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Binomial Proportion Confidence Interval
In statistics, a binomial proportion confidence interval is a confidence interval for the probability of success calculated from the outcome of a series of success–failure experiments (Bernoulli trials). In other words, a binomial proportion confidence interval is an interval estimate of a success probability \ p\ when only the number of experiments \ n\ and the number of successes \ n_\mathsf\ are known. There are several formulas for a binomial confidence interval, but all of them rely on the assumption of a binomial distribution. In general, a binomial distribution applies when an experiment is repeated a fixed number of times, each trial of the experiment has two possible outcomes (success and failure), the probability of success is the same for each trial, and the trials are statistically independent. Because the binomial distribution is a discrete probability distribution (i.e., not continuous) and difficult to calculate for large numbers of trials, a variety of approxima ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Population Proportion
In statistics a population proportion, generally denoted by P or the Greek letter \pi, is a parameter that describes a percentage value associated with a population. A census can be conducted to determine the actual value of a population parameter, but often a census is not practical due to its costs and time consumption. For example, the 2010 United States Census showed that 83.7% of the American population was identified as not being Hispanic or Latino; the value of .837 is a population proportion. In general, the population proportion and other population parameters are unknown. A population proportion is usually estimated through an unbiased sample statistic obtained from an observational study or experiment, resulting in a sample proportion, generally denoted by \hat and in some textbooks by p. For example, the National Technological Literacy Conference conducted a national survey of 2,000 adults to determine the percentage of adults who are economically illiterate; the stud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Distribution
In probability theory and statistics, the binomial distribution with parameters and is the discrete probability distribution of the number of successes in a sequence of statistical independence, independent experiment (probability theory), experiments, each asking a yes–no question, and each with its own Boolean-valued function, Boolean-valued outcome (probability), outcome: ''success'' (with probability ) or ''failure'' (with probability ). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., , the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the binomial test of statistical significance. The binomial distribution is frequently used to model the number of successes in a sample of size drawn with replacement from a population of size . If the sampling is carried out without replacement, the draws ar ... [...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] |
Probit
In probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution. It has applications in data analysis and machine learning, in particular exploratory statistical graphics and specialized regression modeling of binary response variables. Mathematically, the probit is the inverse of the cumulative distribution function of the standard normal distribution, which is denoted as \Phi(z), so the probit is defined as :\operatorname(p) = \Phi^(p) \quad \text \quad p \in (0,1). Largely because of the central limit theorem, the standard normal distribution plays a fundamental role in probability theory and statistics. If we consider the familiar fact that the standard normal distribution places 95% of probability between −1.96 and 1.96 and is symmetric around zero, it follows that :\Phi(-1.96) = 0.025 = 1-\Phi(1.96).\,\! The probit function gives the 'inverse' computation, generating a value of a standard normal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Z-test
A ''Z''-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution. ''Z''-test tests the mean of a distribution. For each statistical significance, significance level in the Confidence intervals, confidence interval, the ''Z''-test has a single critical value (for example, 1.96 for 5% two-tailed), which makes it more convenient than the Student's t-test, Student's ''t''-test whose critical values are defined by the sample size (through the corresponding degrees of freedom (statistics), degrees of freedom). Both the ''Z''-test and Student's ''t''-test have similarities in that they both help determine the significance of a set of data. However, the ''Z''-test is rarely used in practice because the population deviation is difficult to determine. Applicability Because of the central limit theorem, many test statistics are approximately normally distributed for large samples. Therefore, many s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudocount
In statistics, additive smoothing, also called Laplace smoothing or Lidstone smoothing, is a technique used to smooth count data, eliminating issues caused by certain values having 0 occurrences. Given a set of observation counts \mathbf = \langle x_1, x_2, \ldots, x_d \rangle from a d-dimensional multinomial distribution with N trials, a "smoothed" version of the counts gives the estimator : \hat\theta_i = \frac \qquad (i = 1, \ldots, d), where the smoothed count \hat x_i = N \hat\theta_i, and the "pseudocount" ''α'' > 0 is a smoothing parameter, with ''α'' = 0 corresponding to no smoothing (this parameter is explained in below). Additive smoothing is a type of shrinkage estimator, as the resulting estimate will be between the empirical probability ( relative frequency) x_i/N and the uniform probability 1/d. Common choices for ''α'' are 0 (no smoothing), (the Jeffreys prior), or 1 (Laplace's rule of succession), but the parameter may also be set empir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coverage Probability
In statistical estimation theory, the coverage probability, or coverage for short, is the probability that a confidence interval or confidence region will include the true value (parameter) of interest. It can be defined as the proportion of instances where the interval surrounds the true value as assessed by long-run frequency. In statistical prediction, the coverage probability is the probability that a prediction interval will include an out-of-sample value of the random variable. The coverage probability can be defined as the proportion of instances where the interval surrounds an out-of-sample value as assessed by long-run frequency. Concept The fixed degree of certainty pre-specified by the analyst, referred to as the ''confidence level'' or ''confidence coefficient'' of the constructed interval, is effectively the nominal coverage probability of the procedure for constructing confidence intervals. Hence, referring to a "nominal confidence level" or "nominal confi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edwin Bidwell Wilson
Edwin Bidwell Wilson (April 25, 1879 – December 28, 1964) was an American mathematician, statistician, physicist and general polymath. He was the sole protégé of Yale University physicist Josiah Willard Gibbs and was mentor to MIT economist Paul Samuelson. Wilson had a distinguished academic career at Yale and MIT, followed by a long and distinguished period of service as a civilian employee of the US Navy in the Office of Naval Research. In his latter role, he was awarded the Distinguished Civilian Service Award, the highest honorary award available to a civilian employee of the US Navy. Wilson made broad contributions to mathematics, statistics and aeronautics, and is well known for producing a number of widely used textbooks. He is perhaps best known for his derivation of the eponymously named Binomial proportion confidence interval#Wilson score interval, Wilson score interval, which is a confidence interval used widely in statistics. Life Edwin Bidwell Wilson was bor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilson Score Interval And Logistic Example
Wilson may refer to: People *Wilson (name) ** List of people with given name Wilson ** List of people with surname Wilson * Wilson (footballer, 1927–1998), Brazilian manager and defender *Wilson (footballer, born 1984), full name Wilson Rodrigues de Moura Júnior, Brazilian goalkeeper *Wilson (footballer, born 1985), full name Wilson Rodrigues Fonseca, Brazilian forward *Wilson (footballer, born 1975), full name Wilson Roberto dos Santos, Brazilian centre-back Places Australia * Wilson, South Australia * Wilson, Western Australia * Wilson Inlet, Western Australia * Wilson Reef, Queensland * Wilsons Promontory, Victoria, Australia, and hence: :*Wilsons Promontory Islands Important Bird Area :* Wilsons Promontory Lighthouse :*Wilsons Promontory Marine National Park :*Wilsons Promontory National Park Canada * Wilson Avenue (Toronto), Ontario ** Wilson (TTC) subway station ** Wilson Subway Yard Poland * Wilson Square (''Plac Wilsona''), in Warsaw United Kingdom * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weighted Arithmetic Mean
The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics. If all the weights are equal, then the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counterintuitive properties, as captured for instance in Simpson's paradox. Examples Basic example Given two school with 20 students, one with 30 test grades in each class as follows: :Morning class = :Afternoon class = The mean for the morning class is 80 and the mean of the afternoon class is 90. The unweighted mean of the two means is 85. However, this does not account for the difference in numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independent And Identically Distributed Random Variables
Independent or Independents may refer to: Arts, entertainment, and media Artist groups * Independents (artist group), a group of modernist painters based in Pennsylvania, United States * Independentes (English: Independents), a Portuguese artist group Music Groups, labels, and genres * Independent music, a number of genres associated with independent labels * Independent record label, a record label not associated with a major label * Independent Albums, American albums chart Albums * ''Independent'' (Ai album), 2012 * ''Independent'' (Faze album), 2006 * ''Independent'' (Sacred Reich album), 1993 Songs * "Independent" (song), a 2007 song by Webbie * "Independent", a 2002 song by Ayumi Hamasaki from '' H'' News media organizations * Independent Media Center (also known as Indymedia or IMC), an open publishing network of journalist collectives that report on political and social issues, e.g., in ''The Indypendent'' newspaper of NYC * ITV (TV network) (Independent Televi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Short (engineer)
Michael Short (born August 1975) is Professor of Control Engineering and Systems Informatics and leads the Centre for Sustainable Engineering at Teesside University in the UK. He received a BEng (Electrical and Electronic Engineering) in 1999 and a PhD (Robotics) in 2003 from the University of Sunderland. In 2012 he was also awarded a PGCHE from Teesside University. He was previously at the University of Leicester until 2009, and was made Reader (Professor) in January 2015 and full (Chair) Professor (by Research) in August 2020. Michael is also a time-served automation and process control engineer, with eight years' industrial experience. Michael is a full member of the Institute of Engineering and Technology ( MIET) since 1999, a fellow of the Higher Education Academy ( FHEA) since 2012 and a full member of the Institute of Electrical and Electronics Engineers ( MIEEE), and he also sits on the IEEE Industrial Electronics Society Technical Committee on Factory Automation (TCF ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
