On the Weibull record statistics and associated inferences
AbstractOn the basis of some characteristics such as quantile function and skewness coefficient of n th upper/lower record of a given absolutely continuous distribution, as well as a confidence interval for nth upper/lower record statistic of a two-parameter Weibull model, a point estimator for shape parameter of this family also is given. Furthermore, behavior of the skewness coefficient of nth upper/lower record statistic of this family is discussed. Tabulation of the confidence interval of the nth upper/lower record statistics of this family for some levels of confidence and parameters is useful for predicting the future nth
upper/lower record. The performance of the given shape estimator is measured through a simulated data set comparison with the maximum likelihood estimation. Also, skewness analysis of the nth upper/lower record statistic is useful for estimating the nth upper/lower record statistic of this family as it will be discussed.
A. A. SOLIMAN, A. H. ABD ELLAH, K. S. SULTAN (2006), Comparison of estimates using record statistics
fromWeibull model: Bayesian and non-Bayesian approaches, “Computational Statistics and
Data Analysis”, 51, pp. 2065-2077.
B. C. ARNOLD, N. BALAKSISHNAN, H. N. NAGARAJA (1992), A First Course in Order Statistics, Wiley,
D. N. P. MURTHY, M. XIE, R. JIANG (2004), Weibull Models, Wiley, New York.
K. N. CHANDER (1952), The distribution and frequency of record values, “Journal of the Royal Statistical
Society”, Series B, 14, pp. 220-228.
K. S. SULTAN, N. BALAKRISHNAN (1999), Higher order moments of record values from Rayleigh and
Weibull distributions and Edgeworth approximate inference, “Journal of Applied Statistical Science”,
, pp. 193-209.
K. S. SULTAN, M.E. MOSHREF (2000), Higher order moments of record values from generalized Pareto distribution
and associated inference,“Metrika”, 51, pp. 105-116.
M. AHSANULLAH (1988), Introduction to Record Values, Ginn Press, Needham Heights, Massachusetts.
M. AHSANULLAH (1990), Estimation of the parameters of the Gumbel distribution based on the m record
values, “Computational Statistics and Quarterly”, 3, pp. 231-239.
M. AHSANULLAH (1995), Record Statistics, Nova Science Publishers, Inc., NY.
M. AHSANULLAH (2004), Record Values-Theory and Applications, University Press of America,
M. Z. RAQAB (2002), Inferences for generalized exponential distribution based on record statistics, Journal
of Statistical Planning and Inference”, 104, pp. 339-350.
N. BALAKRISHNAN, P. S. CHAN (1993), Record values from Rayleigh and Weibull distributions and associated
inference, National Institute of Standards and Technology Journal of Research,
Special Publication, 866, pp. 41-51.
N. BALAKRISHNAN, M. AHSANULLAH, P. S. CHAN (1995), On the logistic record values and associated
inference. “Journal of Applied Statistical Science”, 2, pp. 233-248.
N. L. JOHNSON, S. KOTZ, N. BALAKRISHNAN (1994), Continuous Univariate Distributions, volume I,
second edition, Wiley, New York.