binomial


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binomial

(bī'nō`mēəl), polynomial expression (see polynomialpolynomial,
mathematical expression which is a finite sum, each term being a constant times a product of one or more variables raised to powers. With only one variable the general form of a polynomial is a0xn+a1x
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) containing two terms, for example, x+y. The binomial theorem, or binomial formula, gives the expansion of the nth power of a binomial (x+y) for n=1, 2, 3, … , as follows:

where the ellipsis (…) indicates a continuation of terms following the same pattern. For example, using the formula and reducing fractions, one obtains (x+y)5=x5+5x4y+10x3y2+10x2y3+5xy4+y5. The coefficients 1, n, n (n−1)/1·2, etc., of x and y may also be found from an array known as Pascal's triangle (for Blaise PascalPascal, Blaise
, 1623–62, French scientist and religious philosopher. Studying under the direction of his father, a civil servant, Pascal showed great precocity, especially in mathematics and science.
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), formed by adding adjacent numbers to find the number below them as follows:

binomial

[bī′nō·mē·əl]
(mathematics)
A polynomial with only two terms.

binomial

1. a mathematical expression consisting of two terms, such as 3x + 2y
2. a two-part taxonomic name for an animal or plant
3. referring to two names or terms
References in periodicals archive ?
Of the 3 data sets that used 4 classes and were not satisfactorily fit, one (Premeaux tier 2) approached statistical significance with the negative binomial distribution, but the other two (Premeaux tier 1 and McCabe) did not come close to a satisfactory fit.
The negative binomial distribution, characterized by the variance being greater than the mean, represents an aggregated or contagious distribution of insects.
Physical conditions: We get Binomial distribution under the following conditions
accelerated life testing, accelerated binomial testing (bogey testing), and accelerated degradation testing, should also be representable in the unified framework in order to embrace multiple applications.
To achieve these objectives, a fixed parameters negative binomial model with constant parameters and a random parameters negative binomial model were developed, and the modeling results were compared to explore which approach maybe appropriate (this statement means that the traditional negative binomial model (fixed parameters) is suitable for some cases and random parameters binomial model is suitable for others; so all considerable models need to be taken into account in the accident frequency analysis).
Keywords: Dengue Fever, Principal component analysis, Negative Binomial Model.
7 Note that a negative binomial NB(n, p) variable is the sum of n independent G(p) variables.
Using a novel statistical approach based on the Generalized Binomial Distribution (Drezner and Farnum, 1993), this paper investigates whether some mutual funds provide positive [alpha]'s over time as a result of skill.
The Wald method has also been used in dealing with linear functions which involve binomial proportions, also known as binomial families.
The company and its advisors believe that this exact binomial method is most applicable and appropriate given the small number of clinical events.