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The chain-ladder or development [1] method is a prominent [2] [3] actuarial loss reserving technique. The chain-ladder method is used in both the property and casualty [1] [4] and health insurance [5] fields. Its intent is to estimate incurred but not reported claims and project ultimate loss amounts. [5]
So, Euclid's method for computing the greatest common divisor of two positive integers consists of replacing the larger number with the difference of the numbers, and repeating this until the two numbers are equal: that is their greatest common divisor. For example, to compute gcd(48,18), one proceeds as follows:
On the right Nicomachus's example with numbers 49 and 21 resulting in their GCD of 7 (derived from Heath 1908:300). In mathematics, the Euclidean algorithm, [note 1] or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers, the largest number that divides them both without a remainder.
Visualisation of using the binary GCD algorithm to find the greatest common divisor (GCD) of 36 and 24. Thus, the GCD is 2 2 × 3 = 12.. The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, [1] [2] is an algorithm that computes the greatest common divisor (GCD) of two nonnegative integers.
The Eclipse process framework (EPF) is an open source project that is managed by the Eclipse Foundation. It lies under the top-level Eclipse Technology Project , and has two goals: To provide an extensible framework and exemplary tools for software process engineering - method and process authoring, library management, configuring and ...
Loss development factors or LDFs are used in insurance pricing and reserving to adjust claims to their projected ultimate level. [1] [2] Insurance claims, especially in long-tailed lines such as liability insurance, are often not paid out immediately.
After computing the GCD of the polynomial and its derivative, further GCD computations provide the complete square-free factorization of the polynomial, which is a factorization = = where, for each i, the polynomial f i either is 1 if f does not have any root of multiplicity i or is a square-free polynomial (that is a polynomial without ...
The Ladder-Step function (given below) used within the ladder is the core of the algorithm and is a combined form of the differential add and doubling operations. The field constant a 24 is defined as a 24 = ( A + 2 ) / 4 {\displaystyle (A+2)/4} , where A {\displaystyle A} is a parameter of the underlying Montgomery curve .