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Terms in statistics and probability theory : Statistics is a type of data analysis whose practice includes the planning, summarizing, and interpreting of observations of a system possibly followed by predicting or forecasting of future events based on a mathematical model of the system being observed. ...
Probability theory is the mathematical study of probability. ...
Concerned fields
Probability theory is the mathematical study of probability. ...
In the algebraic axiomatization of probability theory, one of whose main proponents was Irving Segal, the primary concept is not that of probability of an event, but rather that of a random variable. ...
Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations. ...
Statistics is a type of data analysis whose practice includes the planning, summarizing, and interpreting of observations of a system possibly followed by predicting or forecasting of future events based on a mathematical model of the system being observed. ...
In mathematics, a measure is a function that assigns a number, e. ...
Estimation theory is a branch of statistics and signal processing that deals with estimating the values of parameters based on measured/empirical data. ...
The word probability has been used in a variety of ways since it was first coined in relation to games of chance. ...
Bayesianism is the philosophical tenet that the mathematical theory of probability applies to the degree of plausibility of a statement. ...
Statistical regularity has motivated the development of the relative frequency concept of probability. ...
Many statisticians adopt an eclectic view of the debate between proponents of the frequency interpretation of probability and proponents of personal probability. ...
Glossary - Atomic event : another name for elementary event.
- Bias can refer either to a sample not being representative of the population, or to the difference between the expected value of an estimator and the true value.
- Conditional distribution : Given two jointly distributed random variables X and Y, the conditional probability distribution of Y given X (written "Y | X") is the probability distribution of Y when X is known to be a particular value.
- Conditional probability is the probability of some event A, assuming event B. Conditional probability is written P(A|B), and is read "the probability of A, given B".
- Completeness
- Correlation, also called correlation coefficient, is a numeric measure of the strength of linear relationship between two random variables (one can use it to quantify, for example, how shoe size and height are correlated in the population). An example is the Pearson product-moment correlation coefficient, which is found by dividing the covariance of the two variables by the product of their standard deviations. Independant variables have a correlation of 0.
- The Covariance between two random variables X and Y, with expected values E(X) = μ and E(Y) = ν is defined as the expected value of random variable (X − μ)(Y − ν), and is written . It is used for measuring correlation.
- A data set is a sample' and the associated data points.
- A data point is a typed measurement - it can be a boolean value, a real number, a vector (in which case it's also called a data vector), etc.
- A Distribution function is the function that gives the probability distribution of a random variable. It cannot be negative, and it's integral on the probability space is equal to 1.
- Efficiency
- An Elementary event (or atomic event) is an event with only one element. For example, when pulling a card out of a deck, "getting the jack of spades" is an elementary event, while "getting a king or an ace" is not.
- Estimator is a function of the known data that is used to estimate an unknown parameter; an estimate is the result from the actual application of the function to a particular set of data. The mean can be used as an estimator.
- The Expected value (or expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ("value"). Thus, it represents the average amount one "expects" to win per bet if bets with identical odds are repeated many times. For example, the expected value of a six-sided die roll is 3.5. The concept is similar to the mean. The expected value of random variable X is typically written E(X) or μ (mu).
- Experiment
- An event is a subset of the sample space, to which a probability can be assigned. For example, on rolling a die, "getting a five or a six" is an event (with a probability of one third if the die is fair).
- Generating function
- Independance or Statistical independence : Two events are independent if the outcome of one does not affect that of the other (for example, getting a 1 on one die roll does not affect the probability of getting a 1 on a second roll). Similarly, when we assert that two random variables are independent, we intuitively mean that knowing something about the value of one of them does not yield any information about the value of the other.
- Joint distribution : Given two random variables X and Y, the joint distribution of X and Y is the probability distribution of X and Y together.
- Joint probability is the probability of two events occuring together. The joint probability of A and B is written or
- Kurtosis is a measure of the "peakedness" of the probability distribution of a real-valued random variable. Higher kurtosis means more of the variance is due to infrequent extreme deviations, as opposed to frequent modestly-sized deviations.
- A likelihood function (or just likelihood) is a conditional probability function considered a function of its second argument with its first argument held fixed. For example, imagine pulling a numbered ball with the number k from a bag of n balls, numbered 1 to n. Then you could describe a likelihood function for the random variable N as the probability of getting k given that there are n balls : the likelihood will be 1/n for n greater or equal to k, and 0 for n smaller than k. Unlike a probability distribution function, this likelihood function will not sum up to 1 on the sample space.
- Marginal distribution : given two jointly distributed random variables X and Y, the marginal distribution of X is simply the probability distribution of X ignoring information about Y.
- Marginal probability is the probability of an event, ignoring any information about other events. The marginal probability of A is written P(A). Contrast with conditional probability.
- The Mean of a random variable is it's expected value. The mean (or sample mean of a data set is just the average value.
- Moment about the mean
- Mutual independence : A collection of events is mutually independent if for any subset of the collection, the joint probability of all events occuring is equal to the product of the joint probabilities of the individual events. Think of the result of a series of coin-flips. This is a stronger condition than pairwise independance.
- Pairwise independence : a pairwise independent collection of random variables is a set of random variables any two of which are independent.
- parameter : Can be a population parameter, a distribution parameter, an unobserved parameter (all the same ?). Often written θ.
- Prior probability
- A population or statistical population is a set of entities about which statistical inferences are to be drawn, often based on random sampling. One can also talk about a population of measurements or values.
- Population parameter : See statistical paramter
- Posterior probability
- Probability density is used to describe probability in a continuous probability distribution. For example, you can't say that the probability of a man being six feet tall is 20%, but you can say he has 20% of chances of being between five and six feet tall. Probability density is given by a probability density function. Contrast with probability mass.
- A probability density function gives the probability distribution for a continuous random variable.
- A probability distribution is a function that gives the probability of all elements in a given space. (-> see that page for a list of different distributions)
- A Probability measure gives the probability of events in a probability space.
- A probability space is a sample space over which a probability measure has been defined.
- Random function
- A random variable can be, for example, the possible outcomes of a dice roll (but it is not assigned a value). The distribution function of a random variable gives the probability of different results. We can also derive the mean and variance of a random variable.
- A Random vector (or multivariate random variable) is a vector whose components are random variables on the same probability space.
- A sample is that part of a population which is actually observed.
- The sample space is the set of possible outcomes of an experiment. For example, the sample space for rolling a six-sided die will be {1, 2, 3, 4, 5, 6}.
- Sampling is a process of selecting observations to obtain knowledge about a population. There are many methods to choose on which sample to do the observations.
- A sampling distribution is the probability distribution, under repeated sampling of the population, of a given statistic.
- Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable. Roughly speaking, a distribution has positive skew (right-skewed) if the higher tail is longer and negative skew (left-skewed) if the lower tail is longer (confusing the two is a common error).
- The standard deviation is the most commonly used measure of statistical dispersion. It is the square root of the variance, and is generally written σ (sigma).
- Standardized moment
- A statistic is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
- Statistical inference is inference about a population from a random sample drawn from it or, more generally, about a random process from its observed behavior during a finite period of time.
- Statistical dispersion (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
- A Statistical parameter is a parameter that indexes a family of probability distributions.
- Sufficiency
- The variance of a random variable is a measure of its statistical dispersion, indicating how far from the expected value its values typically are. The variance of random variable X is typically designated as , , or simply σ2.
In statistics, a biased estimator is one that for some reason on average over- or underestimates what is being estimated. ...
Given two jointly distributed random variables X and Y, the conditional probability distribution of Y given X (written Y | X) is the probability distribution of Y when X is known to be a particular value. ...
This article defines some terms which characterize probability distributions of two or more variables. ...
Suppose a random variable X (which may be a sequence (X1, ..., Xn) of scalar-valued random variables), has a probability distribution belonging to a known family of probability distributions, parametrized by θ, which may be either vector- or scalar-valued. ...
In probability theory and statistics, correlation, also called correlation coefficient, is a numeric measure of the strength of linear relationship between two random variables. ...
In mathematics, and in particular statistics, the Pearson product-moment correlation coefficient (r) is a measure of how well a linear equation describes the relation between two variables X and Y measured on the same object or organism. ...
In probability theory and statistics, the covariance between two real_valued random variables X and Y, with expected values and is defined as: where E is the expected value. ...
In statistics, a data set is a set of data consisting of: a list of research subjects and the data vector associated with each. ...
In statistics, a data point is a single typed measurement. ...
Boolean Dealing only with the two logical values: true (1) and false (0). ...
In calculus, the integral of a function is a generalization of area, mass, volume, sum, and total. ...
In statistics, efficiency is one measure of desirability of an estimator. ...
In probability theory, an elementary event or atomic event is a subset of a sample space that contains only one element. ...
In statistics, an estimator is a function of the known data that is used to estimate an unknown parameter; an estimate is the result from the actual application of the function to a particular set of data. ...
In probability (and especially gambling), the expected value (or (mathematical) expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects to win per bet if bets with identical odds...
Mu or MU may refer to: mu (lowercase μ, uppercase Μ), a letter in the Greek alphabet Mu, a lost continent in the Pacific Ocean mu (無), a Japanese word important in Zen koan practice mu (亩), Chinese unit of surface area, defined in modern times as one fifteenth of a hectare the IATA...
From Latin ex- + -periri (akin to periculum attempt). ...
In probability theory, an event is a set of outcomes (a subset of the sample space) to which a probability is assigned. ...
In mathematics a generating function is a formal power series whose coefficients encode information about a sequence an that is indexed by the natural numbers. ...
In probability theory, to say that two events are independent intuitively means that knowing whether or not one of them occurs makes it neither more probable nor less probable that the other occurs. ...
Given two random variables X and Y, the joint probability distribution of X and Y is the probability distribution of X and Y together. ...
This article defines some terms which characterize probability distributions of two or more variables. ...
In probability theory and statistics, kurtosis is a measure of the peakedness of the probability distribution of a real-valued random variable. ...
In statistics, a likelihood function is a conditional probability function considered a function of its second argument with its first argument held fixed, thus: and also any other function proportional to such a function. ...
Given two jointly distributed random variables X and Y, the marginal distribution of X is simply the probability distribution of X ignoring information about Y, typically calculated by summing or integrating the joint probability distribution over Y. For discrete random variables, the marginal probability mass function can be written as...
This article defines some terms which characterize probability distributions of two or more variables. ...
In statistics, mean has two related meanings: the average in ordinary English, which is more correctly called the arithmetic mean, to distinguish it from geometric mean or harmonic mean. ...
In probability theory and statistics, the kth moment about the mean (or kth central moment) of a real-valued random variable X is the quantity E[(X − E[X])k], where E is the expectation operator. ...
In probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent. ...
A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ...
In statistics, a statistical population is a set of entities concerning which statistical inferences are to be drawn, often based on a random sample taken from the population. ...
In Bayesian probability theory, the posterior probability is the conditional probability of some event or proposition, taking empirical data into account. ...
In mathematics, a probability density function (pdf) serves to represent a probability distribution in terms of integrals. ...
In mathematics, a probability distribution assigns to every interval of the real numbers a probability, so that the probability axioms are satisfied. ...
In mathematics, a probability space or probability measure is a set S, together with a σ-algebra X on S and a measure P on that σ-algebra such that P(S) = 1. ...
In the mathematics of probability, a stochastic process can be thought of as a random function. ...
A random variable can be thought of as the numeric result of operating a non-deterministic mechanism or performing a non-deterministic experiment to generate a random result. ...
In mathematics, a random variable is discrete if its probability distribution is discrete; a discrete probability distribution is one that is fully characterized by a probability mass function. ...
By one convention, a random variable X is called continuous if its cumulative distribution function is continuous. ...
A multivariate random variable or random vector is a vector X=(X1,...,Xn) whose components are scalar-valued random variables on the same probability space (Ω, P). ...
A sample is that part of a population which is actually observed. ...
In probability theory, the sample space, often denoted S, Ω or U (for universe), of an experiment or random trial is the set of all possible outcomes. ...
Sampling is that part of statistical practice concerned with the selection of individual observations intended to yield some knowledge about a population of concern, especially for the purposes of statistical inference. ...
In statistics, a sampling distribution is the probability distribution, under repeated sampling of the population, of a given statistic (a numerical quantity calculated from the data values in a sample). ...
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable. ...
In probability and statistics, the standard deviation is the most commonly used measure of statistical dispersion. ...
In mathematics, the principal square root of a non-negative real number is denoted and represents the non-negative real number whose square (the result of multiplying the number by itself) is . ...
Sigma may refer to many things: Sigma (upper case Σ, lower case σ, alternative ς) is a letter in the Greek alphabet. ...
In probability theory and statistics, the kth standardized moment of a probability distribution is μk/σk, where μk is the kth moment about the mean and σ is the standard deviation. ...
A statistic (singular) is the result of applying a statistical algorithm to a set of data. ...
The topics below are usually included in the area of interpreting statistical data. ...
In descriptive statistics, statistical dispersion (also called statistical variability) is quantifiable variation of measurements of differing members of a population within the scale on which they are measured. ...
A statistical parameter is a parameter that indexes a family of probability distributions. ...
In statistics, one often considers a family of probability distributions for a random variable X (and X is often a vector whose components are scalar-valued random variables, frequently independent) parameterized by a scalar- or vector-valued parameter, which let us call θ. ...
In probability theory and statistics, the variance of a random variable is a measure of its statistical dispersion, indicating how far from the expected value its values typically are. ...
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