Skip to main content

Mathematical Statistics and Information Theory

  • Chapter
  • 3004 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1953)

There are many easily found good books on probability theory and mathematical statistics (eg [84, 85, 87, 117, 120, 122, 196]), stochastic processes (eg [31, 161]) and information theory (eg [175, 176]); here we just outline some topics to help make the sequel more self contained. For those who have access to the computer algebra package Mathematica [215], the approach to mathematical statistics and accompanying software in Rose and Smith [177] will be particularly helpful.

The word stochastic comes from the Greek stochastikos, meaning skillful in aiming and stochazesthaito aim at or guess at, and stochosmeans target or aim. In our context, stochastic colloquially means involving chance variations around some event-rather like the variation in positions of strikes aimed at a target. In its turn, the later word statistics comes through eighteenth century German from the Latin root statusmeaning state; originally it meant the study of political facts and figures. The noun random was used in the sixteenth century to mean a haphazard course, from the Germanic randir to run, and as an adjective to mean without a definite aim, rule or method, the opposite of purposive. From the middle of the last century, the concept of a random variable has been used to describe a variable that is a function of the result of a well-defined statistical experiment in which each possible outcome has a definite probability of occurrence. The organization of probabilities of outcomes is achieved by means of a probability function for discrete random variables and by means of a probability density function for continuous random variables. The result of throwing two fair dice and summing what they show is a discrete random variable.

Keywords

  • Probability Density Function
  • Exponential Distribution
  • Poisson Process
  • Gamma Distribution
  • Joint Probability Density Function

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Rights and permissions

Reprints and Permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2008). Mathematical Statistics and Information Theory. In: Information Geometry. Lecture Notes in Mathematics, vol 1953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69393-2_1

Download citation