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Ancillary Statistic
In statistics, ancillarity is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset. An ancillary statistic has the same distribution regardless of the value of the parameters and thus provides no information about them. It is opposed to the concept of a complete statistic which contains no ancillary information. It is closely related to the concept of a sufficient statistic which contains all of the information that the dataset provides about the parameters. A ancillary statistic is a specific case of a pivotal quantity that is computed only from the data and not from the parameters. They can be used to construct prediction intervals. They are also used in connection with Basu's theorem to prove independence between statistics. This concept was first introduced by Ronald Fisher in the 1920s, but its formal definition was only provided in 1964 by Debabrata Basu. Examples Suppose ''X''1, ..., ''X''''n'' are independent a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interquartile Range
In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread. It is defined as the difference between the 75th and 25th percentiles of the data. To calculate the IQR, the data set is divided into quartiles, or four rank-ordered even parts via linear interpolation. These quartiles are denoted by ''Q''1 (also called the lower quartile), ''Q''2 (the median), and ''Q''3 (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = ''Q''3 − ''Q''1. The IQR is an example of a trimmed estimator, defined as the 25% trimmed range, which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points. It is also used as a robust measure of scale It can be clearly visualized by the box on a box plot. Use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sufficiency (statistics)
In statistics, sufficiency is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset. A sufficient statistic contains all of the information that the dataset provides about the model parameters. It is closely related to the concepts of an ancillary statistic which contains no information about the model parameters, and of a complete statistic which only contains information about the parameters and no ancillary information. A related concept is that of linear sufficiency, which is weaker than ''sufficiency'' but can be applied in some cases where there is no sufficient statistic, although it is restricted to linear estimators. The Kolmogorov structure function deals with individual finite data; the related notion there is the algorithmic sufficient statistic. The concept is due to Sir Ronald Fisher in 1920. Stephen Stigler noted in 1973 that the concept of sufficiency had fallen out of favor in descriptive statistics because of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Major League Baseball Batting Champions
In baseball, batting average (baseball), batting average (AVG) is a measure of a Batting (baseball), batter's success rate in achieving a Hit (baseball), hit during an at bat. In Major League Baseball (MLB), it is calculated by dividing a player's hits by his at bats (AB). In MLB, a player in each league wins the "batting title" each season for having the highest batting average that year. The American League (AL) winner is known as the "Rod Carew American League Batting Champion", while the National League (baseball), National League (NL) leader is designated the "Tony Gwynn National League Batting Champion". Since 1957, a player must have 3.1 plate appearances (PA) per scheduled game in that league (for a total of 502 over the current 162-game season) to qualify for the batting title. However, if a player's lead in AVG is sufficiently large that enough hitless at bats can be added to reach this requirement and the player still would have the highest batting average, he wins the ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Batting Average (baseball)
In baseball, batting average (BA) is determined by dividing a player's hits by their total at-bats. It is usually rounded to three decimal places and read without the decimal: A player with a batting average of .300 is said to be "batting three hundred". If necessary to break ties, batting averages could be taken beyond the .001 measurement. In this context, .001 is considered a "point", such that a .235 batter is five points higher than a .230 batter. History Henry Chadwick, an English statistician raised on cricket, was an influential figure in the early history of baseball. He is credited with creating the modern box score, in 1859, and the practice of denoting a strikeout with a "K". Chadwick wrote in 1869: "In making up a score at the close of the match the record should be as follows:–Name of player, total number of times the first base was made by clean hits, total bases so made, left on bases after clean hits, and the number of times the first base has been made on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Independence
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically independent, or stochastically independent if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds. Similarly, two random variables are independent if the realization of one does not affect the probability distribution of the other. When dealing with collections of more than two events, two notions of independence need to be distinguished. The events are called pairwise independent if any two events in the collection are independent of each other, while mutual independence (or collective independence) of events means, informally speaking, that each event is independent of any combination of other events in the collection. A similar notion exists for collections of random variables. Mutual independence implies pairwise independence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baseball
Baseball is a bat-and-ball games, bat-and-ball sport played between two team sport, teams of nine players each, taking turns batting (baseball), batting and Fielding (baseball), fielding. The game occurs over the course of several Pitch (baseball), plays, with each play beginning when a player on the fielding team (baseball), fielding team, called the pitcher, throws a Baseball (ball), ball that a player on the batting team (baseball), batting team, called the Batter (baseball), batter, tries to hit with a baseball bat, bat. The objective of the offensive team (batting team) is to hit the ball into the field of play, away from the other team's players, allowing its players to run the Base (baseball), bases, having them advance counter-clockwise around four bases to score what are called "Run (baseball), runs". The objective of the defensive team (referred to as the fielding team) is to prevent batters from becoming Base running, runners, and to prevent runners base running ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fisher Information
In mathematical statistics, the Fisher information is a way of measuring the amount of information that an observable random variable ''X'' carries about an unknown parameter ''θ'' of a distribution that models ''X''. Formally, it is the variance of the score, or the expected value of the observed information. The role of the Fisher information in the asymptotic theory of maximum-likelihood estimation was emphasized and explored by the statistician Sir Ronald Fisher (following some initial results by Francis Ysidro Edgeworth). The Fisher information matrix is used to calculate the covariance matrices associated with maximum-likelihood estimates. It can also be used in the formulation of test statistics, such as the Wald test. In Bayesian statistics, the Fisher information plays a role in the derivation of non-informative prior distributions according to Jeffreys' rule. It also appears as the large-sample covariance of the posterior distribution, provided that the prior i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Likelihood Estimator
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference. If the likelihood function is differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when the random errors are assumed to have normal distributions with the same variance. From the perspective of Bayesian inference ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sufficiency (statistics)
In statistics, sufficiency is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset. A sufficient statistic contains all of the information that the dataset provides about the model parameters. It is closely related to the concepts of an ancillary statistic which contains no information about the model parameters, and of a complete statistic which only contains information about the parameters and no ancillary information. A related concept is that of linear sufficiency, which is weaker than ''sufficiency'' but can be applied in some cases where there is no sufficient statistic, although it is restricted to linear estimators. The Kolmogorov structure function deals with individual finite data; the related notion there is the algorithmic sufficient statistic. The concept is due to Sir Ronald Fisher in 1920. Stephen Stigler noted in 1973 that the concept of sufficiency had fallen out of favor in descriptive statistics because of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale Family
Scale or scales may refer to: Mathematics * Scale (descriptive set theory), an object defined on a set of points * Scale (ratio), the ratio of a linear dimension of a model to the corresponding dimension of the original * Scale factor, a number which scales, or multiplies, some quantity * Long and short scales, how powers of ten are named and grouped in large numbers * Scale parameter, a description of the spread or dispersion of a probability distribution * Feature scaling, a method used to normalize the range of independent variables or features of data * Scale (analytical tool) Measurements * Scale (map), the ratio of the distance on a map to the corresponding actual distance * Scale (geography) * Weighing scale, an instrument used to measure mass * Scale (ratio), the ratio of the linear dimension of the model to the same dimension of the original * Spatial scale, a classification of sizes * Scale ruler, a tool for measuring lengths and transferring measurements at a fixed r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
