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In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in terms of two positive parameters, denoted by alpha (α) and beta (β), that appear as exponents of the variable and its complement to 1, respectively, and control the shape of the distribution.
The above equations are efficient to use if the mean of the x and y variables (¯ ¯) are known.If the means are not known at the time of calculation, it may be more efficient to use the expanded version of the ^ ^ equations.
Contour plot of the beta function. In mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients.
An alpha beta filter (also called alpha-beta filter, f-g filter or g-h filter [1]) is a simplified form of observer for estimation, data smoothing and control applications. It is closely related to Kalman filters and to linear state observers used in control theory. Its principal advantage is that it does not require a detailed system model.
the beta coefficient, the non-diversifiable risk, of an asset in mathematical finance; the sideslip angle of an airplane; a beta particle (e − or e +) the beta brain wave in brain or cognitive sciences; ecliptic latitude in astronomy; the ratio of plasma pressure to magnetic pressure in plasma physics; β-reduction in lambda calculus
Alpha is a way to measure excess return, while beta is used to measure the volatility, or risk, of an asset. Beta might also be referred to as the return you can earn by passively owning the market.
Illustration of the sum formula. Draw a horizontal line (the x -axis); mark an origin O. Draw a line from O at an angle α {\displaystyle \alpha } above the horizontal line and a second line at an angle β {\displaystyle \beta } above that; the angle between the second line and the x -axis is α + β {\displaystyle \alpha +\beta } .
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