* In statistics, spatial autocorrelation between sample locations also helps one estimate mean value uncertainties when sampling a heterogeneous population.

The radio broadcasts themselves were often so patiently informative, despite the baseball jargon, that girls and women could begin to store up in their minds the same sort of random and meaningless statistics that small boys had long learned better than they ever did their lessons in school.

In probability theory and statistics, the cumulative distribution function ( CDF ), or just distribution function, describes the probability that a real-valued random variable X with a given probability distribution will be found at a value less than or equal to x.

In statistics, a bivariate random vector ( X, Y ) is jointly elliptically distributed if its iso-density contours — loci of equal values of the density function — are ellipses.

In probability theory and statistics, kurtosis ( from the Greek word κυρτός, kyrtos or kurtos, meaning bulging ) is any measure of the " peakedness " of the probability distribution of a real-valued random variable.

* Neutral vector ( statistics ), a multivariate random variable is neutral if it exhibits a particular type of statistical independence seen when considering the Dirichlet distribution

The generation of random numbers has many uses ( mostly in statistics, for random sampling, and simulation ).

The most important distinction between the frequentist and Bayesian paradigms, is that frequentist makes strong distinctions between probability, statistics, and decision-making, whereas Bayesians unify decision-making, statistics and probability under a single philosophically and mathematically consistent framework, unlike the frequentist paradigm which has been proven to be inconsistent, especially for real-world situations where experiments ( or " random events ") can not be repeated more than once.

In probability and statistics, a probability distribution assigns a probability to each of the possible outcomes of a random experiment.

Early systems emphasized predictable outcomes of an industrial product production line, using simple statistics and random sampling.

In probability and statistics, a random variable or stochastic variable is a variable whose value is subject to variations due to chance ( i. e. randomness, in a mathematical sense ).

The basic concept of " random variable " in statistics is real-valued.

Statistical regularity is a notion in statistics and probability theory that random events exhibit regularity when repeated enough times or that enough sufficiently similar random events exhibit regularity.

In statistics, statistical inference is the process of drawing conclusions from data subject to random variation, for example, observational errors or sampling variation.

More substantially, the terms statistical inference, statistical induction and inferential statistics are used to describe systems of procedures that can be used to draw conclusions from datasets arising from systems affected by random variation, such as observational errors, random sampling, or random experimentation.

In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable.

Questions about the statistics describing how often an ideal monkey is expected to type certain strings translate into practical tests for random number generators ; these range from the simple to the " quite sophisticated ".

In probability theory and its applications, such as statistics and cryptography, a random function is a function chosen randomly from a family of possible functions.

In probability and statistics, one important type of random function is studied under the name of stochastic processes, for which there are a variety of models describing systems where an observation is a random function of time or space.

In addition, patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations, and are then used for drawing inferences about the process or population being studied ; this is called inferential statistics.

The notion is used in games of chance, demographic statistics, quality control of a manufacturing process, and in many other parts of our lives.

* Non-parametric: The assumptions made about the process generating the data are much less than in parametric statistics and may be minimal.

In statistics, survey sampling describes the process of selecting a sample of elements from a target population in order to conduct a survey.

Data mining ( the analysis step of the " Knowledge Discovery in Databases " process, or KDD ), is a field at the intersection of computer science and statistics, is the process that attempts to discover patterns in large data sets.

* In probability theory and statistics, a stochastic kernel is the transition function of a stochastic process.

Forgery is the process of making, adapting, or imitating objects, statistics, or documents with the intent to deceive.

In probability theory and statistics, a Markov process or Markoff process, named for the Russian mathematician Andrey Markov, is a stochastic process satisfying a certain property, called the Markov property.

In probability and statistics, a Bernoulli process is a finite or infinite sequence of binary random variables, so it is a discrete-time stochastic process that takes only two values, canonically 0 and 1.

The P measures are the process measures – these statistics that record the number of times things occur.

The R measures are the results measures – these statistics record the ' outcomes ' of the process.

They provide the tools, algebra, statistics and computer algorithms, to process information too voluminous or complex for purely cognitive, informal inference.

At a time when business publications were little more than numbers and statistics printed in black and white, Fortune was an oversized 11 "× 14 ", using creamy heavy paper, and art on a cover printed by a special process.

Filter design is the process of designing a filter ( in the sense in which the term is used in signal processing, statistics, and applied mathematics ), often a linear shift-invariant filter, that satisfies a set of requirements, some of which are contradictory.

By a process similar to that outlined in the Maxwell-Boltzmann statistics article, it can be seen that:

This conversion process is called standardizing or normalizing ; however, " normalizing " can refer to many types of ratios ; see normalization ( statistics ) for more.

The results of a stochastic process ( statistics ) can only be known after computing it.

In probability theory and statistics, a Gaussian process is a stochastic process whose realizations consist of random values associated with every point in a range of times ( or of space ) such that each such random variable has a normal distribution.

The result of the efforts of Bose and Einstein is the concept of a Bose gas, governed by Bose – Einstein statistics, which describes the statistical distribution of identical particles with integer spin, now known as bosons.

Fermi – Dirac statistics is a part of the science of physics that describes the energies of single particles in a system comprising many identical particles that obey the Pauli exclusion principle.

In statistical mechanics, Maxwell – Boltzmann statistics describes the statistical distribution of material particles over various energy states in thermal equilibrium, when the temperature is high enough and density is low enough to render quantum effects negligible.

In statistics and machine learning, overfitting occurs when a statistical model describes random error or noise instead of the underlying relationship.

Here is the operator which symmetrizes or antisymmetrizes a tensor, depending on whether the Hilbert space describes particles obeying bosonic or fermionic statistics.

Please note that anyonic statistics must not be confused with parastatistics which describes statistics of particles whose wavefunctions are higher dimensional representations of the permutation group.

In probability theory and statistics, the geometric standard deviation describes how spread out are a set of numbers whose preferred average is the geometric mean.

In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the simultaneous influence of two variables on a third is not additive.

However, the mean and standard deviation are descriptive statistics, whereas the mean and standard error describes bounds on a random sampling process.

In time series analysis, as applied in statistics, the cross correlation between two time series describes the normalized cross covariance function.

* descriptive statistics-the part of statistics that describes data, i. e. summarises the data and their typical properties.

* See Consistency ( statistics ), which describes:

The first section of the journal records the statistics of Drake, shows the status of his current equipped weapons and describes the characteristics of his partners.

A full description of the monster, including game statistics, appears at the back of the module, which describes the creature as the " Handmaiden of Lolth ".

ISO 13602-1 describes a means of to establish relations between inputs and outputs ( net energy ) and thus to facilitate certification, marking, and labelling, comparable characterizations, coefficient of performance, energy resource planning, environmental impact assessments, meaningful energy statistics and forecasting of the direct natural energy resource or energyware inputs, technical energy system investments and the performed and expected future energy service outputs.

It describes the same data distribution as an inverse gamma distribution, but using a different parametrization, one that may be more convenient for Bayesian statistics.

In statistics and signal processing, a minimum mean square error ( MMSE ) estimator describes the approach which minimizes the mean square error ( MSE ), which is a common measure of estimator quality.