czas-i-pomiary: Normal distribution

Evidence: 100 • authority: 72

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 ) = 1 2 π σ 2 exp ⁡ ( − ( x − μ ) 2 2 σ 2 ) . {\displaystyle f(x)={\frac {1}{\sqrt {2\pi \sigma ^{2}}}}\exp {\left(-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}\right)}\,.} The parameter ⁠ μ {\displaystyle \mu } ⁠ is the mean or expectation of the distribution (and also its median and mode), while the parameter σ 2 {\textstyle \sigma ^{2}} is the variance. The standard deviation of the distribution is the positive value ⁠ σ {\displaystyle \sigma } ⁠ (sigma). A random vari…

Evidence: 65 • authority: 92

Hierarchical Bayesian Regression for experimental psychology: a case study of cognitive control.. Arising from the so-called 'replication crisis' in the experimental psychology literature, there has been a growing call to reassess whether specific analytic practices might enhance the accuracy and precision of reported findings. This issue is explored here, through a case study examination of two previously collected datasets from the Dual Mechanisms of Cognitive Control (DMCC) task battery. This case study highlights the unique advantages afforded by Hierarchical Bayesian Regression (HBR) models as a potentially more rigorous analytic approach to statistical inference. In the DMCC datasets,…

Evidence: 54 • authority: 88

Properties of the Inverse Gaussian Distribution. Abstract For a comprehensive survey of the basic properties of the inverse Gaussian law it is essential to have a clear understanding of the fundamentals of exponential families. The seeds of exponential families were first sown by Fisher (1934) who argued that families of one-dimensional distributions admitting a sufficient reduction have to be exponential. This idea got Dar mois (1935), Koopman (1936), and Pitman (1936) on the trail while some early development can be found in Lehmann (1959) where the details of some basic results on exponential families are introduced. These early ex positions merely scratched the surface until Barndorff-N…