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1.
N. F. Gjeddebæk 《Scandinavian actuarial journal》2013,2013(2):154-159
Abstract 1. Introduction (a) Maximum Likelihood.—In a previous paper (THIS JOURNAL, vol. XXXII, 1949, pp. 135–159) the author gave tables of the functions and where ?(x) denotes the normal law of distribution, φ(x) its integral and ?′(x) its first derivative. With the aid of these tables it is practicable to solve the maximum likelihood equations for coarsely grouped normal observations. The procedure was illustrated by examples. 相似文献
2.
《Scandinavian actuarial journal》2013,2013(3-4)
Abstract Extract d1. Bestern karakteristikkerne for den partielle differentialigning Gør rede for, at der ved begyndelsebetingelsen z=2√x for 0<x<+∞,y=0 fastlægges netop en løsning til (*) i et passende område ω i xy-planen, og bestem denne løsning (herunder et brugbart område ω). 相似文献
3.
《Scandinavian actuarial journal》2013,2013(3-4)
Abstract Extract d1. Vis, at for fast x er en ikke voksende funktion af y og for fast y en ikke aftagende funktion af x, når dødsintensiteterne μg og μ I for de to live er ikke aftagende. Det forudsættes, at dødsaldrene for (x) og (y) er stokastisk uafhængige. 相似文献
4.
《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
5.
Martin Sandelius 《Scandinavian actuarial journal》2013,2013(1-2):41-44
Abstract 1.Introductions Inverse Binomial Sampling. From an infinite population of a's and b's, in proportions p and q = 1-p respectively, individuals are drawn at random until M a's are found. Thus the sample size, n, is a random variable. Its well-known distribution is 相似文献
6.
J. F. Steffensen 《Scandinavian actuarial journal》2013,2013(1-2):13-33
Abstract 1. In an earlier Note1 I have suggested to measure the dependence between statistical variables by the expression where pij is the probability that x assumes the value xi and y the value yj , while By is meant summation with respect to all i and j for which pij > pi* p*j . 相似文献
7.
Erkki Pesonen 《Scandinavian actuarial journal》2013,2013(3-4):156-157
Abstract Some authors define the (elementary) compound Poisson process in wide sense {χ t , 0 ? t < ∞} with help of probability distributions where τ is a so-called operational time, a continuous non-decreasing function of t vanishing for t = 0, and V(q, t) is a non-negative distribution function for every t. 相似文献
8.
Walter Andersson 《Scandinavian actuarial journal》2013,2013(1-2):44-53
Abstract A set of observations contains N elements, and the two measures x and y are observed for each element. Searching the ? best value ? of y as dependent on x, we put 相似文献
9.
Abstract The problem of “optimum stratification” was discussed by the firstmentioned author in an earlier paper (1). The discussion in that paper was limited to sampling from an infinite population, represented by a density function f{y). The optimum points yi of stratification, for estimating the mean µ using were determined by solving the equations: which gives the stratification points Yi that minimize the sampling variance V y (provided the usual condition for the minimum is fulfilled) 相似文献
10.
Henrik L. Selberg 《Scandinavian actuarial journal》2013,2013(3-4):228-246
Abstract Let us survey an economic subject A0 who at the point t0 is planning to offer for sale a number q of lots during a space of time = selling period of lottery ticket. 相似文献
11.
Carl-Erik Quensel 《Scandinavian actuarial journal》2013,2013(1-2):23-30
Abstract As is known, the death-rates of a population are usually worked out by the aid of the formula where Dx denotes the number of deaths at the age x - x + 1 year and where Mx signifies the average population in the same age group or the total observed risktime (expressed in years). 相似文献
12.
B. R. Rao 《Scandinavian actuarial journal》2013,2013(1-2):57-67
Abstract Rao [1] and simultaneously Cramér [2, 3] have shown that if f (x, θ) is the probability density function of a distribution involving an unknown parameter θ and distributed over the range α ? x ? b, where a and b are independent of θ, and if x 1 x 2 ... x n is a random sample of n independent observations from this distribution, the variance of any estimate unbiased for Ψ (θ), satisfies the inequality where E denotes mathematical expectation and is Fisher's information index about θ. In (1), equality holds if, and only if, θ* is sufficient for θ. This inequality is further generalized to the multi-parametric case. 相似文献
13.
Knut H. Ångström 《Scandinavian actuarial journal》2013,2013(1-2):40-46
Abstract Very often one has to make an estimate of some function f (m) of a certain characteristic m belonging to a certain distribution. However, m is often unknown and then it may be necessary, somehow, to estimate m with the corresponding unbiased characteristic x from a sample consisting of n individuals which may be one- or multidimensional. If f (x) is a linear function it is evident that . 相似文献
14.
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
15.
Jan Grandell 《Scandinavian actuarial journal》2013,2013(1-2):76-77
Abstract A mixture-Poisson distribution is defined by where U(x) is a distribution function concentrated on (0, ∞). This distribution has been applied as a model of the number of claims occurring in an insurance business during a certain period of time. 相似文献
16.
Martin Weibull 《Scandinavian actuarial journal》2013,2013(1-2):53-71
Abstract 1. Introduction. A sample of N independently observed points (xo 1 | x11 , x21 ,... , xpt ), i = 1, 2, ... , N≥ p is given, where xk, k = 1, 2, ... , p are known, possibly choosable, non-random variates. Suppose now that, for any fixed values of x1 , x2 ..., xp the random variable o is normally distributed with the mean and the variance λo α x and λo are unknown parameters, not involving xk, the regression coefficients and the residual variance of the parent population respectively. 相似文献
17.
W. Simonsen 《Scandinavian actuarial journal》2013,2013(1-2):80-89
Abstract 1. If (x) and (y) are lives whose remaining lifetimes are stochasticallyindependent, and if the mortality of each of the lives is given by a Makeham expression, then as a well known fact (see e.g. P. F. Hooker & L. H. Longley-Cook, Life and Other Contingencies, Cambridge 1957, vol. II, pp. 137&138) the evaluation of joint-life endowments and joint-life annuities on the lives (x) and (y) may be performed by substituting a single life (u) for (x) and (y) and altering the force of interest, provided that and with the same value of the parameter c( > 1). 相似文献
18.
Anthonie W. van der Stoep Lech A. Grzelak Cornelis W. Oosterlee 《Quantitative Finance》2017,17(9):1347-1366
We present in a Monte Carlo simulation framework, a novel approach for the evaluation of hybrid local volatility [Risk, 1994, 7, 18–20], [Int. J. Theor. Appl. Finance, 1998, 1, 61–110] models. In particular, we consider the stochastic local volatility model—see e.g. Lipton et al. [Quant. Finance, 2014, 14, 1899–1922], Piterbarg [Risk, 2007, April, 84–89], Tataru and Fisher [Quantitative Development Group, Bloomberg Version 1, 2010], Lipton [Risk, 2002, 15, 61–66]—and the local volatility model incorporating stochastic interest rates—see e.g. Atlan [ArXiV preprint math/0604316, 2006], Piterbarg [Risk, 2006, 19, 66–71], Deelstra and Rayée [Appl. Math. Finance, 2012, 1–23], Ren et al. [Risk, 2007, 20, 138–143]. For both model classes a particular (conditional) expectation needs to be evaluated which cannot be extracted from the market and is expensive to compute. We establish accurate and ‘cheap to evaluate’ approximations for the expectations by means of the stochastic collocation method [SIAM J. Numer. Anal., 2007, 45, 1005–1034], [SIAM J. Sci. Comput., 2005, 27, 1118–1139], [Math. Models Methods Appl. Sci., 2012, 22, 1–33], [SIAM J. Numer. Anal., 2008, 46, 2309–2345], [J. Biomech. Eng., 2011, 133, 031001], which was recently applied in the financial context [Available at SSRN 2529691, 2014], [J. Comput. Finance, 2016, 20, 1–19], combined with standard regression techniques. Monte Carlo pricing experiments confirm that our method is highly accurate and fast. 相似文献
19.
Olav Reiersöl 《Scandinavian actuarial journal》2013,2013(3-4):201-227
Abstract Let be the regression of X 1 on X 2, X 3,… Xn (also called the first elementary regression in the set of variables X 1, X 2,…,Xn ). 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