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The Weibull distribution is given by P(x) = alphabeta^(-alpha)x^(alpha-1)e^(-(x/beta)^alpha) (1) D(x) = 1-e^(-(x/beta)^alpha) (2) for x in [0,infty), and is implemented in ...

To predict the result of a measurement requires (1) a model of the system under investigation, and (2) a physical theory linking the parameters of the model to the parameters ...

Consider the probability Q_1(n,d) that no two people out of a group of n will have matching birthdays out of d equally possible birthdays. Start with an arbitrary person's ...

The terms "measure," "measurable," etc. have very precise technical definitions (usually involving sigma-algebras) that can make them appear difficult to understand. However, ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

The Jacobi elliptic functions are standard forms of elliptic functions. The three basic functions are denoted cn(u,k), dn(u,k), and sn(u,k), where k is known as the elliptic ...

A power is an exponent to which a given quantity is raised. The expression x^a is therefore known as "x to the ath power." A number of powers of x are plotted above (cf. ...

A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Every real ...

To fit a functional form y=Ae^(Bx), (1) take the logarithm of both sides lny=lnA+Bx. (2) The best-fit values are then a = ...

The margin of error is an estimate of a confidence interval for a given measurement, result, etc. and is frequently cited in statistics. While phrases such as, "The poll has ...