Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Statistical Properties of Inverse Gaussian Distributions. I.

M. C. K. Tweedie
The Annals of Mathematical Statistics
Vol. 28, No. 2 (Jun., 1957), pp. 362-377
Stable URL: http://www.jstor.org/stable/2237158
Page Count: 16
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Statistical Properties of Inverse Gaussian Distributions. I.
Preview not available

Abstract

A report is presented on some statistical properties of the family of probability density functions $$\exp \lbrack -\lambda(x - \mu)^2/2\mu^2x\rbrack\lbrack\lambda/2\pi x^3\rbrack^{1/2}$$ for a variate $x$ and parameters $\mu$ and $\lambda$, with $x, \mu, \lambda$ each confined to $(0, \infty)$. The expectation of $x$ is $\mu$, while $\lambda$ is a measure of relative precision. The chief result is that the ml estimators of $\mu$ and $\lambda$ have stochastically independent distributions, and are of a nature which permits of the construction of an analogue of the analysis of variance for nested classifications. The ml estimator of $\mu$ is the sample mean, and for a fixed sample size $n$ its distribution is of the same family as $x$, with the same $\mu$ but with $\lambda$ replaced by $\lambda n$. The distribution of the ml estimator of the reciprocal of $\lambda$ is of the chi-square type. The probability distribution of $1/x$, and the estimation of certain functions of the parameters in heterogeneous data, are also considered.

Page Thumbnails

  • Thumbnail: Page 
362
    362
  • Thumbnail: Page 
363
    363
  • Thumbnail: Page 
364
    364
  • Thumbnail: Page 
365
    365
  • Thumbnail: Page 
366
    366
  • Thumbnail: Page 
367
    367
  • Thumbnail: Page 
368
    368
  • Thumbnail: Page 
369
    369
  • Thumbnail: Page 
370
    370
  • Thumbnail: Page 
371
    371
  • Thumbnail: Page 
372
    372
  • Thumbnail: Page 
373
    373
  • Thumbnail: Page 
374
    374
  • Thumbnail: Page 
375
    375
  • Thumbnail: Page 
376
    376
  • Thumbnail: Page 
377
    377