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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 trial, 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 ''nS'' 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 o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German: '' Statistik'', "description of a 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 surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An ... [...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 (TCFA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clopper-Pearson 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 trial, 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 ''nS'' 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 o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Density Function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a ''relative likelihood'' that the value of the random variable would be close to that sample. Probability density is the probability per unit length, in other words, while the ''absolute likelihood'' for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample. In a more precise sense, the PDF is used to specify the probability of the random variable falling ''within a particular range of values'', as opposed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilson Score Pdf And Interval Equality
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 The Wilsons Promontory Marine National Park is a protected marine national park located in the South Gippsland region of Victoria, Australia. The marine park is situated off the southern tip of Wilsons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Score Test
In statistics, the score test assesses constraints on statistical parameters based on the gradient of the likelihood function—known as the ''score''—evaluated at the hypothesized parameter value under the null hypothesis. Intuitively, if the restricted estimator is near the maximum of the likelihood function, the score should not differ from zero by more than sampling error. While the finite sample distributions of score tests are generally unknown, they have an asymptotic χ2-distribution under the null hypothesis as first proved by C. R. Rao in 1948, a fact that can be used to determine statistical significance. Since function maximization subject to equality constraints is most conveniently done using a Lagrangean expression of the problem, the score test can be equivalently understood as a test of the magnitude of the Lagrange multipliers associated with the constraints where, again, if the constraints are non-binding at the maximum likelihood, the vector of Lagrange mu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pearson's Chi-squared Test
Pearson's chi-squared test (\chi^2) is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many chi-squared tests (e.g., Yates, likelihood ratio, portmanteau test in time series, etc.) – statistical procedures whose results are evaluated by reference to the chi-squared distribution. Its properties were first investigated by Karl Pearson in 1900. In contexts where it is important to improve a distinction between the test statistic and its distribution, names similar to ''Pearson χ-squared'' test or statistic are used. It tests a null hypothesis stating that the frequency distribution of certain events observed in a sample is consistent with a particular theoretical distribution. The events considered must be mutually exclusive and have total probability 1. A common case for this is where the events each cover an outcome of a categorical variable. ... [...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-tests test the mean of a distribution. For each significance level in the 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 whose critical values are defined by the sample size (through the corresponding 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 statistical tests can be conveniently performed as approximate ''Z''-tests if the sample size is large or the po ... [...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 categorical data. Given a set of observation counts \textstyle from a \textstyle -dimensional multinomial distribution with \textstyle trials, a "smoothed" version of the counts gives the estimator: :\hat\theta_i= \frac \qquad (i=1,\ldots,d), where the smoothed count \textstyle and the "pseudocount" ''α'' > 0 is a smoothing parameter. ''α'' = 0 corresponds 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) \textstyle , and the uniform probability \textstyle . Invoking Laplace's rule of succession, some authors have argued that ''α'' should be 1 (in which case the term add-one smoothing is also used), though in practice a smaller value is typically chosen. From a Bayesian point o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coverage Probability
In statistics, the coverage probability is a technique for calculating a confidence interval which is the proportion of the time that the interval contains the true value of interest. For example, suppose our interest is in the mean number of months that people with a particular type of cancer remain in remission following successful treatment with chemotherapy. The confidence interval aims to contain the unknown mean remission duration with a given probability. This is the "confidence level" or "confidence coefficient" of the constructed interval which is effectively the "nominal coverage probability" of the procedure for constructing confidence intervals. The "nominal coverage probability" is often set at 0.95. The ''coverage probability'' is the actual probability that the interval contains the true mean remission duration in this example. If all assumptions used in deriving a confidence interval are met, the nominal coverage probability will equal the coverage probability (t ... [...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 Wilson score interval, which is a confidence interval used widely in statistics. Life Edwin Bidwell Wilson was born in Hartford, Connecticut to Edwin Horace Wilson (a teacher ... [...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 Kingdo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
