# On the generalization of the distribution of the significant digits under computation

by James Teng Wong

Written in English

## Subjects:

• Distribution (Probability theory),
• Statistics.

## Edition Notes

The Physical Object ID Numbers Statement by James Teng Wong. Pagination 47 leaves, bound ; Number of Pages 47 Open Library OL15108296M

1. For a normal distribution with a mean of p = 60 and a standard deviation of a = 12, find each probability value requested. a. p(X > 66) b. p(X.   Example Joint Probability Distribution. Consider the two events: “rain today” and “rain tomorrow.” Let the random variable X be 0 if it does not rain today and 1 if it does. Similarly, let the random variable Y be 0 if it does not rain tomorrow and 1 if it does. The four possible values for the random variables X and Y considered together 01, 10, . tial distribution respectively; together they play an important role for the solution of the space-time fractional di usion equation. Our rejection concept is general and can be applied to any distribution for which an analytical transformation is known. It can sample e ciently from arbitrary in nite or nite intervals as opposed to other File Size: 2MB. Other articles where Theory of distributions is discussed: Lars V. Hörmander: was his establishment of a theory of distributions using Fourier analysis. This is an extension of Laurent Schwartz’s concept of a “distribution,” with which he brought rigour to the examination of mass distributions. Hörmander was also one of the principal contributors to the development of the .

Speeding up algorithms via modular computation 84 An e ective version of Fermat’s two squares theorem 86 Rational reconstruction and applications 89 The RSA cryptosystem 99 Notes 5 The distribution of primes Chebyshev’s theorem on the density of primes Bertrand’s postulate Mertens’ theorem The variance shows how widespread the individuals are from the average.. The variance is how much that the estimate varies around its average.. It's a measure of consistency. A very large variance means that the data were all over the place, while a small variance (relatively close to the average) means that the majority of the data are closed. Studies the use of scientific computation as a tool in attacking a number of mathematical problems and conjectures. In this case, scientific computation refers primarily to computations that are carried out with a large number of significant digits, for calculations associated with a variety of numerical techniques such as the (second) Remez algorithm in polynomial and rational . Covered entities may include the first three digits of the ZIP code if, according to the current publicly available data from the Bureau of the Census: (1) The geographic unit formed by combining all ZIP codes with the same three initial digits contains more t people; or (2) the initial three digits of a ZIP code for all such Author: Office For Civil Rights (OCR).

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## On the generalization of the distribution of the significant digits under computation by James Teng Wong Download PDF EPUB FB2

Benford's law, also called the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical law states that in many naturally occurring collections of numbers, the leading significant digit is likely to be small.

For example, in sets that obey the law, the. This paper concerns a On the generalization of the distribution of the significant digits under computation book of the gamma distribution, the specific form being suggested by Liouville's extension to Dirichlet's integral formula .

In this form it also may be regarded as a special case of a function introduced by L. Amoroso  and R. d'Addario  in analyzing the distribution of economic income. Introduction. Shepard () has put forward a ‘Universal Law of Generalization’ as one of the few general psychological results governing human cognition.

The law states that the probability of perceiving similarity or analogy between two items, a and b, is a negative exponential function of the distance d(a,b) between them in an internal psychological by: computation of its distribution function, implement the algorithm in an R pack age, and pro- vide an illustration for practitioners.

The computation of the cdf, however, is non-trivial. A real number can be expressed by a finite number of decimal digits only if it is rational and its fractional part has a denominator whose prime factors are 2 or 5 or both, because these are the prime factors of 10, the base of the decimal system.

Thus, for example, one half isone fifth isone-tenth isand one fiftieth is Fukushima, Computation of a general integral of Fermi-Dirac distribution by Mcdougall-Stoner method, Appl. Math. Comm. ( 4) –  A. Author: Toshio Fukushima. What is the distribution of the randomly selected digits between 0 and 9.

Single-peaked. Normal. Uniform. Left-skewed If a pollster repeats the process of randomly generating 50 digits and finding the mean, what is the distribution of the resulting sample means. Normal. Approximately normal. Left-skewed. Approximately left-skewed. Abstract. This paper introduces a new approach for mining if-then rules in databases with uncertainty and incompleteness.

This approach is based on the combination of Generalization Distribution Table (GDT) and the rough set methodology. The GDT provides a probabilistic basis for evaluating the strength of a by: 5. On the generalization of the distribution of the significant digits under computation.

Ph.D. thesis, Department of Mathematics, Oregon State University, Corvallis, OR, USA. 1 Generative Models for Discrete Data. In molecular biology, many situations involve counting events: how many codons use a certain spelling, how many reads of DNA match a reference, how many CG digrams are observed in a DNA sequence.

These counts give us discrete variables, as opposed to quantities such as mass and intensity that are measured on continuous scales. The generalized Fermi–Dirac integral, F k (η, β), is approximated by a group of polynomials of β as F k (η, β) ≈ ∑ j = 0 J g j β j F k + j (η) where J = 1 (1) Here F k (η) is the Fermi-Dirac integral of order k while g j are the numerical coefficients of the single and double precision minimax polynomial approximations of the generalization factor as 1 + x / 2 ≈ ∑ j = 0 J Cited by: 1.

Question The maximum number of significant digits in values of the double type is Answer: True (The phrase the maximum number of significant digits means the number if values that view the full answer.

General. Validated numerics; Iterative method; Rate of convergence — the speed at which a convergent sequence approaches its limit. Order of accuracy — rate at which numerical solution of differential equation converges to exact solution; Series acceleration — methods to accelerate the speed of convergence of a series.

Aitken's delta-squared process — most useful for. Full text of "Sterbenz Floating Point Computation" See other formats. In this paper, we consider the question and present evidence as to whether or not Benford’s exponential first significant digit (FSD) law reflects a fundamental principle behind the complex and nondeterministic nature of large-scale physical and behavioral systems.

As a behavioral example, we focus on the FSD distribution of Australian micro income data and use Cited by: 3. Pinkham, RS (). On the Distribution of First Significant Digits. Annals of Mathematical Statistics 32(4), pp. ISSN/ISBN Pippenger, N ().

Expected acceptance counts for finite automata with almost uniform input. Algorithms and Computation, Proceedings. Lecture Notes in Computer Sciencepp. ISSN/ISBN. I used the online Number Theory Terminal of BoM to understand some more about the digit distribution of numbers.

I used dcount == d to display all numbers with d distinct digits from 0 up to I found out following sequence: dcount == 0, 0 numbers dcount == 1, 28 numbers dcount == 2, numbers dcount == 3, numbers dcount >= 4, 0 numbers. a value that attempts the impossible by summarizing the entire distribution with a single number, a "typical" value.

a numerical summary of how tightly the values are clustered around the "center" a hump or local high point in the shape of the distribution of a variable; the apparent locations of these can change as the scale of a histogram is.

BL, also known as the first digit law, is a logarithmic distribution function used to predict the first significant digit in numerical data. It asserts that the leading significant digit is not equally likely to be any one of the nine possible digits, but it is 1 more than 30 % of the time, and it is 9 less than 5 % of the time, with the probability of occurrence decreasing Cited by: 4.

Computational Number Theory - CRC Press Book Developed from the author’s popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms.

Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. When expanded as a decimal, the fraction 1/97 has a repetend (the repeating part of the decimal) that begins right after the decimal point and is 96 digits long.

If the last three digits of the rep. On Computing the Distribution Function for the Sum of Independent and Non-identical Random Indicators Yili Hong Department of Statistics Virginia Tech Blacksburg, VAUSA April 5, Abstract The Poisson binomial distribution is the distribution of the sum of independent and non-identical random Size: KB.

Generalized Logistic Distributions Rameshwar D. Gupta1 Debasis Kundu2 Abstract Inthispaperwediscussdiﬁerentpropertiesofthetwogeneralizationsofthelogistic File Size: KB. Theory of computation is of course a very broad and deep area, and it is anyone’s guess what Moreover the book was written for graduate students 1.

More recently (apparently on the strength of having course web pages on Programming, Logic, •fis said to be deﬁned at a∈Aif ahas an image under f. Under the integral of the ﬁnal expression we have (14) f(y)= e −y/ 2y1/2 √ π √ 2 = e y1/ Γ(1/2)21/2 = χ2(2). LECTURES IN MATHEMATICAL STATISTICS Hence y ∼ χ2(2).

The Moment Generating Function of the Gamma Distribution Now let us endeavour to ﬁnd the moment generating function of the. He tells us that a uniform probability distribution (conferring equal probabilities on the digits 1 and 0) is not quite the right one because "1s vastly outnumber 0s in representing that sequence".

Logically, then, we should consider a distribution which corresponds to the actual proportions of 1s and 0s in the sequence, as I suggested in my. : The Mathematics of Information Coding, Extraction and Distribution (The IMA Volumes in Mathematics and its Applications ()) (v.

) (): Cybenko, George, O'Leary, Dianne P., Rissanen, Jorma: BooksFormat: Hardcover. Discrete Mathematics and Its Applications is intended for one or two term introductory Discrete Mathematics courses taken by students from a wide variety of majors, including Computer Science, Mathematics, and Engineering.

This renowned best-selling text, which has been used at over Price: \$ Journal Citation Reports (JCR) is the main source of bibliometric indicators known by the scientific community. This paper presents the results of a study of the distributions of the first and second significant digits according to Benford’s law (BL) of the number of articles, citations, impact factors, half-life and immediacy index bibliometric indicators in journals indexed in the JCR Cited by: 4.

This document is a collection of research notes compiled by Vipul Naik for MIRI on the distribution of computation in the world. It has not been independently vetted, and is chiefly meant as a resource for other researchers interested in the topic.

Answers to major questions on the distribution of computation. How is Chegg Study better than a printed MATHEMATICS 3rd Edition student solution manual from the bookstore? Our interactive player makes it easy to find solutions to MATHEMATICS 3rd Edition problems you're working on - just go to the chapter for your book.The purpose of this page is to provide resources in the rapidly growing area of computer-based statistical data analysis.

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Topics include questionnaire design and survey sampling, forecasting techniques, computational tools and .Problems on graphs. In this chapter we discuss several examples of important computational problems.

Many of the problems will involve have already encountered graphs before (see Section ) but now quickly recall the basic notation.A graph \(G\) consists of a set of vertices \(V\) and edges \(E\) where each edge is a pair of vertices.

We typically denote by .