About distinguishing of BS-distribution from the family of GBS-distributions
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 2, pp. 31-36 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A likelihood-ratio test is constructed which distinguishes the Birnbaum–Saunders distribution from the family of the generalized Birnbaum–Saunders distributions. It is established that the asymptotical distribution of the test statistics is chi-square distribution with one degree of freedom. An accuracy of approximation is investigated by Monte–Carlo method.
@article{UZKU_2006_148_2_a3,
     author = {I. N. Volodin and O. A. Dzhungurova and S. V. Simushkin},
     title = {About distinguishing of {BS-distribution} from the family of {GBS-distributions}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {31--36},
     year = {2006},
     volume = {148},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2006_148_2_a3/}
}
TY  - JOUR
AU  - I. N. Volodin
AU  - O. A. Dzhungurova
AU  - S. V. Simushkin
TI  - About distinguishing of BS-distribution from the family of GBS-distributions
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2006
SP  - 31
EP  - 36
VL  - 148
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UZKU_2006_148_2_a3/
LA  - ru
ID  - UZKU_2006_148_2_a3
ER  - 
%0 Journal Article
%A I. N. Volodin
%A O. A. Dzhungurova
%A S. V. Simushkin
%T About distinguishing of BS-distribution from the family of GBS-distributions
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2006
%P 31-36
%V 148
%N 2
%U http://geodesic.mathdoc.fr/item/UZKU_2006_148_2_a3/
%G ru
%F UZKU_2006_148_2_a3
I. N. Volodin; O. A. Dzhungurova; S. V. Simushkin. About distinguishing of BS-distribution from the family of GBS-distributions. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 2, pp. 31-36. http://geodesic.mathdoc.fr/item/UZKU_2006_148_2_a3/

[1] Dzungurova O. A., Volodin I. N., “On limit distributions emerging in the generalized Birnbaum – Saunders model”, J. Math. Sci., 99:3 (2000), 1348–1366 | DOI | MR

[2] Dzhungurova O. A., “Kriterii otnosheniya pravdopodobiya dlya obobschennoi modeli Birnbauma – Saundersa”, Tez. dokl. “Obozrenie prikl. i prom. matematiki”, Tretii vseross. simpozium po prikladnoi i promyshlennoi matematike (Sochi, 1–6 okt. 2002 g.), 9, no. 2, 2002, 365

[3] Jorgensen B., Seshadri V., Whitmore G. A., “On the mixture of the inverse Gaussian distribution with its complimentary reciprocal”, Scand. J. Statist., 18:1 (1991), 77–79 | MR

[4] Gupta R. C., Akman H. O., “On the reliability studies of a weighted inverse Gaussian model”, J. Statist. Plann. Inference, 48:1 (1995), 69–83 | DOI | MR | Zbl

[5] Vu H. T. V., Zhou S., “Generalization of likelihood ratio tests under nonstandard conditions”, Ann. Statist., 25:2 (1997), 897–916 | DOI | MR | Zbl

[6] Hironori T., “On the likelihood ratio test for a single model against the mixture of two known densities”, Commun. Stat. Theory Meth., 30:5 (2001), 931–942 | DOI | MR | Zbl

[7] Chen J., “Optimal rate of convergence for finite mixture models”, Ann. Statist., 23:1 (1995), 221–233 | DOI | MR | Zbl

[8] Birnbaum Z. W., Saunders S. C., “Estimation for a family of life distribution with application to fatigue”, J. App. Probab., 6:2 (1969), 328–337 | DOI | MR