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Abbe, Ernst Carl (1840-1905; b, Eisenach, Germany: d, Jena, Germany) A German mathematician and physicist. His father was a book printer and factory worker and his childhood one of privation. Abbe studied at the Universities of Jena and Gottingen, receiving his PhD in 1861. In 1863 he was appointed to a lectureship at Jena on the basis of a dissertation that, in effect, derived the chi-squared distribution. Following an approach from Carl Zeiss, most of his subsequent work was concerned with optics and astronomy. A lunar crater is named after him, also minor planet, and several schools in Germany.

Abscissa See Cartesian coordinates.

Absolute difference The absolute value of the difference between two numbers. See also mean deviation.

Absolute value (modulus) The value of a number disregarding its sign. Denoted by a pair of ‘!’ signs: thus the modulus of -2.5 is !-2.5! = 2.5.

Absorbing barrier (absorbing state) See Markov process.

Acceptable quality level See acceptance sampling.

Acceptance region The set of values of the statistic, in a hypothesis test, which lead to acceptance of the null hypothesis.

Acceptance-rejection algorithm A method for generating values of a continuous random variable for use in a simulation. Suppose that the random variable X. which takes values in the interval (a,b), has

Probability density function f. Denote the maximum value of f(x) by M. Let u and v be two random numbers uniformly distributed in the interval (o,1). Writer r=a+(b-a)u and s= Mv, so that r and s are uniformly distributed on (a,b) and (0,M), respectively. Calculate f® if f(r) > s then r is accepted as a value of X. Otherwise, it is rejected and a new pair of values is taken for u and v. See following diagram.