Evidential inference and optimal sample size determination on the basis of record values and record times under random sampling scheme

Estimation of the parameter of a dynamically selected population for two subclasses of the exponential family

“…In this section, we utilize the data set which represents the records of the amount of annual (January 1-December 31) rainfall in inches recorded at Los Angeles Civic Center LACC during the 100-year period from 1890 until 1989, presented by Arnold et al [1998, p. 180]. A member of the F α model (Model 2) with survival function as in (9), that is the Rayleigh distribution with cdf…”

“…Theorem 2 Assume G to be known and let H = − log Ḡ be the cumulative hazard function of G. For the general family (9), an unbiased estimator of θ [n] , under the SEL function, is…”

“…Theorem 4 For the general family (9), and under the SEL function, an unbiased estimator of the risk of an estimator…”

“…Lemma 2 Let X 1 , X 2 , · · · be a sequence of independent random variables with survival function defined in (9). Let u j (x) be a real-valued function such that for j = 1, 2, · · · , ∀θ (ii)…”

“…The next result gives the unbiased estimator of θ [n] , under SEL function, for the general family (9).…”