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In statistics, the phi coefficient (or mean square contingency coefficient and denoted by φ or r φ) is a measure of association for two binary variables.. In machine learning, it is known as the Matthews correlation coefficient (MCC) and used as a measure of the quality of binary (two-class) classifications, introduced by biochemist Brian W. Matthews in 1975.
It is necessary to have the stroked glyph available for some mathematical uses, and U+03D5 GREEK PHI SYMBOL is designed for this function. Prior to Unicode version 3.0 (1998), the glyph assignments in the Unicode code charts were the reverse, and thus older fonts may still show a loopy form φ {\displaystyle \varphi } at U+03D5.
Note: The empty set symbol ∅ looks similar, but is unrelated to the Greek letter. or represents: the golden ratio 1.618... in mathematics, art, and architecture; Euler's totient function in number theory; the argument of a complex number in mathematics; the value of a plane angle in physics and mathematics
By 1910, inventor Mark Barr began using the Greek letter phi ( ) as a symbol for the golden ratio. [32] [e] It has also been represented by tau ( ), the first letter of the ancient Greek τομή ('cut' or 'section'). [35] Dan Shechtman demonstrates quasicrystals at the NIST in 1985 using a Zometoy model.
In statistics, a standard normal table, also called the unit normal table or Z table, [1] is a mathematical table for the values of Φ, the cumulative distribution function of the normal distribution.
Integrated information theory (IIT) the symbol of which is φ is a mathematical theory of consciousness developed under the lead of the neuroscientist Giulio Tononi Standard normal distribution , Φ ( x ) {\displaystyle \Phi (x)} notating its cumulative distribution function and ϕ ( x ) {\displaystyle \phi (x)} its probability density function
Survival functions or complementary cumulative distribution functions are often denoted by placing an overbar over the symbol for the cumulative: ¯ = (), or denoted as (), In particular, the pdf of the standard normal distribution is denoted by φ ( z ) {\textstyle \varphi (z)} , and its cdf by Φ ( z ) {\textstyle \Phi (z)} .
It is sometimes referred to as base-φ, golden mean base, phi-base, or, colloquially, phinary. Any non-negative real number can be represented as a base-φ numeral using only the digits 0 and 1, and avoiding the digit sequence "11" – this is called a standard form .