Search results
Results from the WOW.Com Content Network
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 ...
If is a subset of a vector space then is said to be a symmetric set if it is symmetric with respect to the additive group structure of the vector space; that is, if =, which happens if and only if . The symmetric hull of a subset S {\displaystyle S} is the smallest symmetric set containing S , {\displaystyle S,} and it is equal to S ∪ − S ...
Benford's law, which describes the frequency of the first digit of many naturally occurring data. The ideal and robust soliton distributions. Zipf's law or the Zipf distribution. A discrete power-law distribution, the most famous example of which is the description of the frequency of words in the English language.
Examples of unimodal functions include quadratic polynomial functions with a negative quadratic coefficient, tent map functions, and more. The above is sometimes related to as strong unimodality , from the fact that the monotonicity implied is strong monotonicity .
Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. [1] Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure.
The CumFreqA [71] program for the fitting of composite probability distributions to a data set (X) can divide the set into two parts with a different distribution. The figure shows an example of a double generalized mirrored Gumbel distribution as in distribution fitting with cumulative distribution function (CDF) equations:
In mathematics, the symmetric difference of two sets, also known as the disjunctive union and set sum, is the set of elements which are in either of the sets, but not in their intersection. For example, the symmetric difference of the sets { 1 , 2 , 3 } {\displaystyle \{1,2,3\}} and { 3 , 4 } {\displaystyle \{3,4\}} is { 1 , 2 , 4 ...
Example distribution with positive skewness. These data are from experiments on wheat grass growth. In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined.