Find out how to access previewonly content
On approximate inference for the twoparameter gamma model
 A. Wong
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
In applied work, the twoparameter gamma model gives useful representations of many physical situations. It has a two dimensional sufficient statistic for the two parameters which describe shape and scale. This makes it superficially comparable to the normal model, but accurate and simple statistical inference procedures for each parameter have not been available. In this paper, the saddlepoint approximation is applied to approximate observed levels of significance of the shape parameter. An averaging method is proposed to approximate observed levels of significance of the scale parameter. These methods are extended to the twosample case.
 Bain, L.J. and Engelhardt, M. (1975). A two moment chisquare approximation for the statistic log \(\left( {{{\bar x} \mathord{\left/ {\vphantom {{\bar x} {\tilde x}}} \right. \kern0em} {\tilde x}}} \right)\) .Journal of the American Statistical Association 70, 948–950. CrossRef
 BarndorffNielsen, O.E. (1986). Inference on full or partial parameters based on the standardized signed log likelihood ratio.Biometrika 73, 307–322.
 Bishop, D.J. and Nair, U.S. (1939). A note on certain methods of testing for the homogeneity of a set of estimated variances.Journal of the Royal Statistical Society Supplement 6, 89–99. CrossRef
 Cox, D.R. (1975). A note on partially Bayes inference and linear models.Biometrika 62, 651–654. CrossRef
 Daniels, H.E. (1954). Saddlepoint approximation in statistics.Annals of Mathematical Statistics 25, 631–650. CrossRef
 Fisher, R.A. (1934). Two new properties of mathematical likelihood.Proceedings of the Royal Society A 144, 285–307. CrossRef
 Fraser, D.A.S. (1968).The Structure of Inference. New York: McGraw Hill.
 Fraser, D.A.S. (1991). Statistical inference: likelihood to significance.Journal of the American Statistical Association 86, 258–265. CrossRef
 Fraser, D.A.S., Reid, N. and Wong, A. (1991). Exponential linear models: a two pass procedure for saddlepoint approximation.Journal of the Royal Statistical Society B 53, 483–492.
 Fraser, D.A.S. and Wong, A. (1993). Approximate studentization with marginal and conditional inference.Canadian Journal of Statistics 21, 313–320. CrossRef
 Jensen, J.L. and Kristensen, L.B. (1991). Saddlepoint approximations to exact tests and improved likelihood ratio tests for the gamma distribution.Communication in Statistics: Theory and Methods 20, 1515–1532. CrossRef
 Johnson, N.L. and Kotz, S. (1970).Continuous Distribution I. New York: Wiley.
 Kalbfleisch, J.D. and Sprott, D.A. (1973). Marginal and conditional likelihood.Sankyhā A 35, 311–328.
 Lugannani, R. and Rice, S.O. (1980). Saddlepoint approximation for the distribution of the sum of independent random variables.Advanced Applied Probability 12, 479–490. CrossRef
 Pierce, D.A. and Peters, D. (1992). Practical use of higher order asymptotics for multiparameter exponential families.Journal of the Royal Statistical Society B 54, 701–725.
 Reid, N. (1988). Saddlepoint methods and statistical inference.Statistical Science 3 213–238. CrossRef
 Shuie, W.K. and Bain, L.J. (1983). A twosample test of equal gamma distribution scale parameters with unknown common shape parameter.Technometrics 25, 377–381. CrossRef
 Shuie, W.K., Bain, L.J. and Engelhardt, M. (1988). Test of equal gamma distribution means with unknown and unequal shape parameters.Technometrics 30, 169–174. CrossRef
 Title
 On approximate inference for the twoparameter gamma model
 Journal

Statistical Papers
Volume 36, Issue 1 , pp 4959
 Cover Date
 19951201
 DOI
 10.1007/BF02926018
 Print ISSN
 09325026
 Online ISSN
 16139798
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Averaging
 Confidence distribution function
 Observed level of significance
 Saddlepoint approximation
 Stirling’s formula
 Industry Sectors
 Authors

 A. Wong ^{(1)}
 Author Affiliations

 1. Department of Mathematics and Statistics, York University, 4700 Keele Street, M3J 1P3, North York, Ontario, Canada