Encyclopedia - Variance: Encyclopedia - Variance
In probability theory and statistics, the variance of a random variable is a measure of its statistical dispersion, indicating how far fr...   » Read the article

Encyclopedia - Variance: Encyclopedia Ii - Variance - Population Variance And Sample Variance
In general, the population variance of a finite population is given by where is the population mean. This is merely a special case of...   » Read the article

Encyclopedia - Variance: Encyclopedia Ii - Variance - Properties
If the variance is defined, we can conclude that it is never negative because the squares are positive or zero. The unit of variance is t...   » Read the article

Encyclopedia - Allan Variance: Encyclopedia - Allan Variance
The Allan variance, named after David W. Allan, is a measurement of accuracy in clocks. It is also known as the two-sample variance. It i...   » Read the article

Encyclopedia - Jewish Holiday: Encyclopedia - Jewish Holiday
A Jewish holiday or Jewish Festival is a day or series of days observed by Jews as holy or secular commemorations of important events in ...   » Read the article

Encyclopedia - Stratification: Encyclopedia - Stratification
Stratification is the building up of layers of deposits, and can have several variations of meaning: Social stratification, is the divid...   » Read the article

Encyclopedia - Agnostic Atheism: Encyclopedia - Agnostic Atheism
Agnostic atheism is the philosophy that encompasses both atheism and agnosticism. Due to definitional variance, an agnostic atheist does ...   » Read the article

Encyclopedia - Heterodoxy: Encyclopedia - Heterodoxy
Heterodoxy includes "any opinions or doctrines at variance with an official or orthodox position". [1] As an adjective, heterodox is...   » Read the article

Encyclopedia - Variance: Encyclopedia Ii - Variance - Generalizations
If X is a vector-valued random variable, with values in Rn, and thought of as a column vector, then the natural generalization of varianc...   » Read the article

Encyclopedia - Zoning: Encyclopedia - Zoning
In general, zoning is the division of an area into sub-areas, called zones. This article primarily concerns zoning in its urban planning ...   » Read the article

Encyclopedia - Variance: Encyclopedia Ii - Variance - Definition
If μ = E(X) is the expected value (mean) of the random variable X, then the variance is That is, it is the expected value of the squa...   » Read the article

Encyclopedia - True Variance: Encyclopedia Ii - True Variance - Variance And Information
Binarization of the vector x into its adjacent implicational matrix, shown below and subtraction of the transpose of this binarized impl...   » Read the article

Encyclopedia - True Variance: Encyclopedia Ii - True Variance - Changing True Variance To Unbiased Variance And Vice Versa
The variance can be easily changed from the true variance to the unbiased variance, as and from the unbiased variance to the true vari...   » Read the article

Encyclopedia - True Variance: Encyclopedia Ii - True Variance - Computation Of The True And Unbiased Variance
Mathematical formulae defining the true and the unbiased variance use the Greek letter Σ which means sum all values of a variable. The v...   » Read the article

Encyclopedia - True Variance: Encyclopedia Ii - True Variance - Matrices Of Differences
Using matrix algebra, the true variance can be measured by computing all possible differences between elements of a population. Consider ...   » Read the article

Encyclopedia - Analysis Of Variance: Encyclopedia Ii - Analysis Of Variance - Overview
There are three conceptual classes of such models: Fixed-effects model assumes that the data come from normal populations which differ i...   » Read the article

Encyclopedia - True Variance: Encyclopedia Ii - True Variance - Conventional Language Of Computation
In statistics, the term true variance is often used to refer to the unobservable variance of a whole population, as distinguished from an...   » Read the article

Encyclopedia - True Variance: Encyclopedia Ii - True Variance - Degrees Of Freedom
The n-1 term in the denominator of the unbiased variance formula is referred to as degrees of freedom, signified as df or by the Greek le...   » Read the article

Encyclopedia - True Variance: Encyclopedia Ii - True Variance - Differences Between Data Elements And Their Mean
The above definition of variance in terms of differences contained by the data does not involve the arithmetic mean. It seems plausible t...   » Read the article

Encyclopedia - True Variance: Encyclopedia Ii - True Variance - True Variance And All Possible Differences Between Values Of A Variable
Using all possible differences between values of a variable as a foundation of statistical theory was contemplated by Kendall (1943, p. 4...   » Read the article

Encyclopedia - True Variance: Encyclopedia Ii - True Variance - Degrees Of Freedom: Monte Carlo Simulation
Simulations using the random number generators are often called the Monte Carlo experiments. A common type of this type of an experiment ...   » Read the article

Encyclopedia - Estimator: Encyclopedia Ii - Estimator - Point Estimators
For a point estimator of parameter θ, The error of is The bias of is defined as the expected value of the is an unbiased estimato...   » Read the article

Encyclopedia - Estimator: Encyclopedia Ii - Estimator - Point Estimators
For a point estimator of parameter θ, The error of is The bias of is defined as is an unbiased estimator of θ iff for all θ, o...   » Read the article

Encyclopedia - Hermite Polynomials: Encyclopedia Ii - Hermite Polynomials - Negative Variance
Since polynomial sequences form a group under the operation of umbral composition, one may denote by the sequence that is inverse to t...   » Read the article

Encyclopedia - Jewish Holiday: Encyclopedia Ii - Jewish Holiday - Variances In Observances
The denominations of Reconstructionist Judaism and Reform Judaism generally regard Jewish laws (halakha) relating to all these holidays a...   » Read the article

Encyclopedia - Jewish Holiday: Encyclopedia Ii - Jewish Holiday - Variances In Observances
The denominations of Reconstructionist Judaism and Reform Judaism generally regard Jewish laws (halakha) relating to all these holidays a...   » Read the article

Encyclopedia - Hermite Polynomials: Encyclopedia Ii - Hermite Polynomials - Generalization
The Hermite polynomials defined above are orthogonal with respect to the standard normal probability distribution which has expected v...   » Read the article

Encyclopedia - Estimation Theory: Encyclopedia Ii - Estimation Theory - Example: Dc Gain In White Gaussian Noise
Consider a received discrete signal, x[n], of N independent samples that consists of a DC gain A with Additive white Gaussian noise w[n] ...   » Read the article

Encyclopedia - Effective Population Size: Encyclopedia Ii - Effective Population Size - Definitions
Effective population size may be defined in two ways, variance effective size and inbreeding effective size. These are closely linked, an...   » Read the article

Encyclopedia - Effective Population Size: Encyclopedia Ii - Effective Population Size - Examples
Effective population size - Variations in population size. Population size varies over time. Suppose there are t non-overlapping genera...   » Read the article

Encyclopedia - Prolactin: Encyclopedia Ii - Prolactin - Production Of Milk
Prolactin has many effects, the most significant of which is to stimulate the mammary glands to produce milk (lactation). Increased serum...   » Read the article

Encyclopedia - Estimator: Encyclopedia Ii - Estimator - Efficiency
The quality of an estimator is generally judged by its mean squared error. However, occasionally one chooses the unbiased estimator with ...   » Read the article

Encyclopedia - Modern Portfolio Theory: Encyclopedia Ii - Modern Portfolio Theory - The Risk Free Asset
The risk free asset is the (hypothetical) asset which pays a risk free rate - it is usually proxied by an investment in short-dated Gover...   » Read the article

Encyclopedia - Hermite Polynomials: Encyclopedia Ii - Hermite Polynomials - Eigenfunctions Of The Fourier Transform
The functions are eigenfunctions of the Fourier transform, with eigenvalues − in. ... See also:Hermite polynomials, Hermite polyno...   » Read the article

Encyclopedia - Matrix Subtraction: Encyclopedia Ii - Matrix Subtraction - Applications
The operation of matrix subtraction facilitates expression of many abstract concepts within the matrix algebra framework. For example, th...   » Read the article

Encyclopedia - Standard Deviation: Encyclopedia Ii - Standard Deviation - Interpretation And Application
The standard deviation is a measure of the degree of dispersion of the data from the mean value. Stated another way, the standard deviati...   » Read the article

Encyclopedia - Estimation Theory: Encyclopedia Ii - Estimation Theory - Fields That Use Estimation Theory
There are numerous fields that require the use of estimation theory. Some of these fields include (but by no means limited to): Medicine...   » Read the article

Encyclopedia - Prolactin: Encyclopedia Ii - Prolactin - Use Of Breastfeeding As Contraceptive
As a contraceptive, demand breastfeeding is said to be more than 90% effective in the first month of post-partum even if no other forms o...   » Read the article

Encyclopedia - Hermite Polynomials: Encyclopedia Ii - Hermite Polynomials - Orthogonality
The nth function in this list is an nth-degree polynomial for n = 0, 1, 2, 3, .... These polynomials are orthogonal with respect to the m...   » Read the article

Encyclopedia - Modern Portfolio Theory: Encyclopedia Ii - Modern Portfolio Theory - Asset Pricing
A rational investor would not invest in an asset which does not improve the risk-return characteristics of his existing portfolio. Since ...   » Read the article

Encyclopedia - Hermite Polynomials: Encyclopedia Ii - Hermite Polynomials - Various Properties
The nth Hermite polynomial satisfies Hermite's differential equation: The sequence of Hermite polynomials also satisfies the recursion...   » Read the article

Encyclopedia - List Of Publications In Statistics: Encyclopedia Ii - List Of Publications In Statistics - Bayesian Statistics
An Essay Toward Solving a Problem in the Doctrine of Chances Author: Thomas Bayes Publication data: 1764 Online version: [1] (PostScript...   » Read the article

Encyclopedia - Covariance Matrix: Encyclopedia Ii - Covariance Matrix - Conflicting Nomenclatures And Notations
Nomenclatures differ. Some statisticians, following the probabilist William Feller, call this matrix the variance of the random vector X,...   » Read the article

Encyclopedia - Jewish Holiday: Encyclopedia Ii - Jewish Holiday - Shemini Atzeret And Simchat Torah - Rejoicing With The Law
Simchat Torah (שמחת תורה) means "rejoicing with the Torah" and takes place on the holiday of Shemini Atzeret. This holiday immedi...   » Read the article

Encyclopedia - Jewish Holiday: Encyclopedia Ii - Jewish Holiday - Hanukkah - Festival Of Lights
The story of Hanukkah is preserved in the books of the First and Second Maccabees. These books are not part of the Tanakh (Hebrew Bible),...   » Read the article

Encyclopedia - Standard Deviation: Encyclopedia Ii - Standard Deviation - Rapid Calculation Methods
A slightly faster (significantly for running standard deviation) way to compute the population standard deviation is given by the formula...   » Read the article

Encyclopedia - Jewish Holiday: Encyclopedia Ii - Jewish Holiday - Pesach - Passover
Pesach (Passover) commemorates the liberation of the Israelite slaves from Egypt. The first seder is after the 14th of Nisan since in Jud...   » Read the article

Encyclopedia - Standard Deviation: Encyclopedia Ii - Standard Deviation - An Axiomatic Approach
Let be a vector of real numbers. We write meaning that is estimated by the mean value , and the standard deviation is is a real...   » Read the article

Encyclopedia - Student's T-distribution: Encyclopedia Ii - Student's T-distribution - Occurrence And Specification Of Student's T-distribution
Suppose X1, ..., Xn are independent random variables that are normally distributed with expected value μ and variance σ2. Let be the...   » Read the article

Encyclopedia - Jewish Holiday: Encyclopedia Ii - Jewish Holiday - New Israeli/jewish National Holidays
Since the creation of the State of Israel in 1948, the Chief Rabbinate of Israel has established four new Jewish holidays. Yom Ha'Shoah ...   » Read the article

Encyclopedia - Standard Deviation: Encyclopedia Ii - Standard Deviation - Definition And Shortcut Calculation Of Standard Deviation
Suppose we are given a population x1, ..., xN of values (which are real numbers). The arithmetic mean of this population is defined as ....   » Read the article

Encyclopedia - Jewish Holiday: Encyclopedia Ii - Jewish Holiday - Shavuot - Pentecost
Shavuot, The Feast of Weeks, is sometimes known by the Greek name "Pentecost." One of the three pilgrimage festivals (Shalosh regalim) or...   » Read the article

Encyclopedia - Standard Deviation: Encyclopedia Ii - Standard Deviation - Examples
We will show how to calculate the standard deviation of a population. Our example will use the ages of four young children: { 5, 6, ...   » Read the article

Encyclopedia - Jewish Holiday: Encyclopedia Ii - Jewish Holiday - The Three Weeks And The Nine Days
The days between the 17th of Tammuz and the 9th of Av are days of mourning, on account of the collapse of Jerusalem during the Roman occu...   » Read the article

Encyclopedia - Standard Deviation: Encyclopedia Ii - Standard Deviation - Relationship Between Standard Deviation And Mean
The mean and the standard deviation of a set of data are usually reported together. In a certain sense, the standard deviation is a "natu...   » Read the article

Encyclopedia - Jewish Holiday: Encyclopedia Ii - Jewish Holiday - Yom Kippur - Day Of Atonement
Yom Kippur is considered by Jews to be the holiest and most solemn day of the year. Its central theme is atonement and reconciliation. Ea...   » Read the article

Encyclopedia - Jewish Holiday: Encyclopedia Ii - Jewish Holiday - Shabbat - The Sabbath יום השבת
Jewish law accords the Sabbath the status of a holiday. Jews celebrate a Shabbat, a day of rest, on the seventh day of each week. Jewish ...   » Read the article

Encyclopedia - Degrees Of Freedom Statistics: Encyclopedia Ii - Degrees Of Freedom Statistics - Residuals
In fitting statistical models to data, the vectors of residuals are often constrained to lie in a space of smaller dimension than the num...   » Read the article

Encyclopedia - Degrees Of Freedom Statistics: Encyclopedia Ii - Degrees Of Freedom Statistics - Parameters In Probability Distributions
The probability distributions of residuals are often parametrized by these numbers of degrees of freedom. Thus one speaks of a chi-square...   » Read the article

Encyclopedia - Prolactin: Encyclopedia Ii - Prolactin - Diagnostic Use
Prolactin levels may be checked as part of a sex hormone workup, as elevated prolactin levels suppress FSH and GnRH and hence lead to hyp...   » Read the article

Encyclopedia - Efficiency Statistics: Encyclopedia Ii - Efficiency Statistics - Examples
Consider a sample of size N drawn from a normal distribution of mean μ and unit variance (i.e., ). The sample mean, , of the sample , de...   » Read the article

Encyclopedia - Zoning: Encyclopedia Ii - Zoning - Origins And History Of Zoning
New York City adopted the first zoning regulations to apply city-wide in 1916 as a reaction to construction of The Equitable Building (wh...   » Read the article

Encyclopedia - Zoning: Encyclopedia Ii - Zoning - Constitutional Challenges
There have been notable legal challenges to zoning regulations. In 1926 the Supreme Court upheld zoning as a right of U.S. states (typica...   » Read the article

Encyclopedia - Zoning: Encyclopedia Ii - Zoning - Some Limitations And Criticisms Of Zoning
Land use zoning is widely considered an important tool in the treatment of certain social ills, a part of the larger concept of social en...   » Read the article

Encyclopedia - Efficiency Statistics: Encyclopedia Ii - Efficiency Statistics - Efficient Estimator
If an estimator of a parameter, , attains e(T) = 1 for all values of the parameter, then the estimator is called efficient. Equivalently,...   » Read the article

Encyclopedia - Levy Skew Alpha-stable Distribution: Encyclopedia Ii - Levy Skew Alpha-stable Distribution - Special Cases
There is no general analytic solution for the form of p(x). There are, however three special cases which can be analytically expressed as...   » Read the article

Encyclopedia - Probability Theory: Encyclopedia Ii - Probability Theory - A Somewhat More Abstract View Of Probability
Mathematicians usually take probability theory to be the study of probability spaces and random variables — an approach introduced by K...   » Read the article

Encyclopedia - Homogeneity Psychometrics: Encyclopedia Ii - Homogeneity Psychometrics - Logical Relationships Among Variables
The above theoretical data structures define the prototypical logical relationships among variables, extending the data analysis by incor...   » Read the article

Encyclopedia - Homogeneity Psychometrics: Encyclopedia Ii - Homogeneity Psychometrics - Test Homogeneity
The original concept of homogeneity was introduced in 1948 by Loevinger who defined the coefficient of homogeneity for two items as equal...   » Read the article

Encyclopedia - Homogeneity Psychometrics: Encyclopedia Ii - Homogeneity Psychometrics - Tautologous Lattices: Reliability And Homogeneity Coefficients Equal To Zero
Normal (tautologous) structure for binary variables p, q, and r, shown in Fig. 1 for five variables, can be defined as Y = (p 1 q) & ...   » Read the article

Encyclopedia - Homogeneity Psychometrics: Encyclopedia Ii - Homogeneity Psychometrics - Equivalential Lattices: Reliability Equals One Homogeneity Is Less Than One.
Parallel (equivalential) structure for binary variables p, q, and r can be defined as y = (p = q) & (q = r). When rectified (accordin...   » Read the article

Encyclopedia - Homogeneity Psychometrics: Encyclopedia Ii - Homogeneity Psychometrics - Implicational Lattices: Homogeneity Equals One Reliability Is Less Than One
Hierarchical (implicational) structure for binary variables p, q, and r can be defined as y = (p -> q) & (q -> r). When rectifi...   » Read the article

Encyclopedia - Normalizing Constant: Encyclopedia Ii - Normalizing Constant - Definition And Examples
In probability theory, a normalizing constant is a constant by which an everywhere nonnegative function must be multiplied in order that ...   » Read the article

Encyclopedia - Matrix Subtraction: Encyclopedia Ii - Matrix Subtraction - Subtraction Of Matrix Elements
To subtract elements of matrices A and B, C = A ( − ) B elements of matrix B are subtracted from their corresponding elements in matr...   » Read the article

Encyclopedia - Matrix Subtraction: Encyclopedia Ii - Matrix Subtraction - Subtraction Of Matrices
Textbooks on matrix algebra (cf., Horst, 1963; Shores, 2003), routinely describing major and minor vector products, do not include analog...   » Read the article

Encyclopedia - Matrix Subtraction: Encyclopedia Ii - Matrix Subtraction - Skew-symmetric Matrices
Subtracting a transpose of a matrix from itself yields a skew-symmetric matrix. For instance, A major difference of a vector also resu...   » Read the article

Encyclopedia - Exponential Distribution: Encyclopedia Ii - Exponential Distribution - Properties
Exponential distribution - Mean and standard deviation. The mean or expected value of an exponentially distributed random variable X wi...   » Read the article

Encyclopedia - Matrix Subtraction: Encyclopedia Ii - Matrix Subtraction - Skew-asymmetric Matrices
If the elements of subtracted matrices are ordered, skew-symmetric matrices, can be transformed into skew-asymmetric matrices by triangul...   » Read the article

Encyclopedia - Kurtosis: Encyclopedia Ii - Kurtosis - Sample Kurtosis
For a sample of n values the sample kurtosis is where m4 is the fourth sample moment about the mean, m2 is the second sample moment ab...   » Read the article

Encyclopedia - Matrix Subtraction: Encyclopedia Ii - Matrix Subtraction - Stochastic Skew-asymmetric Matrices
Generalizing the matrix algebra operations on subtracted data matrices as to envelop the stochastic skew-asymmetric matrices, yields dend...   » Read the article

Encyclopedia - Probability Theory: Encyclopedia Ii - Probability Theory - Philosophy Of Application Of Probability
Some statisticians will assign probabilities only to events that are random, i.e., random variables, that are outcomes of actual or theor...   » Read the article

Encyclopedia - Prior Probability: Encyclopedia Ii - Prior Probability - Informative Priors
An informative prior expresses specific, definite information about a variable. An example is a prior distribution for the temperature at...   » Read the article

Encyclopedia - Studentized Residual: Encyclopedia Ii - Studentized Residual - How To Studentize
For this simple model, the design matrix is and the "hat matrix" H is the matrix of the orthogonal projection onto the column space of...   » Read the article

Encyclopedia - Standard Score: Encyclopedia Ii - Standard Score - Standardizing In Mathematical Statistics
In mathematical statistics, a random variable X is standardized using the theoretical (population) mean and standard deviation: where ...   » Read the article

Encyclopedia - Parameter: Encyclopedia Ii - Parameter - Probability Theory
In probability theory, one may describe the distribution of a random variable as belonging to a family of probability distributions, dist...   » Read the article

Encyclopedia - Gini Coefficient: Encyclopedia Ii - Gini Coefficient - Calculation
The small sample variance properties of G are not known, and large sample approximations to the variance of G are poor. In order for G to...   » Read the article

Encyclopedia - Zoning: Encyclopedia Ii - Zoning - Land Use
Zoning is a system of land use regulation which designates the permitted uses of land based on mapped zones, which separate one part of t...   » Read the article

Encyclopedia - Zoning: Encyclopedia Ii - Zoning - Origins And History Of Zoning
New York City adopted the first zoning regulations to apply city-wide in 1916 as a reaction to construction of The Equitable Building (wh...   » Read the article

Encyclopedia - Zoning: Encyclopedia Ii - Zoning - Constitutional Challenges
There have been notable legal challenges to zoning regulations. In 1926 the Supreme Court upheld zoning as a right of U.S. states (typica...   » Read the article

Encyclopedia - Zoning: Encyclopedia Ii - Zoning - Some Limitations And Criticisms Of Zoning
Land use zoning is widely considered an important tool in the treatment of certain social ills, a part of the larger concept of social en...   » Read the article

Encyclopedia - Estimator: Encyclopedia Ii - Estimator - Consistency
A consistent estimator is an estimator that converges in probability to the quantity being estimated as the sample size grows. An estimat...   » Read the article

Encyclopedia - Zoning: Encyclopedia Ii - Zoning - Other Uses Of The Concept Of Zoning
Zoning - Pricing. In many cities, fares for public transport depend on the number of zones in which a rider travels. London has recentl...   » Read the article

Encyclopedia - Student's T-distribution: Encyclopedia Ii - Student's T-distribution - Further Theory
Gosset's result can be stated more generally. (See, for example, Hogg and Craig, Sections 4.4 and 4.8.) Let Z have a normal distribution ...   » Read the article

Encyclopedia - Data Clustering: Encyclopedia Ii - Data Clustering - The Elbow Criterion
The elbow criterion is a common rule of thumb to determine what number of clusters should be chosen, for example for k-means and agglomer...   » Read the article

Encyclopedia - Sharia: Encyclopedia Ii - Sharia - Contemporary Practice Of Sharia Law
There is tremendous variance in the interpretation and implementation of Islamic law in Muslim societies today. Some believe that colonia...   » Read the article

Encyclopedia - Budget: Encyclopedia Ii - Budget - The Future
As the technology of money and banking continues to make spending easier, individuals, families, companies, and governments need to adopt...   » Read the article

Encyclopedia - Cycle Count: Encyclopedia Ii - Cycle Count - Cycle Counting By Frequency
According to the Pareto principle, if 20% of inventory items represent 80% of inventory value, the expensive items should be counted most...   » Read the article

Dictionary - Variance: Oceanography Dictionary - Variance
  Definition and meaning of variance:   variance - the population variance of a random variable is a non-negative number...   » Read the article

Dictionary - Analysis Of Variance: Oceanography Dictionary - Analysis Of Variance
  Definition and meaning of analysis of variance:   analysis of variance - a statistical technique for testing for differ...   » Read the article

Dictionary - Multivariate Analysis Of Variance: Oceanography Dictionary - Multivariate Analysis Of Variance
  Definition and meaning of multivariate analysis of variance:   multivariate analysis of variance - an analysis of vari...   » Read the article