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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 name stands for "stochastic alpha, beta, rho", referring to the parameters of the model. The SABR model is widely used by practitioners in the financial industry, especially in the interest rate derivative markets. It was developed by Patrick S. Hagan, Deep Kumar, Andrew Lesniewski, and Diana Woodward.
where I is the regularized incomplete beta function. While the related beta distribution is the conjugate prior distribution of the parameter of a Bernoulli distribution expressed as a probability, the beta prime distribution is the conjugate prior distribution of the parameter of a Bernoulli distribution expressed in odds.
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.
Portable alpha is an investment strategy in which portfolio managers separate alpha from beta by investing in securities that are not in the market index from which their beta is derived. Alpha is the return on investment achieved over and above the market return—beta—without taking on more risk. In simple terms, portable alpha is a ...
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It is a transformation of the four-parameter beta distribution with an additional assumption that its expected value is μ = a + 4 b + c 6 . {\displaystyle \mu ={\frac {a+4b+c}{6}}.} The mean of the distribution is therefore defined as the weighted average of the minimum, most likely and maximum values that the variable may take, with four ...
The beta-binomial is a one-dimensional version of the Dirichlet-multinomial distribution as the binomial and beta distributions are univariate versions of the multinomial and Dirichlet distributions respectively. The special case where α and β are integers is also known as the negative hypergeometric distribution.