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- Student's_t-distribution abstract "In probability and statistics, Student's t-distribution (or simply the t-distribution) is a family of continuous probability distributions that arise when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown. It plays a role in a number of widely used statistical analyses, including the Student's t-test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis. The Student's t-distribution also arises in the Bayesian analysis of data from a normal family.If we take a sample of n = ν+1 observations from a normal distribution (the black curve on the figure on the right of this page, representing a very large ν), compute the sample mean and plot it, and repeat this process infinitely many times (for the same n), we get the probability density function for that n, as shown in the image on the right.If we also compute the sample variance for these n observations, then the t-distribution (for n-1) can be defined as the distribution of the location of the true mean, relative to the sample mean and divided by the sample standard deviation, after multiplying by the normalizing term , where n is the sample size. In this way, the t-distribution can be used to estimate how likely it is that the true mean lies in any given range.The t-distribution is symmetric and bell-shaped, like the normal distribution, but has heavier tails, meaning that it is more prone to producing values that fall far from its mean. This makes it useful for understanding the statistical behavior of certain types of ratios of random quantities, in which variation in the denominator is amplified and may produce outlying values when the denominator of the ratio falls close to zero. The Student's t-distribution is a special case of the generalised hyperbolic distribution.".
- Student's_t-distribution thumbnail Student_t_pdf.svg?width=300.
- Student's_t-distribution wikiPageExternalLink students-t-distribution-calculator.html.
- Student's_t-distribution wikiPageExternalLink s.html.
- Student's_t-distribution wikiPageExternalLink book.
- Student's_t-distribution wikiPageID "105375".
- Student's_t-distribution wikiPageRevisionID "605929994".
- Student's_t-distribution cdf "<br/ >where 2F1 is the hypergeometric function".
- Student's_t-distribution cdfImage "325".
- Student's_t-distribution char "for ν > 0 * Kν: Modified Bessel function of the second kind".
- Student's_t-distribution entropy "* ψ: digamma function, * B: beta function".
- Student's_t-distribution hasPhotoCollection Student's_t-distribution.
- Student's_t-distribution id "p/s090710".
- Student's_t-distribution kurtosis "for ν > 4, ∞ for 2 < ν ≤ 4, otherwise undefined".
- Student's_t-distribution mean "0".
- Student's_t-distribution median "0".
- Student's_t-distribution mgf "undefined".
- Student's_t-distribution mode "0".
- Student's_t-distribution name "Student's t".
- Student's_t-distribution parameters "ν > 0 degrees of freedom".
- Student's_t-distribution pdfImage "325".
- Student's_t-distribution skewness "0".
- Student's_t-distribution support "x ∈".
- Student's_t-distribution title "Student distribution".
- Student's_t-distribution type "density".
- Student's_t-distribution variance "for ν > 2, ∞ for 1 < ν ≤ 2, otherwise undefined".
- Student's_t-distribution subject Category:Continuous_distributions.
- Student's_t-distribution subject Category:Infinitely_divisible_probability_distributions.
- Student's_t-distribution subject Category:Normal_distribution.
- Student's_t-distribution subject Category:Probability_distributions.
- Student's_t-distribution subject Category:Probability_distributions_with_non-finite_variance.
- Student's_t-distribution subject Category:Special_functions.
- Student's_t-distribution type Abstraction100002137.
- Student's_t-distribution type Arrangement105726596.
- Student's_t-distribution type Cognition100023271.
- Student's_t-distribution type ContinuousDistributions.
- Student's_t-distribution type Distribution105729036.
- Student's_t-distribution type Function113783816.
- Student's_t-distribution type MathematicalRelation113783581.
- Student's_t-distribution type ProbabilityDistributionsWithNon-finiteVariance.
- Student's_t-distribution type PsychologicalFeature100023100.
- Student's_t-distribution type Relation100031921.
- Student's_t-distribution type SpecialFunctions.
- Student's_t-distribution type Structure105726345.
- Student's_t-distribution comment "In probability and statistics, Student's t-distribution (or simply the t-distribution) is a family of continuous probability distributions that arise when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.".
- Student's_t-distribution label "Distribución t de Student".
- Student's_t-distribution label "Distribuição t de Student".
- Student's_t-distribution label "Distribuzione t di Student".
- Student's_t-distribution label "Loi de Student".
- Student's_t-distribution label "Rozkład Studenta".
- Student's_t-distribution label "Student's t-distribution".
- Student's_t-distribution label "Studentsche t-Verteilung".
- Student's_t-distribution label "Studentverdeling".
- Student's_t-distribution label "T分布".
- Student's_t-distribution label "Распределение Стьюдента".
- Student's_t-distribution label "توزيع ستيودنت الاحتمالي".
- Student's_t-distribution label "学生t-分布".
- Student's_t-distribution sameAs Studentovo_rozdělení.
- Student's_t-distribution sameAs Studentsche_t-Verteilung.
- Student's_t-distribution sameAs Distribución_t_de_Student.
- Student's_t-distribution sameAs Loi_de_Student.
- Student's_t-distribution sameAs Distribuzione_t_di_Student.
- Student's_t-distribution sameAs T分布.
- Student's_t-distribution sameAs 스튜던트_t_분포.
- Student's_t-distribution sameAs Studentverdeling.
- Student's_t-distribution sameAs Rozkład_Studenta.
- Student's_t-distribution sameAs Distribuição_t_de_Student.
- Student's_t-distribution sameAs m.0qdxm.
- Student's_t-distribution sameAs Q576072.
- Student's_t-distribution sameAs Q576072.
- Student's_t-distribution sameAs Student's_t-distribution.
- Student's_t-distribution wasDerivedFrom Student's_t-distribution?oldid=605929994.
- Student's_t-distribution depiction Student_t_pdf.svg.
- Student's_t-distribution isPrimaryTopicOf Student's_t-distribution.
