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clear all  View: ## Factor Theorem

The following result, which is an immediate consequence of the Remainder Theorem:TheoremLet f(x) be a polynomial. Then x−h is a factor of f(x) if and only if f(h)=0.The theorem is valuable for ... ## unconditional inequality

Always true, irrespective of the values taken by the variables so x 2+2x+3>0 is unconditional since it can be expressed as (x+1)2+2>0 which is always>0, but x 2+2x−3>0 is a conditional inequality ... ## L-moments

Measures of location, spread, and other properties of distributions that are computed from linear combinations of the ordered data values x(1)≤x(2)≤…≤x(n) (with mean x̄, which is the first L-moment). ... ## Old Faithful

Geyser in the Yellowstone National Park which erupts in a fashion that has challenged analysts of time series. The data in the table refer to the period 1–8 August in 1978. For each day, the table ... ## sign test

A simple non-parametric test that is used in two situations:1. A random sample of n observations x1, x2,…, xn is taken on the random variable X; the null hypothesis is that the population has median ... ## Anderson–Darling test

A general test, published in 1952, that compares the fit of the observed cumulative distribution function with that expected. It was derived by Anderson and David A. Darling as a modification of the ... ## pair

A set with two elements, often with an order implicit in it, such as the coordinate pair (x, y). ## Tk

A toolkit of windowing functions added to Tcl that simplifies the production of X Window system interfaces to applications. ## linear dependence

The variables y and x display linear dependence if, for some constants a and b (≠ 0),y=a+bx. ## autocorrelation

If {x i} is an ordered sequence of observations then the product moment correlation coefficient between pairs (x i, x i+1) is the autocorrelation of lag 1, and between pairs (x i, x i+k) is the ... ## bootstrap

A computer-intensive resampling method for estimating the properties of a distribution while making minimal assumptions. In this respect it resembles the jackknife. The idea is simple. Suppose we ... ## algebraic number

A real number that is the root of a polynomial equation with integer coefficients. All rational numbers are algebraic, since a/b is the root of the equation bx−a=0. Some irrational numbers are ... ## logarithm

The logarithm to base a(>0) of a positive number b is denoted by loga b=x, where ax=b. Logarithms have the fundamental property loga (bc)=loga b+loga c. A logarithm to base 10 is usually denoted by ... ## binomial distribution

The discrete probability distribution for the number of successes when n independent experiments are carried out, each with the same probability p of success. The probability mass function is given ... ## unconditional inequality Quick reference

### The Concise Oxford Dictionary of Mathematics (5 ed.)

Reference type:
Subject Reference
Current Version:
2014

...inequality Always true, irrespective of the values taken by the variables so x 2 +2 x +3>0 is unconditional since it can be expressed as ( x +1) 2 +2>0 which is always>0, but x 2 +2 x − 3>0 is a conditional inequality because it can be expressed as ( x +1) 2 >4 which is only true for x >1 or x... ## Factor Theorem Quick reference

### The Concise Oxford Dictionary of Mathematics (5 ed.)

Reference type:
Subject Reference
Current Version:
2014

...result, which is an immediate consequence of the remainder theorem : Theorem Let f ( x ) be a polynomial. Then x − h is a factor of f ( x ) if and only if f ( h )=0. The theorem is valuable for finding factors of polynomials. For example, to factorize 2 x 3 +3 x 2 −12 x20, look first for possible factors x − h , where h is an integer. Here h must divide 20. Try possible values for h , and calculate f ( h ). It is found that f (−2)=−16+12+24−20=0, and so x +2 is a factor. Now divide the polynomial by this factor to obtain a quadratic which it... ## L-moments Quick reference

### A Dictionary of Statistics (3 ed.)

Reference type:
Subject Reference
Current Version:
2014
Subject:
Science and technology, Mathematics and Computer Science
Length:
118 words
Illustration(s):
1

...-moments Measures of location , spread, and other properties of distributions that are computed from linear combinations of the ordered data values x (1) ≤ x (2) ≤⋯≤ x ( n ) (with mean , which is the first L -moment). Defining the quantities b 1 , b 2 ,…, b n− 1 by the next three L -moments are 2 b 1 − , 6 b 2 − 6 b 1 + , and 20 b 3 −30 b 2 +12 b 1 − . The second L -moment is related to the Gini statistic . An advantage of L -moments is that they can be calculated even when distributions have infinite... ## contour line Quick reference

### The Concise Oxford Dictionary of Mathematics (5 ed.)

Reference type:
Subject Reference
Current Version:
2014

...line A line joining points of a constant value. If z = f ( x , y ) is a function which defines a surface and the line y = g ( x ) has the property that f ( x, g ( x ) is constant then the line y = g ( x ) is a contour line. Physical geography maps show height contours and weather charts show pressure isobars which are contour lines. http://raider.mountunion.edu/~mcnaugma/topographic%20maps/contour.htm An illustrated explanation of contour... ## class boundaries Quick reference

### The Concise Oxford Dictionary of Mathematics (5 ed.)

Reference type:
Subject Reference
Current Version:
2014

...of accuracy, which will then allow you to determine the actual boundary of the interval. For example if intervals are 1.5≤ x <2.0; 2.0x <2.4.…. with observations recorded correct to the nearest 0.1, then the class boundaries are 1.45, 1.85, 2.45, etc. One common special case is when the data refers to ages because the boundary between recording age 22 and age 23 is actually the 23rd birthday, so age classes of 16≤ x <18; 18≤ x <23.…. would have class boundaries at 16, 18, 23,... ## sign test Quick reference

### A Dictionary of Statistics (3 ed.)

Reference type:
Subject Reference
Current Version:
2014

... sample of n observations x 1 , x 2 ,…, x n is taken on the random variable X ; the null hypothesis is that the population has median m 0 . 2. A random sample of n observations ( x 1 , y 1 ), ( x 2 , y 2 ),…, ( x n , y n ) is taken on the pair of random variables ( X , Y ); the null hypothesis is that the distribution of X − Y has median 0. In both cases the analysis begins by noting the signs of the differences d 1 , d 2 ,…, d n , where in case (1) d j = x j − m 0 and in case (2) d j = x j − y j . In either case the...  View: