Homogeneity and scale testing of generalized gamma distribution

The aim of this paper is to derive the exact distributions of the likelihood ratio tests of homogeneity and scale hypothesis when the observations are generalized gamma distributed. The special cases of exponential, Rayleigh, Weibull or gamma distributed observations are discussed exclusively. The photoemulsion experiment analysis and scale test with missing time-to-failure observations are present to illustrate the applications of methods discussed.

[1]  Andrej Pázman,et al.  Nonlinear Statistical Models , 1993 .

[2]  Milan Stehlík Exact likelihood ratio scale and homogeneity testing of some loss processes , 2006 .

[3]  Gaston H. Gonnet,et al.  On the LambertW function , 1996, Adv. Comput. Math..

[4]  Frantisek Rublík On optimality of the LR tests in the sense of exact slopes. I. General case , 1989, Kybernetika.

[5]  Hoang Pham,et al.  Springer Handbook of Engineering Statistics , 2023, Springer Handbooks.

[6]  Michael A. Nowak,et al.  Rossi X-Ray Timing Explorer Observation of Cygnus X-1. III. Implications for Compton Corona and Advection-dominated Accretion Flow Models , 1999 .

[7]  Sylvia Frühwirth-Schnatter,et al.  Finite Mixture and Markov Switching Models , 2006 .

[8]  John H. K. Kao Computer Methods for Estimating Weibull Parameters in Reliability Studies , 1958 .

[9]  Frantisek Rublík On optimality of the LR tests in the sense of exact slopes. II. Application to individual distributions , 1989, Kybernetika.

[10]  J. Lawless Inference in the Generalized Gamma and Log Gamma Distributions , 1980 .

[11]  E. Stacy A Generalization of the Gamma Distribution , 1962 .

[12]  E. Lehmann Testing Statistical Hypotheses , 1960 .

[13]  R. R. Bahadur An optimal property of the likelihood ratio statistic , 1967 .

[14]  John D. Kalbfleisch,et al.  Testing for a finite mixture model with two components , 2004 .

[15]  Telba Irony,et al.  System and Bayesian reliability : essays in honor of Professor Richard E. Barlow on his 70th birthday , 2001 .

[16]  M. Stehlík Distributions of exact tests in the exponential family , 2003 .

[17]  John H. K. Kao A new life-quality measure for electron tubes , 1956 .

[18]  D. Coit,et al.  Gamma distribution parameter estimation for field reliability data with missing failure times , 2000 .

[19]  R. R. Bahadur Rates of Convergence of Estimates and Test Statistics , 1967 .

[20]  E. B. Manoukian Modern concepts and theorems of mathematical statistics , 1985 .

[21]  Lee J. Bain,et al.  Uniformly Most Powerful Unbiased Tests on the Scale Parameter of a Gamma Distribution With a Nuisance Shape Parameter , 1977 .