共查询到20条相似文献,搜索用时 31 毫秒
1.
J. F. Steffensen 《Scandinavian actuarial journal》2013,2013(3-4):193-202
Abstract 1. In the discussion that followed the reading to the Danish Actuarial Society of the paper quoted below1 it was suggested by Mr N. E. Andersen that the hypothesis T. F. (49), or , employed in the second half of the paper, might with advantage be replaced by xo being the initial age. In this way it is obtained that and it then follows, by T. F. (6), that 相似文献
2.
Ivo Lah 《Scandinavian actuarial journal》2013,2013(3-4):165-179
Abstract Im Zinsfussproblem spielen eine wichtige Rolle drei Hilfsfunktionen der Summen der diskontierten Zahlen, die wir vorweg kurz erwahnen wollen. Unter der nten Summe der diskontierten Zahlen Dx verstehen wir SpezieU haben wir: 相似文献
3.
Henrik L. Selberg 《Scandinavian actuarial journal》2013,2013(3-4):121-125
Abstract Sei ?(x) eine für ? ∞ < x < + ∞ definierte reelle nichtnegative Funktion und 相似文献
4.
Håkan Prawitz 《Scandinavian actuarial journal》2013,2013(3):145-156
Abstract Let Xbv (v = 1,2, ..., n) be independent random variables with the distribution functions Fbvx) and suppose . We define a random variable by where and denote the distribution function of X by F (x. 相似文献
5.
D. V. Gokhale 《Scandinavian actuarial journal》2013,2013(3-4):213-215
Abstract For all real values of α and λ satisfying the following inequality holds. When compared with a similar inequality due to Gurland [3] this is seen to be stronger for a certain range of α. 相似文献
6.
Per Ottestad 《Scandinavian actuarial journal》2013,2013(1-2):197-201
Asbtract The hypernormal (or Lexian) frequency function can be defined by the integral where θ(p) is the frequency (or density) function of p defined in the interval. We have, of course, that and that . 相似文献
7.
D. R. Jensen 《Scandinavian actuarial journal》2013,2013(4):215-225
Abstract Let be Pearson's statistics for testing goodness of fit in various marginal distributions associated with a categorized array of N objects. This study is concerned with disturbances in the limiting joint distribution of when maximum likelihood estimates from the original ungrouped data are used instead of the usual estimates from the cell frequencies after grouping. Under regularity conditions the limiting distributions of , and are shown to satisfy for each positive {cb1 x ... x cbT }, where A(c) is the Cartesian product set A(c) = (0, cb1 ] x ... x (0, cbT ]. The limiting distributions are characterized in terms of partitioned Wishart matrices having unit rank and parameters as appropriate. These results are extensions of work by Chernoff and Lehmann (1954) and Jensen (1974). 相似文献
8.
J. Wolfowitz 《Scandinavian actuarial journal》2013,2013(3-4):132-151
Abstract 1. Summary of results. Let E and Eo be chance variables at least one of which is not normally distributed (throughout the present paper a chance variable which is constant with probability one will be considered to be normally distributed with variance zero), and whose distribution is otherwise unknown, except that it is known that with probability one, where 0 and p are unknown constants, . Let (u; v) be jointly normally distributed chance variables with unknown covariance matrix, distributed independently of (ε, ε0). Without loss of generality we assume that the expected values E u and E v, of u and v respectively, are both zero. Define 相似文献
9.
Ibrahim A. Ahmad 《Scandinavian actuarial journal》2013,2013(3):176-181
Abstract Bhattacharyya & Roussas (1969) proposed to estimate the functional Δ = ∫ ?∞/∞ f 2(x)dx by , where is a kernel estimate of the probability density f(x). Schuster (1974) proposed, alternatively, to estimate Δ by , where F n (x) is the sample distribution function, and showed that the two estimates attain the same rate of strong convergence to Δ. In this note, two large sample properties of are presented, first strong convergence of to Δ is established under less assumptions than those of Schuster (1974), and second the asymptotic normality of established. 相似文献
10.
S. Vajda 《Scandinavian actuarial journal》2013,2013(3-4):180-191
Abstract I In an earlier paper [5] we discussed the problem of finding an unbiased estimator of where p (x, 0) is a given frequency density and 0 is a (set of) parameter(s). In general, will not be an unbiased estimator of (1), when Ô is an unbiased estimate of O. In [5] it was shown that is an unbiased estimator of (1), if we define yi , as the larger of 0 and X j - c. It was emphasized that the resulting estimate may very well be zero, even when it is unreasonable to assume that the premium for a stop.loss reinsurance. defined by a frequency p (x, 0) of claims x and a critical limit c, should be zero when the critical limit has not been exceeded during the n years considered for the determination of the premium. 相似文献
11.
Sven G. Lindblom 《Scandinavian actuarial journal》2013,2013(1):12-29
1. Some questions about the connection between statistical tests of significance for simple and multiple correlation coefficients and for differences between sample means (and between sample means and population means) of variables of one or several dimensions are treated in this paper. The distributions of the random variables that are considered in such tests are given, under certain conditions, by frequency functions of the following types 1 : where - ∞ < t < ∞, n≧1; where where 0 < t < ∞, k≧1, n≧k; and where . 相似文献
12.
Birger Meidell 《Scandinavian actuarial journal》2013,2013(4):217-230
Im Gegensatz zur durchschnittlichen Lebensdauer hat die wahrscheinliche Lebensdauer in der Versicherungstechnik wohl kaum je eine wirkliche Anwendung gefunden. Der Grund hierfür dürfte hauptsächlich in der recht schwierigen mathematischen Definition dieser Masszahl zu such en sein. Während die durchschnittliche Lebensdauer bekantlich explicite definiert ist, so ist die wahrscheinliche Lebensdauer — wir werden sie mit ttx bezeichnen — implicite durch die Gleichung definiert. 相似文献
13.
C. G. Esseen 《Scandinavian actuarial journal》2013,2013(2):160-170
Abstract Consider a sequence of independent random variables (r.v.) X 1 X 2, …, Xn , … , with the same distribution function (d.f.) F(x). Let E (Xn ) = 0, E , E (?(X)) denoting the mean value of the r.v. ? (X). Further, let the r.v. where have the d.f. F n (x). It was proved by Berry [1] and the present author (Esseen [2], [4]) that Φ(x) being the normal d.f. 相似文献
14.
A. V. Boyd 《Scandinavian actuarial journal》2013,2013(3-4):134-135
Asbtract Using properties of statistical estimates Gurland [1] has shown that 相似文献
15.
《Scandinavian actuarial journal》2013,2013(3-4):207-218
Abstract Extract d1. Vis, at man for n ? 2 har når x ikke antager nogen af værdierne 0, ?1, ..., ?n+1, og når x ikke antager nogen af værdierne 0, 1, ..., n+1. 相似文献
16.
Gunnar Kulldorff 《Scandinavian actuarial journal》2013,2013(3-4):143-156
Abstract Assume that a large number of observations are made on a normal random variable with the density function where σ σ 0, When the sample is very large the ordinary estimates of µ and a involve considerable computational work. In order to simplify the estimation of µ and/or σ it is sometimes convenient to select a small number of sample quantiles and to use estimates which are linear functions of these sample quantiles, Such a procedure is particularly convenient when the observations occur naturally in order of magnitude, which happens in life testing, for instance, Let 相似文献
17.
Abstract Let be the order statistics in an ordered random sample of size n from the normal population N(±, σ2 with mean ± and standard deviation σ. The present paper (1) provides the optimum ranks coefficients and efficiencies of Lloyd's [6] best linear unbiased estimates (BLUE) of ±, σ (when one is known) and (±, σ) based on the k = 1,2, 3, 4 order statistics selected from (Ll) which give the highest efficiencies and (2) demonstrates that efficiencies are only slightly reduced if the BLUE of ± and σ (when one is known) based on the order statistics with ranks are replaced by the BLUE based on the order statistics with ranks , where are the optimum spacings for Ogawa's [8] asymptotic best linear estimates (ABLE) of ± and σ when one parameter is known, or even are replaced directly by the ABLE with their corresponding optimum spacings. 相似文献
18.
Per Ottestad 《Scandinavian actuarial journal》2013,2013(3-4):1-13
Abstract The hypernormal (or Lexian) frequency functions are defined by the integral . 相似文献
19.
S. Wigert 《Scandinavian actuarial journal》2013,2013(1):186-189
Abstract Dans son traité de la théorie des erreurs 1 M. E. Czuber s'occupe page 202–204 du calcul de la valeur probable de la plus petite erreur dans une série d'observations. En admettant la loi de Gauss il en trouve l'expression , où n est le nombre des observations et . Afin d'évaluer l'intégrale qui représente σ, M. Czuber la remplace par , eu remarquant que la valeur de est très petite, dès que k est en quelque façon considérable. Pour les petites valeurs de x la fonction θ(x) ne diffère que légèrement de hx, dit-il ensuite, de sorte que nous aurons comme valeur approchée de σ . En supposant le nombre n très grand, il est clair, dit M. Czuber, qu'on peut choisir k de manière que (1-hk)n+1 soit négligeable; il parvient ainsi à la valeur definitive . 相似文献
20.
Tore Dalenius 《Scandinavian actuarial journal》2013,2013(3-4):203-213
Abstract Although most applications of stratified sampling represent sampling from a finite population, π(N), consisting of k mutually exclusive sub-populations or strata, n, (N,), it is for purposes of theoretical investigations convenient to deal with a hypothetical population n, represented by a distribution function f(y), a < y < b. This hypothetical population likewise consists of k mutually exclusive strata, πi , i = 1,.2 ... k. The mean of this population is µi being the mean of ni. By means of a random sample of n observations, ni of which are selected from πi , µ, is estimated by: being the estimate of µi . 相似文献