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Student's T Distribution
In probability theory and statistics, Student's distribution (or simply the distribution) t_\nu is a continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped. However, t_\nu has heavier tails, and the amount of probability mass in the tails is controlled by the parameter \nu. For \nu = 1 the Student's distribution t_\nu becomes the standard Cauchy distribution, which has very "fat" tails; whereas for \nu \to \infty it becomes the standard normal distribution \mathcal(0, 1), which has very "thin" tails. The name "Student" is a pseudonym used by William Sealy Gosset in his scientific paper publications during his work at the Guinness Brewery in Dublin, Ireland. The Student's distribution plays a role in a number of widely used statistical analyses, including Student's -test for assessing the statistical significance of the difference between two sample means, the cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Student T Pdf
A student is a person enrolled in a school or other educational institution, or more generally, a person who takes a special interest in a subject. In the United Kingdom and most The Commonwealth, commonwealth countries, a "student" attends a secondary school or higher (e.g., college or university); those in primary or elementary schools are "pupils". Africa Nigeria In Nigeria, Education in Nigeria, education is classified into four systems known as a 6-3-3-4 system of education. It implies six years in primary school, three years in junior secondary, three years in senior secondary and four years in the university. However, the number of years to be spent in university is mostly determined by the course of study. Some courses have longer study lengths than others. Those in primary school are often referred to as pupils. Those in university, as well as those in secondary school, are referred to as students. The Nigerian system of education also has other recognized categorie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heavy-tailed Distribution
In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution. Roughly speaking, “heavy-tailed” means the distribution decreases more slowly than an exponential distribution, so extreme values are more likely. In many applications it is the right tail of the distribution that is of interest, but a distribution may have a heavy left tail, or both tails may be heavy. There are three important subclasses of heavy-tailed distributions: the fat-tailed distributions, the long-tailed distributions, and the subexponential distributions. In practice, all commonly used heavy-tailed distributions belong to the subexponential class, introduced by Jozef Teugels. There is still some discrepancy over the use of the term heavy-tailed. There are two other definitions in use. Some authors use the term to refer to those distributions which do not have all their p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degrees Of Freedom (statistics)
In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a parameter is called the degrees of freedom. In general, the degrees of freedom of an estimate of a parameter are equal to the number of independent scores that go into the estimate minus the number of parameters used as intermediate steps in the estimation of the parameter itself. For example, if the variance is to be estimated from a random sample of N independent scores, then the degrees of freedom is equal to the number of independent scores (''N'') minus the number of parameters estimated as intermediate steps (one, namely, the sample mean) and is therefore equal to N-1. Mathematically, degrees of freedom is the number of dimensions of the domain of a random vector, or e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compound Probability Distribution
In probability and statistics, a compound probability distribution (also known as a mixture distribution or contagious distribution) is the probability distribution that results from assuming that a random variable is distributed according to some parametrized distribution, with (some of) the parameters of that distribution themselves being random variables. If the parameter is a scale parameter, the resulting mixture is also called a scale mixture. The compound distribution ("unconditional distribution") is the result of marginalizing (integrating) over the ''latent'' random variable(s) representing the parameter(s) of the parametrized distribution ("conditional distribution"). Definition A compound probability distribution is the probability distribution that results from assuming that a random variable X is distributed according to some parametrized distribution F with an unknown parameter \theta that is again distributed according to some other distribution G. The resulting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Analysis
Thomas Bayes ( ; c. 1701 – 1761) was an English statistician, philosopher, and Presbyterian Presbyterianism is a historically Reformed Protestant tradition named for its form of church government by representative assemblies of elders, known as "presbyters". Though other Reformed churches are structurally similar, the word ''Pr ... minister. Bayesian ( or ) may be either any of a range of concepts and approaches that relate to statistical methods based on Bayes' theorem, or a follower of these methods. Bayes * * * * * * * * * * * – sometimes called ''Bayes' rule'' or ''Bayesian updating'' * * * * * * Bayesian *'' Bayesian'', a superyacht sunk off Palermo in 2024 * * * * * * * * * * * * * * * * * * (BIC) * Widely applicable Bayesian information criterion (WBIC) * * * * * * (BMA) * (BMC) * * * * * * * (BAYOMA) * * * * * * * * * * * * * * * * * * * * * * (PBE) * * * * * See also * * * *, a cryptanalytic process * * * * (BUGS) * * (BATMAN) * * * *, a gene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac e^\,. The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma^2 is the variance. The standard deviation of the distribution is (sigma). A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Significance
In statistical hypothesis testing, a result has statistical significance when a result at least as "extreme" would be very infrequent if the null hypothesis were true. More precisely, a study's defined significance level, denoted by \alpha, is the probability of the study rejecting the null hypothesis, given that the null hypothesis is true; and the p-value, ''p''-value of a result, ''p'', is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. The result is said to be ''statistically significant'', by the standards of the study, when p \le \alpha. The significance level for a study is chosen before data collection, and is typically set to 5% or much lower—depending on the field of study. In any experiment or Observational study, observation that involves drawing a Sampling (statistics), sample from a Statistical population, population, there is always the possibility that an observed effect would have occurred due to sampling error al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Student's T-test
Student's ''t''-test is a statistical test used to test whether the difference between the response of two groups is statistically significant or not. It is any statistical hypothesis test in which the test statistic follows a Student's ''t''-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known (typically, the scaling term is unknown and is therefore a nuisance parameter). When the scaling term is estimated based on the data, the test statistic—under certain conditions—follows a Student's ''t'' distribution. The ''t''-test's most common application is to test whether the means of two populations are significantly different. In many cases, a ''Z''-test will yield very similar results to a ''t''-test because the latter converges to the former as the size of the dataset increases. History The term "''t''-statistic" is abbreviated from " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dublin, Ireland
Dublin is the capital and largest city of Republic of Ireland, Ireland. Situated on Dublin Bay at the mouth of the River Liffey, it is in the Provinces of Ireland, province of Leinster, and is bordered on the south by the Dublin Mountains, part of the Wicklow Mountains range. Dublin is the largest city by population on the island of Ireland; at the 2022 census of Ireland, 2022 census, the city council area had a population of 592,713, while the city including suburbs had a population of 1,263,219, County Dublin had a population of 1,501,500. Various definitions of a metropolitan Greater Dublin Area exist. A settlement was established in the area by the Gaels during or before the 7th century, followed by the Vikings. As the Kingdom of Dublin grew, it became Ireland's principal settlement by the 12th century Anglo-Norman invasion of Ireland. The city expanded rapidly from the 17th century and was briefly the second largest in the British Empire and sixth largest in Western Europ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guinness Brewery
St. James's Gate Brewery is a brewery founded in 1759 in Dublin, Ireland, by Arthur Guinness. The company is now a part of Diageo, a company formed from the merger of Guinness and Grand Metropolitan in 1997. The main product of the brewery is Draught Guinness. Originally leased in 1759 to Arthur Guinness at £45 per year for 9,000 years, the St. James's Gate area has been the home of Guinness ever since. It became the largest brewery in Ireland in 1838, and the largest in the world by 1886, with an annual output of 1.2 million barrels. Although no longer the largest brewery in the world, it remains as the largest brewer of stout. The company has since bought out the originally leased property, and during the 19th and early 20th centuries, the brewery owned most of the buildings in the surrounding area, including many streets of housing for brewery employees, and offices associated with the brewery. The brewery had its own power plant. There is an attached exhibition o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
