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A funnel plot is a scatterplot of treatment effect against a measure of study precision. It is used primarily as a visual aid for detecting bias or systematic heterogeneity. A symmetric inverted funnel shape arises from a ‘well-behaved’ data set, in which publication bias is unlikely. An asymmetric funnel indicates a relationship between ...
The hyperbolic secant distribution shares many properties with the standard normal distribution: it is symmetric with unit variance and zero mean, median and mode, and its probability density function is proportional to its characteristic function.
Since the Tukey lambda distribution is a symmetric distribution, the use of the Tukey lambda PPCC plot to determine a reasonable distribution to model the data only applies to symmetric distributions. A histogram of the data should provide evidence as to whether the data can be reasonably modeled with a symmetric distribution. [4]
The asymmetric generalized normal distribution is a family of continuous probability distributions in which the shape parameter can be used to introduce asymmetry or skewness. [ 15 ] [ 16 ] When the shape parameter is zero, the normal distribution results.
The expectile distribution, which nests the Gaussian distribution in the symmetric case. The Fisher–Tippett, extreme value, or log-Weibull distribution; Fisher's z-distribution; The skewed generalized t distribution; The gamma-difference distribution, which is the distribution of the difference of independent gamma random variables.
In the 2-dimensional case, if the density exists, each iso-density locus (the set of x 1,x 2 pairs all giving a particular value of ()) is an ellipse or a union of ellipses (hence the name elliptical distribution). More generally, for arbitrary n, the iso-density loci are unions of ellipsoids. All these ellipsoids or ellipses have the common ...
This distribution is a useful model for symmetric bimodal processes. Other continuous distributions allow more flexibility, in terms of relaxing the symmetry and the quadratic shape of the density function, which are enforced in the U-quadratic distribution – e.g., beta distribution and gamma distribution.
In statistics, a symmetric probability distribution is a probability distribution—an assignment of probabilities to possible occurrences—which is unchanged when its probability density function (for continuous probability distribution) or probability mass function (for discrete random variables) is reflected around a vertical line at some ...