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2703 results in General statistics and probability

Page 14 of 136

  • 16 - One Numerical Sample

  • from Part III - Elements of Statistical Inference
  • Ery Arias-Castro, University of California, San Diego
  • Book:
    Principles of Statistical Analysis
    Published online:
    22 July 2022
    Print publication:
    25 August 2022, pp 230-270

  • Summary

    We consider an experiment that yields, as data, a sample of independent and identically distributed (real-valued) random variables with a common distribution on the real line. The estimation of the underlying mean and median is discussed at length, and bootstrap confidence intervals are constructed. Tests comparing the underlying distribution to a given distribution (e.g., the standard normal distribution) or a family of distribution (e.g., the normal family of distributions) are introduced. Censoring, which is very common in some clinical trials, is briefly discuss.

Quantitative Enterprise Risk Management
  • Mary R. Hardy, David Saunders
  • Published online:
    28 July 2022
    Print publication:
    05 May 2022
  • This well-balanced introduction to enterprise risk management integrates quantitative and qualitative approaches and motivates key mathematical and statistical methods with abundant real-world cases - both successes and failures. Worked examples and end-of-chapter exercises support readers in consolidating what they learn. The mathematical level, which is suitable for graduate and senior undergraduate students in quantitative programs, is pitched to give readers a solid understanding of the concepts and principles involved, without diving too deeply into more complex theory. To reveal the connections between different topics, and their relevance to the real world, the presentation has a coherent narrative flow, from risk governance, through risk identification, risk modelling, and risk mitigation, capped off with holistic topics - regulation, behavioural biases, and crisis management - that influence the whole structure of ERM. The result is a text and reference that is ideal for graduate and senior undergraduate students, risk managers in industry, and anyone preparing for ERM actuarial exams.

Principles of Statistical Analysis
  • Learning from Randomized Experiments
  • Ery Arias-Castro
  • Published online:
    22 July 2022
    Print publication:
    25 August 2022
  • This compact course is written for the mathematically literate reader who wants to learn to analyze data in a principled fashion. The language of mathematics enables clear exposition that can go quite deep, quite quickly, and naturally supports an axiomatic and inductive approach to data analysis. Starting with a good grounding in probability, the reader moves to statistical inference via topics of great practical importance – simulation and sampling, as well as experimental design and data collection – that are typically displaced from introductory accounts. The core of the book then covers both standard methods and such advanced topics as multiple testing, meta-analysis, and causal inference.

  • 7 - Extremal Processes

  • from Part II - Emergence
  • Jayakrishnan Nair, Indian Institute of Technology, Bombay, Adam Wierman, California Institute of Technology, Bert Zwart, Stichting Centrum voor Wiskunde en Informatica (CWI), Amsterdam
  • Book:
    The Fundamentals of Heavy Tails
    Published online:
    17 May 2022
    Print publication:
    09 June 2022, pp 148-174

  • Summary

    An introduction to the emergence of heavy-tailed distributions in the context of extremal processes.Max-stable distributions are introduced, and the extremal central limit theory is presented.Further, an example of the emergence of heavy tails in the extremes of random walks is presented.

  • 6 - Multiplicative Processes

  • from Part II - Emergence
  • Jayakrishnan Nair, Indian Institute of Technology, Bombay, Adam Wierman, California Institute of Technology, Bert Zwart, Stichting Centrum voor Wiskunde en Informatica (CWI), Amsterdam
  • Book:
    The Fundamentals of Heavy Tails
    Published online:
    17 May 2022
    Print publication:
    09 June 2022, pp 127-147

  • Summary

    An introduction to the emergence of heavy-tailed distributions in the context of multiplicative processes.The multiplicative central limit theorem is presented, and variations of multiplicative processes with lower barriers and noise are studied.Further, an example of the emergence of heavy tails in random graphs via preferential attachment is included.

Page 14 of 136