerns events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger
Probability
Extra-dimensional model of the universe
spacetime that is only warped along the fifth dimension, the graviton's probability function is extremely high at the Planckbrane, but it drops exponentially
Randall–Sundrum_model
Shorthand used in statistics
notation, these facts can be expressed as follows, where Pr() is the probability function, Χ is an observation from a normally distributed random variable
68–95–99.7_rule
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
Collection of random variables
In probability theory and related fields a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random
Stochastic_process
Generalization of the concept from statistical mechanics
The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition
Partition function (mathematics)
Partition_function_(mathematics)
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
Variable representing a random phenomenon
distribution is a discrete probability distribution, i.e. can be described by a probability mass function that assigns a probability to each value in the image
Random_variable
Kind of mathematical function
in the definition of the Lebesgue integral. In probability theory, a measurable function on a probability space is known as a random variable. Let ( X
Measurable_function
Probability of an event occurring, given that another event has already occurred
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption
Conditional_probability
Function in statistics
{\textstyle {\frac {p}{1-p}}} where p is a probability. Thus, the logit is a type of function that maps probability values from ( 0 , 1 ) {\displaystyle (0
Logit
Probability distribution
distribution for a real-valued random variable. The general form of its probability density function is f ( x ) = 1 2 π σ 2 exp ( − ( x − μ ) 2 2 σ 2 ) . {\displaystyle
Normal_distribution
Probability function
large deviations theory, a rate function is a function used to quantify the probabilities of rare events. Such functions are used to formulate large deviation
Rate_function
Mathematical function characterizing set membership
"characteristic function" has an unrelated meaning in classic probability theory. For this reason, traditional probabilists use the term indicator function for the
Indicator_function
Statistical method
set has been chosen, the reference data set must be converted to a probability function. To do this, let x1, x2,..., xn denote the ordered categories of
Ridit_scoring
Concept in probability theory
In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It
Law_of_total_probability
Model in probability theory
\chi _{F}} denotes the indicator function of the event F {\displaystyle F} . In Grimmett and Stirzaker's Probability and Random Processes, this last condition
Martingale (probability theory)
Martingale_(probability_theory)
S-shaped curve
"natural parametrization" of a binary probability. For example, the softplus function (the integral of the logistic function) is a smooth version of max ( 0
Logistic_function
Probability distribution
To understand the above definition of the probability mass function, note that the probability for every specific sequence of r successes and k failures
Negative binomial distribution
Negative_binomial_distribution
Probability distribution
over the variance parameter. Student's t distribution has the probability density function (PDF) given by f ( t ) = Γ ( ν + 1 2 ) π ν Γ ( ν 2 ) ( 1 + t
Student's_t-distribution
Value for the flow of probability in quantum mechanics
current (i.e. the probability current density) is related to the probability density function via a continuity equation. The probability current is invariant
Probability_current
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
Value that appears most often in a set of data
discrete random variable, the mode is the value x at which the probability mass function P(X) takes its maximum value, i.e., x = argmaxxi P(X = xi). In
Mode_(statistics)
joint probability mass function or probability density function as f ( x , y ) {\displaystyle f(x,y)} and joint cumulative distribution function as F (
Notation in probability and statistics
Notation_in_probability_and_statistics
Method for optimizing information security investments
effectiveness of the security measures, known as the security breach probability function. Gordon and Loeb demonstrated that the optimal level of security
Gordon–Loeb_model
Uniform distribution on an interval
than that it is contained in the distribution's support. The probability density function of the continuous uniform distribution is f ( x ) = { 1 b − a
Continuous uniform distribution
Continuous_uniform_distribution
Average value of a random variable
In probability theory, the expected value (also called expectation, mean, or first moment) is a generalization of the weighted average. Provided that
Expected_value
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
tall. Probability density is given by a probability density function. Contrast probability mass. probability density function The probability distribution
Glossary of probability and statistics
Glossary_of_probability_and_statistics
Concept in probability theory
L1 distance between the probability functions: on discrete domains, this is the distance between the probability mass functions δ ( P , Q ) = 1 2 ∑ x |
Total variation distance of probability measures
Total_variation_distance_of_probability_measures
Probability distribution
half-plane. It is one of the few stable distributions with a probability density function that can be expressed analytically, the others being the normal
Cauchy_distribution
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
Logarithm of probabilities, useful for calculations
In probability theory and computer science, a log probability is simply a logarithm of a probability. The use of log probabilities means representing
Log_probability
Probability distribution
In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: The probability distribution
Geometric_distribution
Mathematical rule for inverting probabilities
used to invert the probability of observations given a model configuration (i.e., the likelihood function) to obtain the probability of the model configuration
Bayes'_theorem
Quantum mechanical property
in reality its location in space is described by probability functions. Each probability function has a different average energy level, and corresponds
Orbital_motion_(quantum)
Statistical function that converts a probability to a standard normal score
In statistics, the probit function converts a probability (a number between 0 and 1) into a score. This score indicates how many standard deviations a
Probit
Probability distribution of energy states of a system
distribution) is a probability distribution or probability measure that gives the probability that a system will be in a certain state as a function of that state's
Boltzmann_distribution
When the occurrence of one event does not affect the likelihood of another
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically
Independence (probability theory)
Independence_(probability_theory)
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 to that
Empirical distribution function
Empirical_distribution_function
Probability distribution
the normal, binomial, gamma, and Poisson distributions. The probability density function (pdf) of an exponential distribution is f ( x ; λ ) = { λ e −
Exponential_distribution
Mathematical function having a characteristic S-shaped curve or sigmoid curve
distribution functions (which go from 0 to 1), such as the integrals of the logistic density, the normal density, and Student's t probability density functions. The
Sigmoid_function
Concept in Bayesian statistics
the unknown parameter is a location parameter (i.e. the forward probability function has the form P r ( x | μ ) = f ( x − μ ) {\displaystyle \mathrm {Pr}
Credible_interval
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
definition of a probability function for events, P, that satisfies the equation P(if A then B) = P(A and B) / P(A). In standard probability theory the occurrence
Conditional_event_algebra
Aspect of probability and statistics
distribution is known, then the marginal probability density function for X can be obtained by integrating the joint probability density, f, over Y, and vice versa
Marginal_distribution
Class of statistical models
exponential families of probability distributions, 2. A linear predictor η = X β {\displaystyle \eta =X\beta } , and 3. A link function g {\displaystyle g}
Generalized_linear_model
Topics referred to by the same term
Modified Wigner distribution function, used in signal processing Wigner semicircle distribution, a probability function used in mathematics Breit–Wigner
Wigner_distribution
Concept in economics
p_{k}} is the probability that outcome indexed by k {\displaystyle k} with payoff x k {\displaystyle x_{k}} is realized, and function u expresses the
Expected_utility_hypothesis
Observed value of a random variable
are often called "empirical", as in empirical distribution function or empirical probability. Conventionally, to avoid confusion, upper case letters denote
Realization_(probability)
Mapping arbitrary data to fixed-size values
minimize duplication of output values (collisions). Hash functions rely on generating favorable probability distributions for their effectiveness, reducing access
Hash_function
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
Topics referred to by the same term
theory, the branch of mathematics concerned with probability Probability function (disambiguation) Probability (moral theology), a theory in Catholic moral
Probability_(disambiguation)
model Probability Probability bounds analysis Probability box Probability density function Probability distribution Probability distribution function (disambiguation)
List_of_statistics_articles
Statistical probability Distribution for discrete event counts
called it "Hermite distribution" from the fact its probability function and the moment generating function can be expressed in terms of the coefficients of
Hermite_distribution
Base of natural logarithms
deviation is known as the standard normal distribution, given by the probability density function ϕ ( x ) = 1 2 π e − 1 2 x 2 . {\displaystyle \phi (x)={\frac
E_(mathematical_constant)
Mathematical function
prime distribution, two probability distributions related to the beta function Jacobi sum, the analogue of the beta function over finite fields. Nørlund–Rice
Beta_function
Probabilistic graphical representation of causal relationships
the joint probability function Pr ( G , S , R ) {\displaystyle \Pr(G,S,R)} and the conditional probabilities from the conditional probability tables (CPTs)
Bayesian_network
Table of probabilities related to the normal distribution
values of Φ, the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic is observed below, above
Standard_normal_table
Statistical model for a binary dependent variable
probability of the value labeled "1" can vary between 0 (certainly the value "0") and 1 (certainly the value "1"), hence the labeling; the function that
Logistic_regression
Probability theory term
distributions are treated on three levels: discrete probabilities, probability density functions, and measure theory. Conditioning leads to a non-random
Conditioning_(probability)
Continuous function that is not absolutely continuous
represented as an integral of a probability density function; integrating any putative probability density function that is not almost everywhere zero
Cantor_function
Probability of shared birthdays
In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday
Birthday_problem
Notions of probabilistic convergence, applied to estimation and asymptotic analysis
In probability theory, there exist several different notions of convergence of sequences of random variables, including convergence in probability, convergence
Convergence of random variables
Convergence_of_random_variables
Probability distribution
probability distribution whose cumulative distribution function is the Cantor function. This distribution has neither a probability density function nor
Cantor_distribution
Possible result of an experiment or trial
or experiment Probability distribution – Mathematical function for the probability a given outcome occurs in an experiment Probability space – Mathematical
Outcome_(probability)
Probability in decision theory
distinguished and probability functions are used to quantify beliefs at both levels. The justification for the use of probability functions is usually linked
Pignistic_probability
Estimate of an unobservable underlying probability density function
observed data, of an unobservable underlying probability density function. The unobservable density function is thought of as the density according to which
Density_estimation
Probability distribution
{\displaystyle \operatorname {Laplace} (\mu ,b)} distribution if its probability density function is f ( x ∣ μ , b ) = 1 2 b e − | x − μ | b , {\displaystyle f(x\mid
Laplace_distribution
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