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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
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
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 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(k;n
Binomial_distribution
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
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
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)
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
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
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
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
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
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
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
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
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
Discrete probability distribution
to have a Poisson distribution with parameter λ>0 if it has a probability mass function given by: f(k;λ)=Pr(X=k)=λke−λk!, where k is the number of occurrences
Poisson_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
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
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
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
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
Probability distribution
distribution for a real-valued random variable. The general form of its probability density function is f(x)=12πσ2exp(−(x−μ)22σ2). The parameter μ is the mean
Normal_distribution
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
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
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
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
Probabilistic optimization technique and metaheuristic
The probability of making the transition from the current state s to a candidate new state snew is specified by an acceptance probability function P(e
Simulated_annealing
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
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
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
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
PIL are compatible, so no prior probability function exists that satisfies them all. Some prior probability functions however are distinguished through
Pure_inductive_logic
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
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
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
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)
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 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
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
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
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
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
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)
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
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
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)
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
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
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
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
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
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
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)
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)
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
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
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
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
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
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
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
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
Probability distribution
In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: The probability distribution
Geometric_distribution
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
Theorem of convex functions
the context of probability theory, it is generally stated in the following form: if X is a random variable and φ is a convex function, then φ(E[X])≤E[φ(X)]
Jensen's_inequality
Average uncertainty in variable's states
the function log(1p(E)), where log is the logarithm, which gives 0 surprise when the probability of the event is 1. In fact, log is the only function that
Entropy_(information_theory)
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
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
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
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)
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)
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
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
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
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
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
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
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
Function used in computer cryptography
x, y such that f(x) = f(y)—with non-negligible probability. A hard-core predicate of a one-way function f is a predicate (i.e. single bit) b such that
One-way_function
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
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
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
Term in statistical hypothesis testing
between the two distributions being a function of the effect size), the power of the test would be the probability, under H1, that the sample t falls into
Power_(statistics)
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)
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
Base of natural logarithms
deviation is known as the standard normal distribution, given by the probability density function ϕ(x)=12πe−12x2. The constraint of unit standard deviation (and
E_(mathematical_constant)
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
Probability distribution
probability distribution whose cumulative distribution function is the Cantor function. This distribution has neither a probability density function nor
Cantor_distribution
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
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
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
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
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
Theory of behavioral economics
are framed. The function π is a probability weighting function and captures the idea that people tend to overreact to small probability events, but underreact
Prospect_theory
Information-theoretic measure
the underlying probability distribution, for large N we expect p(X=x)≈#x/N, by the law of large numbers. Writing our likelihood function as the product
Cross-entropy
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
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
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
travel, tourism, insurance
PROBABILITY FUNCTION
PROBABILITY FUNCTION
Male
Egyptian
, an Egyptian functionary.
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : in all probability from the Swale river in Yorkshire. (Reaney and Wilson list a 17th-century example, Swayles, with this origin.) Alternatively, it may be a metronymic from the Old Norse female personal name Svala.
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Biblical
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Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Male
Egyptian
, a great functionary.
Male
Egyptian
, a high Egyptian functionary.
Male
Celtic
, great justiciary, or functionary.
Male
Egyptian
, the son of the functionary Heknofre.
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Male
Egyptian
, Functionary of the Interior.
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Male
Egyptian
, an Egyptian functionary.
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Surname or Lastname
English
English : in all probability an English variant of Scottish Lachlan (see McLachlan), altered through folk etymology. However, Black cites one John sine terra (c. 1180–1214), suggesting that the surname could have arisen quite literally as a nickname for a man with no land.
PROBABILITY FUNCTION
PROBABILITY FUNCTION
PROBABILITY FUNCTION
PROBABILITY FUNCTION
PROBABILITY FUNCTION
PROBABILITY FUNCTION
PROBABILITY FUNCTION
travel, tourism, insurance