The general-gamma distribution and reaction times

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Abstract

The general-gamma distribution describes input-output times in a multistage process consisting of exponential components whose constants are all different. The distribution and its unique history are examined. A stochastic process that leads to it is presented. The conditional density (hazard) function is studied as a means for estimating parameters. Finally, the multistage process model is applied to simple reaction times in an effort to reveal underlying detection and response components.

References (34)

  • R.J. Audley

    A stochastic model for individual choice behavior

    Psychol. Rev

    (1960)
  • M.S. Bartlett

    An introduction to stochastic processes

    (1955)
  • H. Bateman

    The solution of a system of differential equations occurring in the theory of radioactive transformations

  • A.T. Bharucha-Reid

    Elements of the theory of Markov processes and their applications

    (1960)
  • R.R. Bush et al.

    Stochastic models for learning

    (1955)
  • R. Chocholle

    Variation des temps de réaction auditifs en fonction de l'intensité a diverse fréquences

    Année Psychol

    (1940)
  • D.R. Cox et al.
  • L.S. Christie et al.

    Decision structure and time relations in simple choice behavior

    Bull. math. Biophys

    (1956)
  • D.J. Davis

    An analysis of some failure data

    J. Amer. statist. Assn

    (1952)
  • A.K. Erlang

    The application of the theory of probability in telephone administration

  • W. Feller

    On the theory of stochastic processes with particular reference to applications

  • W. Feller

    An introduction to the theory of probability and its applications

    (1957)
  • D.M. Green

    Psychoacoustics and detection theory

    J. acoust. Soc. Amer

    (1960)
  • H.B. Greenbaum

    Simple reaction time: a case in signal detection

  • E. Hearst

    The behavioral effects of some temporally defined schedules of reinforcement

    J. exp. anal. Behav

    (1958)
  • H. Jeffreys et al.

    Methods of mathematical physics

    (1956)
  • A. Jensen

    An elucidation of Erlang's statistical works through the theory of stochastic processes

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    This paper was begun in a graduate seminar at Columbia University, extended and revised at Lincoln Laboratory in Lexington, Massachusetts, Columbia University, and at the Institute for Mathematical Studies in the Social Sciences at Stanford University. The work was supported by AFC 49(638)-1253.

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    Special NIMH Fellow at the Institute for Mathematical Studies in the Social Sciences, Stanford University, 1963-64.

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